Lapras vs. Chansey: parafusion calcs.

[magic9mushroom]

So I've seen a lot of arguing over exactly how likely it is for Lapras to beat Thunderbolt Chansey with its vaunted parafusion. I thought this was pretty silly, since the actual probability is an undisputable fact. So I figured I'd run the numbers myself and see what popped out.

Now I realise why nobody did this before.


There are a few simplifications and assumptions I've made, so I'll go into them first.

- Simplification: Body Slam is an assumed 5HKO, and Softboiled heals 2 Body Slams.
- Justification: Modelling all 703 HP values of Chansey inflates the number of states by about 140x. The probability for Body Slam to 4HKO is about 0.2%, rising to about 2% with self-confusion damage. I split the difference by assuming it was always an "almost 4HKO".

- Simplification: No 255s.
- Justification: I didn't want to make the 1/256 exception in every single attack throughout the entire working. Also, the 255 failure of Softboiled cannot be modelled without modelling all 703 HP values, which I just said I wasn't going to do, so leaving out the other 255s balances out.

- Simplification: No PP exhaustion.
- Justification: Considering this inflates the number of states by something like 150x because it eliminates the recursion that makes Markov chains so powerful.

- Assumption: Lapras does not have Rest or Hyper Beam.
- Justification: I don't know if Rest is optimal under any circumstances; I suspect it's not given that Chansey has a nigh-assured 3HKO and Confuse Ray lasts for a limited time. Hyper Beam is certainly very useful to Lapras in this matchup, but I've never seen a Lapras with Blizzard/Body Slam/Hyper Beam/Confuse Ray.

- Assumption: Chansey has Thunderbolt and Thunder Wave, but does not have Reflect or Counter.
- Justification: If Chansey does not have Thunderbolt, the result is patently obvious. One could model Ice Beam/Thunderbolt/Reflect/Softboiled Chansey vs. Lapras, but that's both somewhat more obvious and not as common. Counter is prediction-based and therefore cannot be modelled.

- Assumption: Lapras uses Body Slam if it will OHKO, or if Chansey is confused; otherwise, it uses Confuse Ray.
- Justification: This is obvious.

- Assumption: Chansey uses Thunderbolt if it will OHKO guaranteed, or if it is at full health and Lapras is paralysed, or if it is hit once and not confused and Lapras is paralysed; it uses Thunder Wave if it is at full health and Lapras is not paralysed, or if it is hit once and not confused and Lapras is not paralysed; otherwise, it uses Softboiled.
- Justification: Basic first-approximation. You could refine it recursively by looking at the states where Thunderbolt could OHKO, and checking whether Thunderbolt or Softboiled would have a greater chance to win, or by looking at the states where Lapras isn't paralysed and checking whether Thunder Wave or Softboiled would have a greater chance to win, but I've had enough maths for now.

- Assumption: Chansey is paralysed.
- Justification: If Chansey isn't paralysed, Lapras should really be trying to freeze it, making parafusion irrelevant. Also, I didn't want to have to do these entire calculations in duplicate to account for that.


There's a couple of relevant damage calcs here, which Isa did for me. Props to Isa - every little bit helps.

- Chansey Tbolt vs. Lapras 92.1% 3HKO
- Chansey Tbolt vs. Lapras 1011/1521 2HKO with one crit


Okay, time to get down to brass tacks. Here's the Markov chain as I elucidated it:

SPOILER: Click to show

(0) Chansey at full, paralysed
Lapras: Confuse Ray
Chansey: 5/8 nothing (1), 3/8 Thunder Wave (21)

(1) Chansey at full, parafused (2nd turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*3/4 nothing (12|7), 3/8*3/4 Thunder Wave (32|27), 3/4*1/4 Thunder Wave+confusion ends (30|25), 1/4*1/4 nothing+confusion ends (10|5)

(2) Chansey at full, parafused (3rd turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*2/3 nothing (13|8), 3/8*2/3 Thunder Wave (33|28), 3/4*1/3 Thunder Wave+confusion ends (30|25), 1/4*1/3 nothing+confusion ends (10|5)

(3) Chansey at full, parafused (4th turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*1/2 nothing (14|9), 3/8*1/2 Thunder Wave (34|29), 3/4*1/2 Thunder Wave+confusion ends (30|25), 1/4*1/2 nothing+confusion ends (10|5)

(4) Chansey at full, parafused (5th turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 3/4 Thunder Wave+confusion ends (30|25), 1/4 nothing+confusion ends (10|5)

(5) Chansey hit once, paralysed
Lapras: Confuse Ray
Chansey: 5/8 nothing (6), 3/8 Thunder Wave (26)

(6) Chansey hit once, parafused (2nd turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*3/4 nothing (17|12), 3/8*3/4 Softboiled (7|2), 3/4*1/4 Softboiled+confusion ends (5|0), 1/4*1/4 nothing+confusion ends (15|10)

(7) Chansey hit once, parafused (3rd turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*2/3 nothing (18|13), 3/8*2/3 Softboiled (8|3), 3/4*1/3 Softboiled+confusion ends (5|0), 1/4*1/3 nothing+confusion ends (15|10)

(8) Chansey hit once, parafused (4th turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*1/2 nothing (19|14), 3/8*1/2 Softboiled (9|4), 3/4*1/2 Softboiled+confusion ends (5|0), 1/4*1/2 nothing+confusion ends (15|10)

(9) Chansey hit once, parafused (5th turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 3/4 Softboiled+confusion ends (5|0), 1/4 nothing+confusion ends (15|10)

(10) Chansey hit twice, paralysed
Lapras: Confuse Ray
Chansey: 5/8 nothing (11), 3/8 Softboiled (1)

(11) Chansey hit twice, parafused (2nd turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*3/4 nothing (Lapras win|17), 3/8*3/4 Softboiled (12|7), 3/4*1/4 Softboiled+confusion ends (10|5), 1/4*1/4 nothing+confusion ends (Lapras win|15)

(12) Chansey hit twice, parafused (3rd turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*2/3 nothing (Lapras win|18), 3/8*2/3 Softboiled (13|8), 3/4*1/3 Softboiled+confusion ends (10|5), 1/4*1/3 nothing+confusion ends (Lapras win|15)

(13) Chansey hit twice, parafused (4th turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*1/2 nothing (Lapras win|19), 3/8*1/2 Softboiled (14|9), 3/4*1/2 Softboiled+confusion ends (10|5), 1/4*1/2 nothing+confusion ends (Lapras win|15)

(14) Chansey hit twice, parafused (5th turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 3/4 Softboiled+confusion ends (10|5), 1/4 nothing+confusion ends (Lapras win|15)

(15) Chansey hit thrice, paralysed
Lapras: Confuse Ray
Chansey: 5/8 nothing (16), 3/8 Softboiled (6)

(16) Chansey hit thrice, parafused (2nd turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*3/4 nothing (Lapras win), 3/8*3/4 Softboiled (Lapras win|12), 3/4*1/4 Softboiled+confusion ends (Lapras win|10), 1/4*1/4 nothing+confusion ends (Lapras win)

(17) Chansey hit thrice, parafused (3rd turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*2/3 nothing (Lapras win), 3/8*2/3 Softboiled (Lapras win|13), 3/4*1/3 Softboiled+confusion ends (Lapras win|10), 1/4*1/3 nothing+confusion ends (Lapras win)

(18) Chansey hit thrice, parafused (4th turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 5/8*1/2 nothing (Lapras win), 3/8*1/2 Softboiled (Lapras win|14), 3/4*1/2 Softboiled+confusion ends (Lapras win|10), 1/4*1/2 nothing+confusion ends (Lapras win)

(19) Chansey hit thrice, parafused (5th turn)
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 3/4 Softboiled+confusion ends (Lapras win|10), 1/4 nothing+confusion ends (Lapras win)

(20) Chansey at full, paralysed; Lapras paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (21), 3/8*3/4*231/256 Thunderbolt (46), 3/8*3/4*25/256 critical Thunderbolt (71), 3/4*1/4*231/256 Thunderbolt (45), 3/4*1/4*25/256 critical Thunderbolt (70), 1/4*1/4 nothing (20)

(21) Chansey at full, parafused (2nd turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (32|27|22), 3/8*3/4*231/256 Thunderbolt (57|52|47), 3/8*3/4*25/256 critical Thunderbolt (82|77|72), 3/4*1/4*231/256 Thunderbolt+confusion ends (55|50|45), 3/4*1/4*25/256 critical Thunderbolt+confusion ends (80|75|70), 1/4*1/4 nothing+confusion ends (30|25|20)

(22) Chansey at full, parafused (3rd turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (33|28|23), 3/8*2/3*231/256 Thunderbolt (58|53|48), 3/8*2/3*25/256 critical Thunderbolt (83|78|73), 3/4*1/3*231/256 Thunderbolt+confusion ends (55|50|45), 3/4*1/3*25/256 critical Thunderbolt+confusion ends (80|75|70), 1/4*1/3 nothing+confusion ends (30|25|20)

(23) Chansey at full, parafused (4th turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (34|29|24), 3/8*1/2*231/256 Thunderbolt (59|54|49), 3/8*1/2*25/256 critical Thunderbolt (84|79|74), 3/4*1/2*231/256 Thunderbolt+confusion ends (55|50|45), 3/4*1/2*25/256 critical Thunderbolt+confusion ends (80|75|70), 1/4*1/2 nothing+confusion ends (30|25|20)

(24) Chansey at full, parafused (5th turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4*231/256 Thunderbolt+confusion ends (55|50|45), 3/4*25/256 critical Thunderbolt+confusion ends (80|75|70), 1/4 nothing+confusion ends (30|25|20)

(25) Chansey hit once, paralysed; Lapras paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (26), 3/8*3/4*231/256 Thunderbolt (51), 3/8*3/4*25/256 critical Thunderbolt (76), 3/4*1/4*231/256 Thunderbolt (50), 3/4*1/4*25/256 critical Thunderbolt (75), 1/4*1/4 nothing (25)

(26) Chansey hit once, parafused (2nd turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (37|32|27), 3/8*3/4 Softboiled (27|22|22), 3/4*1/4 Softboiled+confusion ends (25|20|20), 1/4*1/4 nothing+confusion ends (35|30|25)

(27) Chansey hit once, parafused (3rd turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (38|33|28), 3/8*2/3 Softboiled (28|23|23), 3/4*1/3 Softboiled+confusion ends (25|20|20), 1/4*1/3 nothing+confusion ends (35|30|25)

(28) Chansey hit once, parafused (4th turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (39|34|29), 3/8*1/2 Softboiled (29|24|24), 3/4*1/2 Softboiled+confusion ends (25|20|20), 1/4*1/2 nothing+confusion ends (35|30|25)

(29) Chansey hit once, parafused (5th turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (25|20|20), 1/4 nothing+confusion ends (35|30|25)

(30) Chansey hit twice, paralysed; Lapras paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (31), 3/8*3/4 Softboiled (21), 3/4*1/4 Softboiled (20), 1/4*1/4 nothing (30)

(31) Chansey hit twice, parafused (2nd turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (42|37|32), 3/8*3/4 Softboiled (32|27|22), 3/4*1/4 Softboiled+confusion ends (30|25|20), 1/4*1/4 nothing+confusion ends (40|35|30)

(32) Chansey hit twice, parafused (3rd turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (43|38|33), 3/8*2/3 Softboiled (33|28|23), 3/4*1/3 Softboiled+confusion ends (30|25|20), 1/4*1/3 nothing+confusion ends (40|35|30)

(33) Chansey hit twice, parafused (4th turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (44|39|34), 3/8*1/2 Softboiled (34|29|24), 3/4*1/2 Softboiled+confusion ends (30|25|20), 1/4*1/2 nothing+confusion ends (40|35|30)

(34) Chansey hit twice, parafused (5th turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (30|25|20), 1/4 nothing+confusion ends (40|35|30)

(35) Chansey hit thrice, paralysed; Lapras paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (36), 3/8*3/4 Softboiled (26), 3/4*1/4 Softboiled (25), 1/4*1/4 nothing (35)

(36) Chansey hit thrice, parafused (2nd turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (Lapras win|42|37), 3/8*3/4 Softboiled (Lapras win|32|27), 3/4*1/4 Softboiled+confusion ends (Lapras win|30|25), 1/4*1/4 nothing+confusion ends (Lapras win|40|35)

(37) Chansey hit thrice, parafused (3rd turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|43|38), 3/8*2/3 Softboiled (Lapras win|33|28), 3/4*1/3 Softboiled+confusion ends (Lapras win|30|25), 1/4*1/3 nothing+confusion ends (Lapras win|40|35)

(38) Chansey hit thrice, parafused (4th turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|44|39), 3/8*1/2 Softboiled (Lapras win|34|29), 3/4*1/2 Softboiled+confusion ends (Lapras win|30|25), 1/4*1/2 nothing+confusion ends (Lapras win|40|35)

(39) Chansey hit thrice, parafused (5th turn); Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (Lapras win|30|25), 1/4 nothing+confusion ends (Lapras win|40|35)

(40) Chansey hit four times, paralysed; Lapras paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (Lapras win|30), 1/4 nothing (Lapras win|40)

(41) Chansey hit four times, parafused (2nd turn); Lapras paralysed
Unattainable

(42) Chansey hit four times, parafused (3rd turn); Lapras paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|43), 3/8*2/3 Softboiled (Lapras win|33), 3/4*1/3 Softboiled+confusion ends (Lapras win|30), 1/4*1/3 nothing+confusion ends (Lapras win|40)

(43) Chansey hit four times, parafused (4th turn); Lapras paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|44), 3/8*1/2 Softboiled (Lapras win|34), 3/4*1/2 Softboiled+confusion ends (Lapras win|30), 1/4*1/2 nothing+confusion ends (Lapras win|40)

(44) Chansey hit four times, parafused (5th turn); Lapras paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (Lapras win|30), 1/4 nothing+confusion ends (Lapras win|40)

(45) Chansey at full, paralysed; Lapras hit once, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (46), 3/8*3/4*231/256 Thunderbolt (96), 3/8*3/4*25/256*1011/1521 fatal critical Thunderbolt (Chansey win), 3/8*3/4*25/256*510/1521 non-fatal critical Thunderbolt (121), 3/4*1/4*231/256 Thunderbolt (95), 3/4*1/4*25/256*1011/1521 fatal critical Thunderbolt (Chansey win), 3/4*1/4*25/256*510/1521 non-fatal critical Thunderbolt (120), 1/4*1/4 nothing (45)

(46) Chansey at full, parafused (2nd turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (57|52|47), 3/8*3/4*231/256 Thunderbolt (107|102|97), 3/8*3/4*25/256*1011/1521 fatal critical Thunderbolt (Chansey win), 3/8*3/4*25/256*510/1521 non-fatal critical Thunderbolt (132|127|122), 3/4*1/4*231/256 Thunderbolt+confusion ends (105|100|95), 3/4*1/4*25/256*1011/1521 fatal critical Thunderbolt+confusion ends (Chansey win), 3/4*1/4*25/256*510/1521 non-fatal critical Thunderbolt+confusion ends (130|125|120), 1/4*1/4 nothing+confusion ends (55|50|45)

(47) Chansey at full, parafused (3rd turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (58|53|48), 3/8*2/3*231/256 Thunderbolt (108|103|98), 3/8*2/3*25/256*1011/1521 fatal critical Thunderbolt (Chansey win), 3/8*2/3*25/256*510/1521 non-fatal critical Thunderbolt (133|128|123), 3/4*1/3*231/256 Thunderbolt+confusion ends (105|100|95), 3/4*1/3*25/256*1011/1521 fatal critical Thunderbolt+confusion ends (Chansey win), 3/4*1/3*25/256*510/1521 non-fatal critical Thunderbolt+confusion ends (130|125|120), 1/4*1/3 nothing+confusion ends (55|50|45)

(48) Chansey at full, parafused (4th turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (59|54|49), 3/8*1/2*231/256 Thunderbolt (109|104|99), 3/8*1/2*25/256*1011/1521 fatal critical Thunderbolt (Chansey win), 3/8*1/2*25/256*510/1521 non-fatal critical Thunderbolt (134|129|124), 3/4*1/2*231/256 Thunderbolt+confusion ends (105|100|95), 3/4*1/2*25/256*1011/1521 fatal critical Thunderbolt+confusion ends (Chansey win), 3/4*1/2*25/256*510/1521 non-fatal critical Thunderbolt+confusion ends (130|125|120), 1/4*1/2 nothing+confusion ends (55|50|45)

(49) Chansey at full, parafused (5th turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4*231/256 Thunderbolt+confusion ends (105|100|95), 3/4*25/256*1011/1521 fatal critical Thunderbolt+confusion ends (Chansey win), 3/4*25/256*510/1521 non-fatal critical Thunderbolt+confusion ends (130|125|120), 1/4 nothing+confusion ends (55|50|45)

(50) Chansey hit once, paralysed; Lapras hit once, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (51), 3/8*3/4*231/256 Thunderbolt (101), 3/8*3/4*25/256*1011/1521 fatal critical Thunderbolt (Chansey win), 3/8*3/4*25/256*510/1521 non-fatal critical Thunderbolt (126), 3/4*1/4*231/256 Thunderbolt (100), 3/4*1/4*25/256*1011/1521 fatal critical Thunderbolt (Chansey win), 3/4*1/4*25/256*510/1521 non-fatal critical Thunderbolt (125), 1/4*1/4 nothing (50)

(51) Chansey hit once, parafused (2nd turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (62|57|52), 3/8*3/4 Softboiled (52|47|47), 3/4*1/4 Softboiled+confusion ends (50|45|45), 1/4*1/4 nothing+confusion ends (60|55|50)

(52) Chansey hit once, parafused (3rd turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (63|58|53), 3/8*2/3 Softboiled (53|48|48), 3/4*1/3 Softboiled+confusion ends (50|45|45), 1/4*1/3 nothing+confusion ends (60|55|50)

(53) Chansey hit once, parafused (4th turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (64|59|54), 3/8*1/2 Softboiled (54|49|49), 3/4*1/2 Softboiled+confusion ends (50|45|45), 1/4*1/2 nothing+confusion ends (60|55|50)

(54) Chansey hit once, parafused (5th turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (50|45|45), 1/4 nothing+confusion ends (60|55|50)

(55) Chansey hit twice, paralysed; Lapras hit once, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (56), 3/8*3/4 Softboiled (46), 3/4*1/4 Softboiled (45), 1/4*1/4 nothing (55)

(56) Chansey hit twice, parafused (2nd turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (67|62|57), 3/8*3/4 Softboiled (57|52|47), 3/4*1/4 Softboiled+confusion ends (55|50|45), 1/4*1/4 nothing+confusion ends (65|60|55)

(57) Chansey hit twice, parafused (3rd turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (68|63|58), 3/8*2/3 Softboiled (58|53|48), 3/4*1/3 Softboiled+confusion ends (55|50|45), 1/4*1/3 nothing+confusion ends (65|60|55)

(58) Chansey hit twice, parafused (4th turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (69|64|59), 3/8*1/2 Softboiled (59|54|49), 3/4*1/2 Softboiled+confusion ends (55|50|45), 1/4*1/2 nothing+confusion ends (65|60|55)

(59) Chansey hit twice, parafused (5th turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (55|50|45), 1/4 nothing+confusion ends (65|60|55)

(60) Chansey hit thrice, paralysed; Lapras hit once, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (61), 3/8*3/4 Softboiled (51), 3/4*1/4 Softboiled (50), 1/4*1/4 nothing (60)

(61) Chansey hit thrice, parafused (2nd turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (Lapras win|67|62), 3/8*3/4 Softboiled (Lapras win|57|52), 3/4*1/4 Softboiled+confusion ends (Lapras win|55|50), 1/4*1/4 nothing+confusion ends (Lapras win|65|60)

(62) Chansey hit thrice, parafused (3rd turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|68|63), 3/8*2/3 Softboiled (Lapras win|58|53), 3/4*1/3 Softboiled+confusion ends (Lapras win|55|50), 1/4*1/3 nothing+confusion ends (Lapras win|65|60)

(63) Chansey hit thrice, parafused (4th turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|69|64), 3/8*1/2 Softboiled (Lapras win|59|54), 3/4*1/2 Softboiled+confusion ends (Lapras win|55|50), 1/4*1/2 nothing+confusion ends (Lapras win|65|60)

(64) Chansey hit thrice, parafused (5th turn); Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (Lapras win|55|50), 1/4 nothing+confusion ends (Lapras win|65|60)

(65) Chansey hit four times, paralysed; Lapras hit once, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (Lapras win|55), 1/4 nothing (Lapras win|65)

(66) Chansey hit four times, parafused (2nd turn); Lapras hit once, paralysed
Unattainable

(67) Chansey hit four times, parafused (3rd turn); Lapras hit once, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|68), 3/8*2/3 Softboiled (Lapras win|58), 3/4*1/3 Softboiled+confusion ends (Lapras win|55), 1/4*1/3 nothing+confusion ends (Lapras win|65)

(68) Chansey hit four times, parafused (4th turn); Lapras hit once, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|69), 3/8*1/2 Softboiled (Lapras win|59), 3/4*1/2 Softboiled+confusion ends (Lapras win|55), 1/4*1/2 nothing+confusion ends (Lapras win|65)

(69) Chansey hit four times, parafused (5th turn); Lapras hit once, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (Lapras win|55), 1/4 nothing+confusion ends (Lapras win|65)

(70) Chansey at full, paralysed; Lapras critted, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (71), 3/8*3/4*231/256*1011/1521 fatal Thunderbolt (Chansey win), 3/8*3/4*231/256*510/1521 non-fatal Thunderbolt (121), 3/8*3/4*25/256 critical Thunderbolt (Chansey win), 3/4*1/4*231/256*1011/1521 fatal Thunderbolt (Chansey win), 3/4*1/4*231/256*510/1521 non-fatal Thunderbolt (120), 3/4*1/4*25/256 critical Thunderbolt (Chansey win), 1/4*1/4 nothing (70)

(71) Chansey at full, parafused (2nd turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (82|77|72), 3/8*3/4*231/256*1011/1521 fatal Thunderbolt (Chansey win), 3/8*3/4*231/256*510/1521 non-fatal Thunderbolt (132|127|122), 3/8*3/4*25/256 critical Thunderbolt (Chansey win), 3/4*1/4*231/256*1011/1521 fatal Thunderbolt+confusion ends (Chansey win), 3/4*1/4*231/256*510/1521 non-fatal Thunderbolt+confusion ends (130|125|120), 3/4*1/4*25/256 critical Thunderbolt+confusion ends (Chansey win), 1/4*1/4 nothing+confusion ends (80|75|70)

(72) Chansey at full, parafused (3rd turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (83|78|73), 3/8*2/3*231/256*1011/1521 fatal Thunderbolt (Chansey win), 3/8*2/3*231/256*510/1521 non-fatal Thunderbolt (133|128|123), 3/8*2/3*25/256 critical Thunderbolt (Chansey win), 3/4*1/3*231/256*1011/1521 fatal Thunderbolt+confusion ends (Chansey win), 3/4*1/3*231/256*510/1521 non-fatal Thunderbolt+confusion ends (130|125|120), 3/4*1/3*25/256 critical Thunderbolt+confusion ends (Chansey win), 1/4*1/3 nothing+confusion ends (80|75|70)

(73) Chansey at full, parafused (4th turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (84|79|74), 3/8*1/2*231/256*1011/1521 fatal Thunderbolt (Chansey win), 3/8*1/2*231/256*510/1521 non-fatal Thunderbolt (134|129|124), 3/8*1/2*25/256 critical Thunderbolt (Chansey win), 3/4*1/2*231/256*1011/1521 fatal Thunderbolt+confusion ends (Chansey win), 3/4*1/2*231/256*510/1521 non-fatal Thunderbolt+confusion ends (130|125|120), 3/4*1/2*25/256 critical Thunderbolt+confusion ends (Chansey win), 1/4*1/2 nothing+confusion ends (80|75|70)

(74) Chansey at full, parafused (5th turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4*231/256*1011/1521 fatal Thunderbolt+confusion ends (Chansey win), 3/4*231/256*510/1521 non-fatal Thunderbolt+confusion ends (130|125|120), 3/4*25/256 critical Thunderbolt+confusion ends (Chansey win), 1/4 nothing+confusion ends (80|75|70)

(75) Chansey hit once, paralysed; Lapras critted, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (76), 3/8*3/4*231/256*1011/1521 fatal Thunderbolt (Chansey win), 3/8*3/4*231/256*510/1521 non-fatal Thunderbolt (126), 3/8*3/4*25/256 critical Thunderbolt (Chansey win), 3/4*1/4*231/256*1011/1521 fatal Thunderbolt (Chansey win), 3/4*1/4*231/256*510/1521 non-fatal Thunderbolt (125), 3/4*1/4*25/256 critical Thunderbolt (Chansey win), 1/4*1/4 nothing (75)

(76) Chansey hit once, parafused (2nd turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (87|82|77), 3/8*3/4 Softboiled (77|72|72), 3/4*1/4 Softboiled+confusion ends (75|70|70), 1/4*1/4 nothing+confusion ends (85|80|75)

(77) Chansey hit once, parafused (3rd turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (88|83|78), 3/8*2/3 Softboiled (78|73|73), 3/4*1/3 Softboiled+confusion ends (75|70|70), 1/4*1/3 nothing+confusion ends (85|80|75)

(78) Chansey hit once, parafused (4th turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (89|84|79), 3/8*1/2 Softboiled (79|74|74), 3/4*1/2 Softboiled+confusion ends (75|70|70), 1/4*1/2 nothing+confusion ends (85|80|75)

(79) Chansey hit once, parafused (5th turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (75|70|70), 1/4 nothing+confusion ends (85|80|75)

(80) Chansey hit twice, paralysed; Lapras critted, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (81), 3/8*3/4 Softboiled (71), 3/4*1/4 Softboiled (70), 1/4*1/4 nothing (80)

(81) Chansey hit twice, parafused (2nd turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (92|87|82), 3/8*3/4 Softboiled (82|77|72), 3/4*1/4 Softboiled+confusion ends (80|75|70), 1/4*1/4 nothing+confusion ends (90|85|80)

(82) Chansey hit twice, parafused (3rd turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (93|88|83), 3/8*2/3 Softboiled (83|78|73), 3/4*1/3 Softboiled+confusion ends (80|75|70), 1/4*1/3 nothing+confusion ends (90|85|80)

(83) Chansey hit twice, parafused (4th turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (94|89|84), 3/8*1/2 Softboiled (84|79|74), 3/4*1/2 Softboiled+confusion ends (80|75|70), 1/4*1/2 nothing+confusion ends (90|85|80)

(84) Chansey hit twice, parafused (5th turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (80|75|70), 1/4 nothing+confusion ends (90|85|80)

(85) Chansey hit thrice, paralysed; Lapras critted, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (86), 3/8*3/4 Softboiled (76), 3/4*1/4 Softboiled (75), 1/4*1/4 nothing (85)

(86) Chansey hit thrice, parafused (2nd turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (Lapras win|92|87), 3/8*3/4 Softboiled (Lapras win|82|77), 3/4*1/4 Softboiled+confusion ends (Lapras win|80|75), 1/4*1/4 nothing+confusion ends (Lapras win|90|85)

(87) Chansey hit thrice, parafused (3rd turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|93|88), 3/8*2/3 Softboiled (Lapras win|83|78), 3/4*1/3 Softboiled+confusion ends (Lapras win|80|75), 1/4*1/3 nothing+confusion ends (Lapras win|90|85)

(88) Chansey hit thrice, parafused (4th turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|94|89), 3/8*1/2 Softboiled (Lapras win|84|79), 3/4*1/2 Softboiled+confusion ends (Lapras win|80|75), 1/4*1/2 nothing+confusion ends (Lapras win|90|85)

(89) Chansey hit thrice, parafused (5th turn); Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (Lapras win|80|75), 1/4 nothing+confusion ends (Lapras win|90|85)

(90) Chansey hit four times, paralysed; Lapras critted, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (Lapras win|80), 1/4 nothing (Lapras win|90)

(91) Chansey hit four times, parafused (2nd turn); Lapras critted, paralysed
Unattainable

(92) Chansey hit four times, parafused (3rd turn); Lapras critted, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|93), 3/8*2/3 Softboiled (Lapras win|83), 3/4*1/3 Softboiled+confusion ends (Lapras win|80), 1/4*1/3 nothing+confusion ends (Lapras win|90)

(93) Chansey hit four times, parafused (4th turn); Lapras critted, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|94), 3/8*1/2 Softboiled (Lapras win|84), 3/4*1/2 Softboiled+confusion ends (Lapras win|80), 1/4*1/2 nothing+confusion ends (Lapras win|90)

(94) Chansey hit four times, parafused (5th turn); Lapras critted, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (Lapras win|80), 1/4 nothing+confusion ends (Lapras win|90)

(95) Chansey at full, paralysed; Lapras hit twice, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (96), 3/8*3/4*231/256*0.921 fatal Thunderbolt (Chansey win), 3/8*3/4*231/256*0.079 non-fatal Thunderbolt (121), 3/8*3/4*25/256 critical Thunderbolt (Chansey win), 3/4*1/4*231/256*0.921 fatal Thunderbolt (Chansey win), 3/4*1/4*231/256*0.079 non-fatal Thunderbolt (120), 3/4*1/4*25/256 critical Thunderbolt (Chansey win), 1/4*1/4 nothing (95)

(96) Chansey at full, parafused (2nd turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (107|102|97), 3/8*3/4*231/256*0.921 fatal Thunderbolt (Chansey win), 3/8*3/4*231/256*0.079 non-fatal Thunderbolt (132|127|122), 3/8*3/4*25/256 critical Thunderbolt (Chansey win), 3/4*1/4*231/256*0.921 fatal Thunderbolt+confusion ends (Chansey win), 3/4*1/4*231/256*0.079 non-fatal Thunderbolt+confusion ends (130|125|120), 3/4*1/4*25/256 critical Thunderbolt+confusion ends (Chansey win), 1/4*1/4 nothing+confusion ends (105|100|95)

(97) Chansey at full, parafused (3rd turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (108|103|98), 3/8*2/3*231/256*0.921 fatal Thunderbolt (Chansey win), 3/8*2/3*231/256*0.079 non-fatal Thunderbolt (133|128|123), 3/8*2/3*25/256 critical Thunderbolt (Chansey win), 3/4*1/3*231/256*0.921 fatal Thunderbolt+confusion ends (Chansey win), 3/4*1/3*231/256*0.079 non-fatal Thunderbolt+confusion ends (130|125|120), 3/4*1/3*25/256 critical Thunderbolt+confusion ends (Chansey win), 1/4*1/3 nothing+confusion ends (105|100|95)

(98) Chansey at full, parafused (4th turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (109|104|99), 3/8*1/2*231/256*0.921 fatal Thunderbolt (Chansey win), 3/8*1/2*231/256*0.079 non-fatal Thunderbolt (134|129|124), 3/8*1/2*25/256 critical Thunderbolt (Chansey win), 3/4*1/2*231/256*0.921 fatal Thunderbolt+confusion ends (Chansey win), 3/4*1/2*231/256*0.079 non-fatal Thunderbolt+confusion ends (130|125|120), 3/4*1/2*25/256 critical Thunderbolt+confusion ends (Chansey win), 1/4*1/2 nothing+confusion ends (105|100|95)

(99) Chansey at full, parafused (5th turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4*231/256*0.921 fatal Thunderbolt+confusion ends (Chansey win), 3/4*231/256*0.079 non-fatal Thunderbolt+confusion ends (130|125|120), 3/4*25/256 critical Thunderbolt+confusion ends (Chansey win), 1/4 nothing+confusion ends (105|100|95)

(100) Chansey hit once, paralysed; Lapras hit twice, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (101), 3/8*3/4*231/256*0.921 fatal Thunderbolt (Chansey win), 3/8*3/4*231/256*0.079 non-fatal Thunderbolt (126), 3/8*3/4*25/256 critical Thunderbolt (Chansey win), 3/4*1/4*231/256*0.921 fatal Thunderbolt (Chansey win), 3/4*1/4*231/256*0.079 non-fatal Thunderbolt (125), 3/4*1/4*25/256 critical Thunderbolt (Chansey win), 1/4*1/4 nothing (100)

(101) Chansey hit once, parafused (2nd turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (112|107|102), 3/8*3/4 Softboiled (102|97|97), 3/4*1/4 Softboiled+confusion ends (100|95|95), 1/4*1/4 nothing+confusion ends (110|105|100)

(102) Chansey hit once, parafused (3rd turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (113|108|103), 3/8*2/3 Softboiled (103|98|98), 3/4*1/3 Softboiled+confusion ends (100|95|95), 1/4*1/3 nothing+confusion ends (110|105|100)

(103) Chansey hit once, parafused (4th turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (114|109|104), 3/8*1/2 Softboiled (104|99|99), 3/4*1/2 Softboiled+confusion ends (100|95|95), 1/4*1/2 nothing+confusion ends (110|105|100)

(104) Chansey hit once, parafused (5th turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (100|95|95), 1/4 nothing+confusion ends (110|105|100)

(105) Chansey hit twice, paralysed; Lapras hit twice, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (106), 3/8*3/4 Softboiled (96), 3/4*1/4 Softboiled (95), 1/4*1/4 nothing (105)

(106) Chansey hit twice, parafused (2nd turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (117|112|107), 3/8*3/4 Softboiled (107|102|97), 3/4*1/4 Softboiled+confusion ends (105|100|95), 1/4*1/4 nothing+confusion ends (115|110|105)

(107) Chansey hit twice, parafused (3rd turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (118|113|108), 3/8*2/3 Softboiled (108|103|98), 3/4*1/3 Softboiled+confusion ends (105|100|95), 1/4*1/3 nothing+confusion ends (115|110|105)

(108) Chansey hit twice, parafused (4th turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (119|114|109), 3/8*1/2 Softboiled (109|104|99), 3/4*1/2 Softboiled+confusion ends (105|100|95), 1/4*1/2 nothing+confusion ends (115|110|105)

(109) Chansey hit twice, parafused (5th turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (105|100|95), 1/4 nothing+confusion ends (115|110|105)

(110) Chansey hit thrice, paralysed; Lapras hit twice, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (111), 3/8*3/4 Softboiled (101), 3/4*1/4 Softboiled (100), 1/4*1/4 nothing (110)

(111) Chansey hit thrice, parafused (2nd turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (Lapras win|117|112), 3/8*3/4 Softboiled (Lapras win|107|102), 3/4*1/4 Softboiled+confusion ends (Lapras win|105|100), 1/4*1/4 nothing+confusion ends (Lapras win|115|110)

(112) Chansey hit thrice, parafused (3rd turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|118|113), 3/8*2/3 Softboiled (Lapras win|108|103), 3/4*1/3 Softboiled+confusion ends (Lapras win|105|100), 1/4*1/3 nothing+confusion ends (Lapras win|115|110)

(113) Chansey hit thrice, parafused (4th turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|119|114), 3/8*1/2 Softboiled (Lapras win|109|104), 3/4*1/2 Softboiled+confusion ends (Lapras win|105|100), 1/4*1/2 nothing+confusion ends (Lapras win|115|110)

(114) Chansey hit thrice, parafused (5th turn); Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (Lapras win|105|100), 1/4 nothing+confusion ends (Lapras win|115|110)

(115) Chansey hit four times, paralysed; Lapras hit twice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (Lapras win|105), 1/4 nothing (Lapras win|115)

(116) Chansey hit four times, parafused (2nd turn); Lapras hit twice, paralysed
Unattainable

(117) Chansey hit four times, parafused (3rd turn); Lapras hit twice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|118), 3/8*2/3 Softboiled (Lapras win|108), 3/4*1/3 Softboiled+confusion ends (Lapras win|105), 1/4*1/3 nothing+confusion ends (Lapras win|115)

(118) Chansey hit four times, parafused (4th turn); Lapras hit twice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|119), 3/8*1/2 Softboiled (Lapras win|109), 3/4*1/2 Softboiled+confusion ends (Lapras win|105), 1/4*1/2 nothing+confusion ends (Lapras win|115)

(119) Chansey hit four times, parafused (5th turn); Lapras hit twice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled+confusion ends (Lapras win|105), 1/4 nothing+confusion ends (Lapras win|115)

(120) Chansey at full, paralysed; Lapras hit thrice, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (121), 3/8*3/4 Thunderbolt (Chansey win), 3/4*1/4 Thunderbolt (Chansey win), 1/4*1/4 nothing (120)

(121) Chansey at full, parafused (2nd turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (132|127|122), 3/8*3/4 Thunderbolt (Chansey win), 3/4*1/4 Thunderbolt+confusion ends (Chansey win), 1/4*1/4 nothing+confusion ends (130|125|120)

(122) Chansey at full, parafused (3rd turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (133|128|123), 3/8*2/3 Thunderbolt (Chansey win), 3/4*1/3 Thunderbolt+confusion ends (Chansey win), 1/4*1/3 nothing+confusion ends (130|125|120)

(123) Chansey at full, parafused (4th turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (134|129|124), 3/8*1/2 Thunderbolt (Chansey win), 3/4*1/2 Thunderbolt+confusion ends (Chansey win), 1/4*1/2 nothing+confusion ends (130|125|120)

(124) Chansey at full, parafused (5th turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt+confusion ends (Chansey win), 1/4 nothing+confusion ends (130|125|120)

(125) Chansey hit once, paralysed; Lapras hit thrice, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (126), 3/8*3/4 Thunderbolt (Chansey win), 3/4*1/4 Thunderbolt (Chansey win), 1/4*1/4 nothing (125)

(126) Chansey hit once, parafused (2nd turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (137|132|127), 3/8*3/4 Thunderbolt (Chansey win), 3/4*1/4 Thunderbolt+confusion ends (Chansey win), 1/4*1/4 nothing+confusion ends (135|130|125)

(127) Chansey hit once, parafused (3rd turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (138|133|128), 3/8*2/3 Thunderbolt (Chansey win), 3/4*1/3 Thunderbolt+confusion ends (Chansey win), 1/4*1/3 nothing+confusion ends (135|130|125)

(128) Chansey hit once, parafused (4th turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (139|134|129), 3/8*1/2 Thunderbolt (Chansey win), 3/4*1/2 Thunderbolt+confusion ends (Chansey win), 1/4*1/2 nothing+confusion ends (135|130|125)

(129) Chansey hit once, parafused (5th turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt+confusion ends (Chansey win), 1/4 nothing+confusion ends (135|130|125)

(130) Chansey hit twice, paralysed; Lapras hit thrice, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (131), 3/8*3/4 Thunderbolt (Chansey win), 3/4*1/4 Thunderbolt (Chansey win), 1/4*1/4 nothing (130)

(131) Chansey hit twice, parafused (2nd turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (142|137|132), 3/8*3/4 Thunderbolt (Chansey win), 3/4*1/4 Thunderbolt+confusion ends (Chansey win), 1/4*1/4 nothing+confusion ends (140|135|130)

(132) Chansey hit twice, parafused (3rd turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (143|138|133), 3/8*2/3 Thunderbolt (Chansey win), 3/4*1/3 Thunderbolt+confusion ends (Chansey win), 1/4*1/3 nothing+confusion ends (140|135|130)

(133) Chansey hit twice, parafused (4th turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (144|139|134), 3/8*1/2 Thunderbolt (Chansey win), 3/4*1/2 Thunderbolt+confusion ends (Chansey win), 1/4*1/2 nothing+confusion ends (140|135|130)

(134) Chansey hit twice, parafused (5th turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt+confusion ends (Chansey win), 1/4 nothing+confusion ends (140|135|130)

(135) Chansey hit thrice, paralysed; Lapras hit thrice, paralysed
Lapras: 3/4 Confuse Ray, 1/4 nothing
Chansey*: 5/8*3/4 nothing (136), 3/8*3/4 Thunderbolt (Chansey win), 3/4*1/4 Thunderbolt (Chansey win), 1/4*1/4 nothing (135)

(136) Chansey hit thrice, parafused (2nd turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*3/4 nothing (Lapras win|142|137), 3/8*3/4 Thunderbolt (Lapras win|Chansey win|Chansey win), 3/4*1/4 Thunderbolt+confusion ends (Lapras win|Chansey win|Chansey win), 1/4*1/4 nothing+confusion ends (Lapras win|140|135)

(137) Chansey hit thrice, parafused (3rd turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|143|138), 3/8*2/3 Thunderbolt (Lapras win|Chansey win|Chansey win), 3/4*1/3 Thunderbolt+confusion ends (Lapras win|Chansey win|Chansey win), 1/4*1/3 nothing+confusion ends (Lapras win|140|135)

(138) Chansey hit thrice, parafused (4th turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|144|139), 3/8*1/2 Thunderbolt (Lapras win|Chansey win|Chansey win), 3/4*1/2 Thunderbolt+confusion ends (Lapras win|Chansey win|Chansey win), 1/4*1/2 nothing+confusion ends (Lapras win|140|135)

(139) Chansey hit thrice, parafused (5th turn); Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt+confusion ends (Lapras win|Chansey win|Chansey win), 1/4 nothing+confusion ends (Lapras win|140|135)

(140) Chansey hit four times, paralysed; Lapras hit thrice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt (Lapras win|Chansey win), 1/4 nothing (Lapras win|140)

(141) Chansey hit four times, parafused (2nd turn); Lapras hit thrice, paralysed
Unattainable

(142) Chansey hit four times, parafused (3rd turn); Lapras hit thrice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*2/3 nothing (Lapras win|143), 3/8*2/3 Thunderbolt (Lapras win|Chansey win), 3/4*1/3 Thunderbolt+confusion ends (Lapras win|Chansey win), 1/4*1/3 nothing+confusion ends (Lapras win|140)

(143) Chansey hit four times, parafused (4th turn); Lapras hit thrice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 5/8*1/2 nothing (Lapras win|144), 3/8*1/2 Thunderbolt (Lapras win|Chansey win), 3/4*1/2 Thunderbolt+confusion ends (Lapras win|Chansey win), 1/4*1/2 nothing+confusion ends (Lapras win|140)

(144) Chansey hit four times, parafused (5th turn); Lapras hit thrice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt+confusion ends (Lapras win|Chansey win), 1/4 nothing+confusion ends (Lapras win|140)

Here's the 140 simultaneous equations I put into Mathematica:

SPOILER: Click to show

Reduce[x0 == 5/8*x1+3/8*x21 && x1 == 15/128*5/8*3/4*x12+113/128*5/8*3/4*x7+15/128*3/8*3/4*x32+113/128*3/8*3/4*x27+15/128*3/4*1/4*x30+113/128*3/4*1/4*x25+15/128*1/4*1/4*x10+113/128*1/4*1/4*x5 && x2 == 15/128*5/8*2/3*x13+113/128*5/8*2/3*x8+15/128*3/8*2/3*x33+113/128*3/8*2/3*x28+15/128*3/4*1/3*x30+113/128*3/4*1/3*x25+15/128*1/4*1/3*x10+113/128*1/4*1/3*x5 && x3 == 15/128*5/8*1/2*x14+113/128*5/8*1/2*x9+15/128*3/8*1/2*x34+113/128*3/8*1/2*x29+15/128*3/4*1/2*x30+113/128*3/4*1/2*x25+15/128*1/4*1/2*x10+113/128*1/4*1/2*x5 && x4 == 15/128*3/4*x30+113/128*3/4*x25+15/128*1/4*x10+113/128*1/4*x5 && x5 == 5/8*x6+3/8*x26 && x6 == 15/128*5/8*3/4*x17+113/128*5/8*3/4*x12+15/128*3/8*3/4*x7+113/128*3/8*3/4*x2+15/128*3/4*1/4*x5+113/128*3/4*1/4*x0+15/128*1/4*1/4*x15+113/128*1/4*1/4*x10 && x7 == 15/128*5/8*2/3*x18+113/128*5/8*2/3*x13+15/128*3/8*2/3*x8+113/128*3/8*2/3*x3+15/128*3/4*1/3*x5+113/128*3/4*1/3*x0+15/128*1/4*1/3*x15+113/128*1/4*1/3*x10 && x8 == 15/128*5/8*1/2*x19+113/128*5/8*1/2*x14+15/128*3/8*1/2*x9+113/128*3/8*1/2*x4+15/128*3/4*1/2*x5+113/128*3/4*1/2*x0+15/128*1/4*1/2*x15+113/128*1/4*1/2*x10 && x9 == 15/128*3/4*x5+113/128*3/4*x0+15/128*1/4*x15+113/128*1/4*x10 && x10 == 5/8*x11+3/8*x1 && x11 == 15/128*5/8*3/4*a+113/128*5/8*3/4*x17+15/128*3/8*3/4*x12+113/128*3/8*3/4*x7+15/128*3/4*1/4*x10+113/128*3/4*1/4*x5+15/128*1/4*1/4*a+113/128*1/4*1/4*x15 && x12 == 15/128*5/8*2/3*a+113/128*5/8*2/3*x18+15/128*3/8*2/3*x13+113/128*3/8*2/3*x8+15/128*3/4*1/3*x10+113/128*3/4*1/3*x5+15/128*1/4*1/3*a+113/128*1/4*1/3*x15 && x13 == 15/128*5/8*1/2*a+113/128*5/8*1/2*x19+15/128*3/8*1/2*x14+113/128*3/8*1/2*x9+15/128*3/4*1/2*x10+113/128*3/4*1/2*x5+15/128*1/4*1/2*a+113/128*1/4*1/2*x15 && x14 == 15/128*3/4*x10+113/128*3/4*x5+15/128*1/4*a+113/128*1/4*x15 && x15 == 5/8*x16+3/8*x6 && x16 == 5/8*3/4*a+15/128*3/8*3/4*a+113/128*3/8*3/4*x12+15/128*3/4*1/4*a+113/128*3/4*1/4*x10+1/4*1/4*a && x17 == 5/8*2/3*a+15/128*3/8*2/3*a+113/128*3/8*2/3*x13+15/128*3/4*1/3*a+113/128*3/4*1/3*x10+1/4*1/3*a && x18 == 5/8*1/2*a+15/128*3/8*1/2*a+113/128*3/8*1/2*x14+15/128*3/4*1/2*a+113/128*3/4*1/2*x10+1/4*1/2*a && x19 == 15/128*3/4*a+113/128*3/4*x10+1/4*a && x20 == 5/8*3/4*x21+3/8*3/4*231/256*x46+3/8*3/4*25/256*x71+3/4*1/4*231/256*x45+3/4*1/4*25/256*x70+1/4*1/4*x20 && x21 == 3/4*15/128*5/8*3/4*x32+3/4*113/128*5/8*3/4*x27+1/4*5/8*3/4*x22+3/4*15/128*3/8*3/4*231/256*x57+3/4*113/128*3/8*3/4*231/256*x52+1/4*3/8*3/4*231/256*x47+3/4*15/128*3/8*3/4*25/256*x82+3/4*113/128*3/8*3/4*25/256*x77+1/4*3/8*3/4*25/256*x72+3/4*15/128*3/4*1/4*231/256*x55+3/4*113/128*3/4*1/4*231/256*x50+1/4*3/4*1/4*231/256*x45+3/4*15/128*3/4*1/4*25/256*x80+3/4*113/128*3/4*1/4*25/256*x75+1/4*3/4*1/4*25/256*x70+3/4*15/128*1/4*1/4*x30+3/4*113/128*1/4*1/4*x25+1/4*1/4*1/4*x20 && x22 == 3/4*15/128*5/8*2/3*x33+3/4*113/128*5/8*2/3*x28+1/4*5/8*2/3*x23+3/4*15/128*3/8*2/3*231/256*x58+3/4*113/128*3/8*2/3*231/256*x53+1/4*3/8*2/3*231/256*x48+3/4*15/128*3/8*2/3*25/256*x83+3/4*113/128*3/8*2/3*25/256*x78+1/4*3/8*2/3*25/256*x73+3/4*15/128*3/4*1/3*231/256*x55+3/4*113/128*3/4*1/3*231/256*x50+1/4*3/4*1/3*231/256*x45+3/4*15/128*3/4*1/3*25/256*x80+3/4*113/128*3/4*1/3*25/256*x75+1/4*3/4*1/3*25/256*x70+3/4*15/128*1/4*1/3*x30+3/4*113/128*1/4*1/3*x25+1/4*1/4*1/3*x20 && x23 == 3/4*15/128*5/8*1/2*x34+3/4*113/128*5/8*1/2*x29+1/4*5/8*1/2*x24+3/4*15/128*3/8*1/2*231/256*x59+3/4*113/128*3/8*1/2*231/256*x54+1/4*3/8*1/2*231/256*x49+3/4*15/128*3/8*1/2*25/256*x84+3/4*113/128*3/8*1/2*25/256*x79+1/4*3/8*1/2*25/256*x74+3/4*15/128*3/4*1/2*231/256*x55+3/4*113/128*3/4*1/2*231/256*x50+1/4*3/4*1/2*231/256*x45+3/4*15/128*3/4*1/2*25/256*x80+3/4*113/128*3/4*1/2*25/256*x75+1/4*3/4*1/2*25/256*x70+3/4*15/128*1/4*1/2*x30+3/4*113/128*1/4*1/2*x25+1/4*1/4*1/2*x20 && x24 == 3/4*15/128*3/4*231/256*x55+3/4*113/128*3/4*231/256*x50+1/4*3/4*231/256*x45+3/4*15/128*3/4*25/256*x80+3/4*113/128*3/4*25/256*x75+1/4*3/4*25/256*x70+3/4*15/128*1/4*x30+3/4*113/128*1/4*x25+1/4*1/4*x20 && x25 == 5/8*3/4*x26+3/8*3/4*231/256*x51+3/8*3/4*25/256*x76+3/4*1/4*231/256*x50+3/4*1/4*25/256*x75+1/4*1/4*x25 && x26 == 3/4*15/128*5/8*3/4*x37+3/4*113/128*5/8*3/4*x32+1/4*5/8*3/4*x27+3/4*15/128*3/8*3/4*x27+3/4*113/128*3/8*3/4*x22+1/4*3/8*3/4*x22+3/4*15/128*3/4*1/4*x25+3/4*113/128*3/4*1/4*x20+1/4*3/4*1/4*x20+3/4*15/128*1/4*1/4*x35+3/4*113/128*1/4*1/4*x30+1/4*1/4*1/4*x25 && x27 == 3/4*15/128*5/8*2/3*x38+3/4*113/128*5/8*2/3*x33+1/4*5/8*2/3*x28+3/4*15/128*3/8*2/3*x28+3/4*113/128*3/8*2/3*x23+1/4*3/8*2/3*x23+3/4*15/128*3/4*1/3*x25+3/4*113/128*3/4*1/3*x20+1/4*3/4*1/3*x20+3/4*15/128*1/4*1/3*x35+3/4*113/128*1/4*1/3*x30+1/4*1/4*1/3*x25 && x28 == 3/4*15/128*5/8*1/2*x39+3/4*113/128*5/8*1/2*x34+1/4*5/8*1/2*x29+3/4*15/128*3/8*1/2*x29+3/4*113/128*3/8*1/2*x24+1/4*3/8*1/2*x24+3/4*15/128*3/4*1/2*x25+3/4*113/128*3/4*1/2*x20+1/4*3/4*1/2*x20+3/4*15/128*1/4*1/2*x35+3/4*113/128*1/4*1/2*x30+1/4*1/4*1/2*x25 && x29 == 3/4*15/128*3/4*x25+3/4*113/128*3/4*x20+1/4*3/4*x20+3/4*15/128*1/4*x35+3/4*113/128*1/4*x30+1/4*1/4*x25 && x30 == 5/8*3/4*x31+3/8*3/4*x21+3/4*1/4*x20+1/4*1/4*x30 && x31 == 3/4*15/128*5/8*3/4*x42+3/4*113/128*5/8*3/4*x37+1/4*5/8*3/4*x32+3/4*15/128*3/8*3/4*x32+3/4*113/128*3/8*3/4*x27+1/4*3/8*3/4*x22+3/4*15/128*3/4*1/4*x30+3/4*113/128*3/4*1/4*x25+1/4*3/4*1/4*x20+3/4*15/128*1/4*1/4*x40+3/4*113/128*1/4*1/4*x35+1/4*1/4*1/4*x30 && x32 == 3/4*15/128*5/8*2/3*x43+3/4*113/128*5/8*2/3*x38+1/4*5/8*2/3*x33+3/4*15/128*3/8*2/3*x33+3/4*113/128*3/8*2/3*x28+1/4*3/8*2/3*x23+3/4*15/128*3/4*1/3*x30+3/4*113/128*3/4*1/3*x25+1/4*3/4*1/3*x20+3/4*15/128*1/4*1/3*x40+3/4*113/128*1/4*1/3*x35+1/4*1/4*1/3*x30 && x33 == 3/4*15/128*5/8*1/2*x44+3/4*113/128*5/8*1/2*x39+1/4*5/8*1/2*x34+3/4*15/128*3/8*1/2*x34+3/4*113/128*3/8*1/2*x29+1/4*3/8*1/2*x24+3/4*15/128*3/4*1/2*x30+3/4*113/128*3/4*1/2*x25+1/4*3/4*1/2*x20+3/4*15/128*1/4*1/2*x40+3/4*113/128*1/4*1/2*x35+1/4*1/4*1/2*x30 && x34 == 3/4*15/128*3/4*x30+3/4*113/128*3/4*x25+1/4*3/4*x20+3/4*15/128*1/4*x40+3/4*113/128*1/4*x35+1/4*1/4*x30 && x35 == 5/8*3/4*x36+3/8*3/4*x26+3/4*1/4*x25+1/4*1/4*x35 && x36 == 3/4*15/128*5/8*3/4*b+3/4*113/128*5/8*3/4*x42+1/4*5/8*3/4*x37+3/4*15/128*3/8*3/4*b+3/4*113/128*3/8*3/4*x32+1/4*3/8*3/4*x27+3/4*15/128*3/4*1/4*b+3/4*113/128*3/4*1/4*x30+1/4*3/4*1/4*x25+3/4*15/128*1/4*1/4*b+3/4*113/128*1/4*1/4*x40+1/4*1/4*1/4*x35 && x37 == 3/4*15/128*5/8*2/3*b+3/4*113/128*5/8*2/3*x43+1/4*5/8*2/3*x38+3/4*15/128*3/8*2/3*b+3/4*113/128*3/8*2/3*x33+1/4*3/8*2/3*x28+3/4*15/128*3/4*1/3*b+3/4*113/128*3/4*1/3*x30+1/4*3/4*1/3*x25+3/4*15/128*1/4*1/3*b+3/4*113/128*1/4*1/3*x40+1/4*1/4*1/3*x35 && x38 == 3/4*15/128*5/8*1/2*b+3/4*113/128*5/8*1/2*x44+1/4*5/8*1/2*x39+3/4*15/128*3/8*1/2*b+3/4*113/128*3/8*1/2*x34+1/4*3/8*1/2*x29+3/4*15/128*3/4*1/2*b+3/4*113/128*3/4*1/2*x30+1/4*3/4*1/2*x25+3/4*15/128*1/4*1/2*b+3/4*113/128*1/4*1/2*x40+1/4*1/4*1/2*x35 && x39 == 3/4*15/128*3/4*b+3/4*113/128*3/4*x30+1/4*3/4*x25+3/4*15/128*1/4*b+3/4*113/128*1/4*x40+1/4*1/4*x35 && x40 == 3/4*3/4*b+1/4*3/4*x30+3/4*1/4*b+1/4*1/4*x40 && x42 == 3/4*5/8*2/3*b+1/4*5/8*2/3*x43+3/4*3/8*2/3*b+1/4*3/8*2/3*x33+3/4*3/4*1/3*b+1/4*3/4*1/3*x30+3/4*1/4*1/3*b+1/4*1/4*1/3*x40 && x43 == 3/4*5/8*1/2*b+1/4*5/8*1/2*x44+3/4*3/8*1/2*b+1/4*3/8*1/2*x34+3/4*3/4*1/2*b+1/4*3/4*1/2*x30+3/4*1/4*1/2*b+1/4*1/4*1/2*x40 && x44 == 3/4*3/4*b+1/4*3/4*x30+3/4*1/4*b+1/4*1/4*x40 && x45 == 5/8*3/4*x46+3/8*3/4*231/256*x96+3/8*3/4*25/256*1011/1521*c+3/8*3/4*25/256*510/1521*x121+3/4*1/4*231/256*x95+3/4*1/4*25/256*1011/1521*c+3/4*1/4*25/256*510/1521*x120+1/4*1/4*x45 && x46 == 3/4*15/128*5/8*3/4*x57+3/4*113/128*5/8*3/4*x52+1/4*5/8*3/4*x47+3/4*15/128*3/8*3/4*231/256*x107+3/4*113/128*3/8*3/4*231/256*x102+1/4*3/8*3/4*231/256*x97+3/8*3/4*25/256*1011/1521*c+3/4*15/128*3/8*3/4*25/256*510/1521*x132+3/4*113/128*3/8*3/4*25/256*510/1521*x127+1/4*3/8*3/4*25/256*510/1521*x122+3/4*15/128*3/4*1/4*231/256*x105+3/4*113/128*3/4*1/4*231/256*x100+1/4*3/4*1/4*231/256*x95+3/4*1/4*25/256*1011/1521*c+3/4*15/128*3/4*1/4*25/256*510/1521*x130+3/4*113/128*3/4*1/4*25/256*510/1521*x125+1/4*3/4*1/4*25/256*510/1521*x120+3/4*15/128*1/4*1/4*x55+3/4*113/128*1/4*1/4*x50+1/4*1/4*1/4*x45 && x47 == 3/4*15/128*5/8*2/3*x58+3/4*113/128*5/8*2/3*x53+1/4*5/8*2/3*x48+3/4*15/128*3/8*2/3*231/256*x108+3/4*113/128*3/8*2/3*231/256*x103+1/4*3/8*2/3*231/256*x98+3/8*2/3*25/256*1011/1521*c+3/4*15/128*3/8*2/3*25/256*510/1521*x133+3/4*113/128*3/8*2/3*25/256*510/1521*x128+1/4*3/8*2/3*25/256*510/1521*x123+3/4*15/128*3/4*1/3*231/256*x105+3/4*113/128*3/4*1/3*231/256*x100+1/4*3/4*1/3*231/256*x95+3/4*1/3*25/256*1011/1521*c+3/4*15/128*3/4*1/3*25/256*510/1521*x130+3/4*113/128*3/4*1/3*25/256*510/1521*x125+1/4*3/4*1/3*25/256*510/1521*x120+3/4*15/128*1/4*1/3*x55+3/4*113/128*1/4*1/3*x50+1/4*1/4*1/3*x45 && x48 == 3/4*15/128*5/8*1/2*x59+3/4*113/128*5/8*1/2*x54+1/4*5/8*1/2*x49+3/4*15/128*3/8*1/2*231/256*x109+3/4*113/128*3/8*1/2*231/256*x104+1/4*3/8*1/2*231/256*x99+3/8*1/2*25/256*1011/1521*c+3/4*15/128*3/8*1/2*25/256*510/1521*x134+3/4*113/128*3/8*1/2*25/256*510/1521*x129+1/4*3/8*1/2*25/256*510/1521*x124+3/4*15/128*3/4*1/2*231/256*x105+3/4*113/128*3/4*1/2*231/256*x100+1/4*3/4*1/2*231/256*x95+3/4*1/2*25/256*1011/1521*c+3/4*15/128*3/4*1/2*25/256*510/1521*x130+3/4*113/128*3/4*1/2*25/256*510/1521*x125+1/4*3/4*1/2*25/256*510/1521*x120+3/4*15/128*1/4*1/2*x55+3/4*113/128*1/4*1/2*x50+1/4*1/4*1/2*x45 && x49 == 3/4*15/128*3/4*231/256*x105+3/4*113/128*3/4*231/256*x100+1/4*3/4*231/256*x95+3/4*25/256*1011/1521*c+3/4*15/128*3/4*25/256*510/1521*x130+3/4*113/128*3/4*25/256*510/1521*x125+1/4*3/4*25/256*510/1521*x120+3/4*15/128*1/4*x55+3/4*113/128*1/4*x50+1/4*1/4*x45 && x50 == 5/8*3/4*x51+3/8*3/4*231/256*x101+3/8*3/4*25/256*1011/1521*c+3/8*3/4*25/256*510/1521*x126+3/4*1/4*231/256*x100+3/4*1/4*25/256*1011/1521*c+3/4*1/4*25/256*510/1521*x125+1/4*1/4*x50 && x51 == 3/4*15/128*5/8*3/4*x62+3/4*113/128*5/8*3/4*x57+1/4*5/8*3/4*x52+3/4*15/128*3/8*3/4*x52+3/4*113/128*3/8*3/4*x47+1/4*3/8*3/4*x47+3/4*15/128*3/4*1/4*x50+3/4*113/128*3/4*1/4*x45+1/4*3/4*1/4*x45+3/4*15/128*1/4*1/4*x60+3/4*113/128*1/4*1/4*x55+1/4*1/4*1/4*x50 && x52 == 3/4*15/128*5/8*2/3*x63+3/4*113/128*5/8*2/3*x58+1/4*5/8*2/3*x53+3/4*15/128*3/8*2/3*x53+3/4*113/128*3/8*2/3*x48+1/4*3/8*2/3*x48+3/4*15/128*3/4*1/3*x50+3/4*113/128*3/4*1/3*x45+1/4*3/4*1/3*x45+3/4*15/128*1/4*1/3*x60+3/4*113/128*1/4*1/3*x55+1/4*1/4*1/3*x50 && x53 == 3/4*15/128*5/8*1/2*x64+3/4*113/128*5/8*1/2*x59+1/4*5/8*1/2*x54+3/4*15/128*3/8*1/2*x54+3/4*113/128*3/8*1/2*x49+1/4*3/8*1/2*x49+3/4*15/128*3/4*1/2*x50+3/4*113/128*3/4*1/2*x45+1/4*3/4*1/2*x45+3/4*15/128*1/4*1/2*x60+3/4*113/128*1/4*1/2*x55+1/4*1/4*1/2*x50 && x54 == 3/4*15/128*3/4*x50+3/4*113/128*3/4*x45+1/4*3/4*x45+3/4*15/128*1/4*x60+3/4*113/128*1/4*x55+1/4*1/4*x50 && x55 == 5/8*3/4*x56+3/8*3/4*x46+3/4*1/4*x45+1/4*1/4*x55 && x56 == 3/4*15/128*5/8*3/4*x67+3/4*113/128*5/8*3/4*x62+1/4*5/8*3/4*x57+3/4*15/128*3/8*3/4*x57+3/4*113/128*3/8*3/4*x52+1/4*3/8*3/4*x47+3/4*15/128*3/4*1/4*x55+3/4*113/128*3/4*1/4*x50+1/4*3/4*1/4*x45+3/4*15/128*1/4*1/4*x65+3/4*113/128*1/4*1/4*x60+1/4*1/4*1/4*x55 && x57 == 3/4*15/128*5/8*2/3*x68+3/4*113/128*5/8*2/3*x63+1/4*5/8*2/3*x58+3/4*15/128*3/8*2/3*x58+3/4*113/128*3/8*2/3*x53+1/4*3/8*2/3*x48+3/4*15/128*3/4*1/3*x55+3/4*113/128*3/4*1/3*x50+1/4*3/4*1/3*x45+3/4*15/128*1/4*1/3*x65+3/4*113/128*1/4*1/3*x60+1/4*1/4*1/3*x55 && x58 == 3/4*15/128*5/8*1/2*x69+3/4*113/128*5/8*1/2*x64+1/4*5/8*1/2*x59+3/4*15/128*3/8*1/2*x59+3/4*113/128*3/8*1/2*x54+1/4*3/8*1/2*x49+3/4*15/128*3/4*1/2*x55+3/4*113/128*3/4*1/2*x50+1/4*3/4*1/2*x45+3/4*15/128*1/4*1/2*x65+3/4*113/128*1/4*1/2*x60+1/4*1/4*1/2*x55 && x59 == 3/4*15/128*3/4*x55+3/4*113/128*3/4*x50+1/4*3/4*x45+3/4*15/128*1/4*x65+3/4*113/128*1/4*x60+1/4*1/4*x55 && x60 == 5/8*3/4*x61+3/8*3/4*x51+3/4*1/4*x50+1/4*1/4*x60 && x61 == 3/4*15/128*5/8*3/4*b+3/4*113/128*5/8*3/4*x67+1/4*5/8*3/4*x62+3/4*15/128*3/8*3/4*b+3/4*113/128*3/8*3/4*x57+1/4*3/8*3/4*x52+3/4*15/128*3/4*1/4*b+3/4*113/128*3/4*1/4*x55+1/4*3/4*1/4*x50+3/4*15/128*1/4*1/4*b+3/4*113/128*1/4*1/4*x65+1/4*1/4*1/4*x60 && x62 == 3/4*15/128*5/8*2/3*b+3/4*113/128*5/8*2/3*x68+1/4*5/8*2/3*x63+3/4*15/128*3/8*2/3*b+3/4*113/128*3/8*2/3*x58+1/4*3/8*2/3*x53+3/4*15/128*3/4*1/3*b+3/4*113/128*3/4*1/3*x55+1/4*3/4*1/3*x50+3/4*15/128*1/4*1/3*b+3/4*113/128*1/4*1/3*x65+1/4*1/4*1/3*x60 && x63 == 3/4*15/128*5/8*1/2*b+3/4*113/128*5/8*1/2*x69+1/4*5/8*1/2*x64+3/4*15/128*3/8*1/2*b+3/4*113/128*3/8*1/2*x59+1/4*3/8*1/2*x54+3/4*15/128*3/4*1/2*b+3/4*113/128*3/4*1/2*x55+1/4*3/4*1/2*x50+3/4*15/128*1/4*1/2*b+3/4*113/128*1/4*1/2*x65+1/4*1/4*1/2*x60 && x64 == 3/4*15/128*3/4*b+3/4*113/128*3/4*x55+1/4*3/4*x50+3/4*15/128*1/4*b+3/4*113/128*1/4*x65+1/4*1/4*x60 && x65 == 3/4*3/4*b+1/4*3/4*x55+3/4*1/4*b+1/4*1/4*x65 && x67 == 3/4*5/8*2/3*b+1/4*5/8*2/3*x68+3/4*3/8*2/3*b+1/4*3/8*2/3*x58+3/4*3/4*1/3*b+1/4*3/4*1/3*x55+3/4*1/4*1/3*b+1/4*1/4*1/3*x65 && x68 == 3/4*5/8*1/2*b+1/4*5/8*1/2*x69+3/4*3/8*1/2*b+1/4*3/8*1/2*x59+3/4*3/4*1/2*b+1/4*3/4*1/2*x55+3/4*1/4*1/2*b+1/4*1/4*1/2*x65 && x69 == 3/4*3/4*b+1/4*3/4*x55+3/4*1/4*b+1/4*1/4*x65 && x70 == 5/8*3/4*x71+3/8*3/4*231/256*1011/1521*c+3/8*3/4*231/256*510/1521*x121+3/8*3/4*25/256*c+3/4*1/4*231/256*1011/1521*c+3/4*1/4*231/256*510/1521*x120+3/4*1/4*25/256*c+1/4*1/4*x70 && x71 == 3/4*15/128*5/8*3/4*x82+3/4*113/128*5/8*3/4*x77+1/4*5/8*3/4*x72+3/8*3/4*231/256*1011/1521*c+3/4*15/128*3/8*3/4*231/256*510/1521*x132+3/4*113/128*3/8*3/4*231/256*510/1521*x127+1/4*3/8*3/4*231/256*510/1521*x122+3/8*3/4*25/256*c+3/4*1/4*231/256*1011/1521*c+3/4*15/128*3/4*1/4*231/256*510/1521*x130+3/4*113/128*3/4*1/4*231/256*510/1521*x125+1/4*3/4*1/4*231/256*510/1521*x120+3/4*1/4*25/256*c+3/4*15/128*1/4*1/4*x80+3/4*113/128*1/4*1/4*x75+1/4*1/4*1/4*x70 && x72 == 3/4*15/128*5/8*2/3*x83+3/4*113/128*5/8*2/3*x78+1/4*5/8*2/3*x73+3/8*2/3*231/256*1011/1521*c+3/4*15/128*3/8*2/3*231/256*510/1521*x133+3/4*113/128*3/8*2/3*231/256*510/1521*x128+1/4*3/8*2/3*231/256*510/1521*x123+3/8*2/3*25/256*c+3/4*1/3*231/256*1011/1521*c+3/4*15/128*3/4*1/3*231/256*510/1521*x130+3/4*113/128*3/4*1/3*231/256*510/1521*x125+1/4*3/4*1/3*231/256*510/1521*x120+3/4*1/3*25/256*c+3/4*15/128*1/4*1/3*x80+3/4*113/128*1/4*1/3*x75+1/4*1/4*1/3*x70 && x73 == 3/4*15/128*5/8*1/2*x84+3/4*113/128*5/8*1/2*x79+1/4*5/8*1/2*x74+3/8*1/2*231/256*1011/1521*c+3/4*15/128*3/8*1/2*231/256*510/1521*x134+3/4*113/128*3/8*1/2*231/256*510/1521*x129+1/4*3/8*1/2*231/256*510/1521*x124+3/8*1/2*25/256*c+3/4*1/2*231/256*1011/1521*c+3/4*15/128*3/4*1/2*231/256*510/1521*x130+3/4*113/128*3/4*1/2*231/256*510/1521*x125+1/4*3/4*1/2*231/256*510/1521*x120+3/4*1/2*25/256*c+3/4*15/128*1/4*1/2*x80+3/4*113/128*1/4*1/2*x75+1/4*1/4*1/2*x70 && x74 == 3/4*231/256*1011/1521*c+3/4*15/128*3/4*231/256*510/1521*x130+3/4*113/128*3/4*231/256*510/1521*x125+1/4*3/4*231/256*510/1521*x120+3/4*25/256*c+3/4*15/128*1/4*x80+3/4*113/128*1/4*x75+1/4*1/4*x70 && x75 == 5/8*3/4*x76+3/8*3/4*231/256*1011/1521*c+3/8*3/4*231/256*510/1521*x126+3/8*3/4*25/256*c+3/4*1/4*231/256*1011/1521*c+3/4*1/4*231/256*510/1521*x125+3/4*1/4*25/256*c+1/4*1/4*x75 && x76 == 3/4*15/128*5/8*3/4*x87+3/4*113/128*5/8*3/4*x82+1/4*5/8*3/4*x77+3/4*15/128*3/8*3/4*x77+3/4*113/128*3/8*3/4*x72+1/4*3/8*3/4*x72+3/4*15/128*3/4*1/4*x75+3/4*113/128*3/4*1/4*x70+1/4*3/4*1/4*x70+3/4*15/128*1/4*1/4*x85+3/4*113/128*1/4*1/4*x80+1/4*1/4*1/4*x75 && x77 == 3/4*15/128*5/8*2/3*x88+3/4*113/128*5/8*2/3*x83+1/4*5/8*2/3*x78+3/4*15/128*3/8*2/3*x78+3/4*113/128*3/8*2/3*x73+1/4*3/8*2/3*x73+3/4*15/128*3/4*1/3*x75+3/4*113/128*3/4*1/3*x70+1/4*3/4*1/3*x70+3/4*15/128*1/4*1/3*x85+3/4*113/128*1/4*1/3*x80+1/4*1/4*1/3*x75 && x78 == 3/4*15/128*5/8*1/2*x89+3/4*113/128*5/8*1/2*x84+1/4*5/8*1/2*x79+3/4*15/128*3/8*1/2*x79+3/4*113/128*3/8*1/2*x74+1/4*3/8*1/2*x74+3/4*15/128*3/4*1/2*x75+3/4*113/128*3/4*1/2*x70+1/4*3/4*1/2*x70+3/4*15/128*1/4*1/2*x85+3/4*113/128*1/4*1/2*x80+1/4*1/4*1/2*x75 && x79 == 3/4*15/128*3/4*x75+3/4*113/128*3/4*x70+1/4*3/4*x70+3/4*15/128*1/4*x85+3/4*113/128*1/4*x80+1/4*1/4*x75 && x80 == 5/8*3/4*x81+3/8*3/4*x71+3/4*1/4*x70+1/4*1/4*x80 && x81 == 3/4*15/128*5/8*3/4*x92+3/4*113/128*5/8*3/4*x87+1/4*5/8*3/4*x82+3/4*15/128*3/8*3/4*x82+3/4*113/128*3/8*3/4*x77+1/4*3/8*3/4*x72+3/4*15/128*3/4*1/4*x80+3/4*113/128*3/4*1/4*x75+1/4*3/4*1/4*x70+3/4*15/128*1/4*1/4*x90+3/4*113/128*1/4*1/4*x85+1/4*1/4*1/4*x80 && x82 == 3/4*15/128*5/8*2/3*x93+3/4*113/128*5/8*2/3*x88+1/4*5/8*2/3*x83+3/4*15/128*3/8*2/3*x83+3/4*113/128*3/8*2/3*x78+1/4*3/8*2/3*x73+3/4*15/128*3/4*1/3*x80+3/4*113/128*3/4*1/3*x75+1/4*3/4*1/3*x70+3/4*15/128*1/4*1/3*x90+3/4*113/128*1/4*1/3*x85+1/4*1/4*1/3*x80 && x83 == 3/4*15/128*5/8*1/2*x94+3/4*113/128*5/8*1/2*x89+1/4*5/8*1/2*x84+3/4*15/128*3/8*1/2*x84+3/4*113/128*3/8*1/2*x79+1/4*3/8*1/2*x74+3/4*15/128*3/4*1/2*x80+3/4*113/128*3/4*1/2*x75+1/4*3/4*1/2*x70+3/4*15/128*1/4*1/2*x90+3/4*113/128*1/4*1/2*x85+1/4*1/4*1/2*x80 && x84 == 3/4*15/128*3/4*x80+3/4*113/128*3/4*x75+1/4*3/4*x70+3/4*15/128*1/4*x90+3/4*113/128*1/4*x85+1/4*1/4*x80 && x85 == 5/8*3/4*x86+3/8*3/4*x76+3/4*1/4*x75+1/4*1/4*x85 && x86 == 3/4*15/128*5/8*3/4*b+3/4*113/128*5/8*3/4*x92+1/4*5/8*3/4*x87+3/4*15/128*3/8*3/4*b+3/4*113/128*3/8*3/4*x82+1/4*3/8*3/4*x77+3/4*15/128*3/4*1/4*b+3/4*113/128*3/4*1/4*x80+1/4*3/4*1/4*x75+3/4*15/128*1/4*1/4*b+3/4*113/128*1/4*1/4*x90+1/4*1/4*1/4*x85 && x87 == 3/4*15/128*5/8*2/3*b+3/4*113/128*5/8*2/3*x93+1/4*5/8*2/3*x88+3/4*15/128*3/8*2/3*b+3/4*113/128*3/8*2/3*x83+1/4*3/8*2/3*x78+3/4*15/128*3/4*1/3*b+3/4*113/128*3/4*1/3*x80+1/4*3/4*1/3*x75+3/4*15/128*1/4*1/3*b+3/4*113/128*1/4*1/3*x90+1/4*1/4*1/3*x85 && x88 == 3/4*15/128*5/8*1/2*b+3/4*113/128*5/8*1/2*x94+1/4*5/8*1/2*x89+3/4*15/128*3/8*1/2*b+3/4*113/128*3/8*1/2*x84+1/4*3/8*1/2*x79+3/4*15/128*3/4*1/2*b+3/4*113/128*3/4*1/2*x80+1/4*3/4*1/2*x75+3/4*15/128*1/4*1/2*b+3/4*113/128*1/4*1/2*x90+1/4*1/4*1/2*x85 && x89 == 3/4*15/128*3/4*b+3/4*113/128*3/4*x80+1/4*3/4*x75+3/4*15/128*1/4*b+3/4*113/128*1/4*x90+1/4*1/4*x85 && x90 == 3/4*3/4*b+1/4*3/4*x80+3/4*1/4*b+1/4*1/4*x90 && x92 == 3/4*5/8*2/3*b+1/4*5/8*2/3*x93+3/4*3/8*2/3*b+1/4*3/8*2/3*x83+3/4*3/4*1/3*b+1/4*3/4*1/3*x80+3/4*1/4*1/3*b+1/4*1/4*1/3*x90 && x93 == 3/4*5/8*1/2*b+1/4*5/8*1/2*x94+3/4*3/8*1/2*b+1/4*3/8*1/2*x84+3/4*3/4*1/2*b+1/4*3/4*1/2*x80+3/4*1/4*1/2*b+1/4*1/4*1/2*x90 && x94 == 3/4*3/4*b+1/4*3/4*x80+3/4*1/4*b+1/4*1/4*x90 && x95 == 5/8*3/4*x96+3/8*3/4*231/256*921/1000*c+3/8*3/4*231/256*79/1000*x121+3/8*3/4*25/256*c+3/4*1/4*231/256*921/1000*c+3/4*1/4*231/256*79/1000*x120+3/4*1/4*25/256*c+1/4*1/4*x95 && x96 == 3/4*15/128*5/8*3/4*x107+3/4*113/128*5/8*3/4*x102+1/4*5/8*3/4*x97+3/8*3/4*231/256*921/1000*c+3/4*15/128*3/8*3/4*231/256*79/1000*x132+3/4*113/128*3/8*3/4*231/256*79/1000*x127+1/4*3/8*3/4*231/256*79/1000*x122+3/8*3/4*25/256*c+3/4*1/4*231/256*921/1000*c+3/4*15/128*3/4*1/4*231/256*79/1000*x130+3/4*113/128*3/4*1/4*231/256*79/1000*x125+1/4*3/4*1/4*231/256*79/1000*x120+3/4*1/4*25/256*c+3/4*15/128*1/4*1/4*x105+3/4*113/128*1/4*1/4*x100+1/4*1/4*1/4*x95 && x97 == 3/4*15/128*5/8*2/3*x108+3/4*113/128*5/8*2/3*x103+1/4*5/8*2/3*x98+3/8*2/3*231/256*921/1000*c+3/4*15/128*3/8*2/3*231/256*79/1000*x133+3/4*113/128*3/8*2/3*231/256*79/1000*x128+1/4*3/8*2/3*231/256*79/1000*x123+3/8*2/3*25/256*c+3/4*1/3*231/256*921/1000*c+3/4*15/128*3/4*1/3*231/256*79/1000*x130+3/4*113/128*3/4*1/3*231/256*79/1000*x125+1/4*3/4*1/3*231/256*79/1000*x120+3/4*1/3*25/256*c+3/4*15/128*1/4*1/3*x105+3/4*113/128*1/4*1/3*x100+1/4*1/4*1/3*x95 && x98 == 3/4*15/128*5/8*1/2*x109+3/4*113/128*5/8*1/2*x104+1/4*5/8*1/2*x99+3/8*1/2*231/256*921/1000*c+3/4*15/128*3/8*1/2*231/256*79/1000*x134+3/4*113/128*3/8*1/2*231/256*79/1000*x129+1/4*3/8*1/2*231/256*79/1000*x124+3/8*1/2*25/256*c+3/4*1/2*231/256*921/1000*c+3/4*15/128*3/4*1/2*231/256*79/1000*x130+3/4*113/128*3/4*1/2*231/256*79/1000*x125+1/4*3/4*1/2*231/256*79/1000*x120+3/4*1/2*25/256*c+3/4*15/128*1/4*1/2*x105+3/4*113/128*1/4*1/2*x100+1/4*1/4*1/2*x95 && x99 == 3/4*231/256*921/1000*c+3/4*15/128*3/4*231/256*79/1000*x130+3/4*113/128*3/4*231/256*79/1000*x125+1/4*3/4*231/256*79/1000*x120+3/4*25/256*c+3/4*15/128*1/4*x105+3/4*113/128*1/4*x100+1/4*1/4*x95 && x100 == 5/8*3/4*x101+3/8*3/4*231/256*921/1000*c+3/8*3/4*231/256*79/1000*x126+3/8*3/4*25/256*c+3/4*1/4*231/256*921/1000*c+3/4*1/4*231/256*79/1000*x125+3/4*1/4*25/256*c+1/4*1/4*x100 && x101 == 3/4*15/128*5/8*3/4*x112+3/4*113/128*5/8*3/4*x107+1/4*5/8*3/4*x102+3/4*15/128*3/8*3/4*x102+3/4*113/128*3/8*3/4*x97+1/4*3/8*3/4*x97+3/4*15/128*3/4*1/4*x100+3/4*113/128*3/4*1/4*x95+1/4*3/4*1/4*x95+3/4*15/128*1/4*1/4*x110+3/4*113/128*1/4*1/4*x105+1/4*1/4*1/4*x100 && x102 == 3/4*15/128*5/8*2/3*x113+3/4*113/128*5/8*2/3*x108+1/4*5/8*2/3*x103+3/4*15/128*3/8*2/3*x103+3/4*113/128*3/8*2/3*x98+1/4*3/8*2/3*x98+3/4*15/128*3/4*1/3*x100+3/4*113/128*3/4*1/3*x95+1/4*3/4*1/3*x95+3/4*15/128*1/4*1/3*x110+3/4*113/128*1/4*1/3*x105+1/4*1/4*1/3*x100 && x103 == 3/4*15/128*5/8*1/2*x114+3/4*113/128*5/8*1/2*x109+1/4*5/8*1/2*x104+3/4*15/128*3/8*1/2*x104+3/4*113/128*3/8*1/2*x99+1/4*3/8*1/2*x99+3/4*15/128*3/4*1/2*x100+3/4*113/128*3/4*1/2*x95+1/4*3/4*1/2*x95+3/4*15/128*1/4*1/2*x110+3/4*113/128*1/4*1/2*x105+1/4*1/4*1/2*x100 && x104 == 3/4*15/128*3/4*x100+3/4*113/128*3/4*x95+1/4*3/4*x95+3/4*15/128*1/4*x110+3/4*113/128*1/4*x105+1/4*1/4*x100 && x105 == 5/8*3/4*x106+3/8*3/4*x96+3/4*1/4*x95+1/4*1/4*x105 && x106 == 3/4*15/128*5/8*3/4*x117+3/4*113/128*5/8*3/4*x112+1/4*5/8*3/4*x107+3/4*15/128*3/8*3/4*x107+3/4*113/128*3/8*3/4*x102+1/4*3/8*3/4*x97+3/4*15/128*3/4*1/4*x105+3/4*113/128*3/4*1/4*x100+1/4*3/4*1/4*x95+3/4*15/128*1/4*1/4*x115+3/4*113/128*1/4*1/4*x110+1/4*1/4*1/4*x105 && x107 == 3/4*15/128*5/8*2/3*x118+3/4*113/128*5/8*2/3*x113+1/4*5/8*2/3*x108+3/4*15/128*3/8*2/3*x108+3/4*113/128*3/8*2/3*x103+1/4*3/8*2/3*x98+3/4*15/128*3/4*1/3*x105+3/4*113/128*3/4*1/3*x100+1/4*3/4*1/3*x95+3/4*15/128*1/4*1/3*x115+3/4*113/128*1/4*1/3*x110+1/4*1/4*1/3*x105 && x108 == 3/4*15/128*5/8*1/2*x119+3/4*113/128*5/8*1/2*x114+1/4*5/8*1/2*x109+3/4*15/128*3/8*1/2*x109+3/4*113/128*3/8*1/2*x104+1/4*3/8*1/2*x99+3/4*15/128*3/4*1/2*x105+3/4*113/128*3/4*1/2*x100+1/4*3/4*1/2*x95+3/4*15/128*1/4*1/2*x115+3/4*113/128*1/4*1/2*x110+1/4*1/4*1/2*x105 && x109 == 3/4*15/128*3/4*x105+3/4*113/128*3/4*x100+1/4*3/4*x95+3/4*15/128*1/4*x115+3/4*113/128*1/4*x110+1/4*1/4*x105 && x110 == 5/8*3/4*x111+3/8*3/4*x101+3/4*1/4*x100+1/4*1/4*x110 && x111 == 3/4*15/128*5/8*3/4*b+3/4*113/128*5/8*3/4*x117+1/4*5/8*3/4*x112+3/4*15/128*3/8*3/4*b+3/4*113/128*3/8*3/4*x107+1/4*3/8*3/4*x102+3/4*15/128*3/4*1/4*b+3/4*113/128*3/4*1/4*x105+1/4*3/4*1/4*x100+3/4*15/128*1/4*1/4*b+3/4*113/128*1/4*1/4*x115+1/4*1/4*1/4*x110 && x112 == 3/4*15/128*5/8*2/3*b+3/4*113/128*5/8*2/3*x118+1/4*5/8*2/3*x113+3/4*15/128*3/8*2/3*b+3/4*113/128*3/8*2/3*x108+1/4*3/8*2/3*x103+3/4*15/128*3/4*1/3*b+3/4*113/128*3/4*1/3*x105+1/4*3/4*1/3*x100+3/4*15/128*1/4*1/3*b+3/4*113/128*1/4*1/3*x115+1/4*1/4*1/3*x110 && x113 == 3/4*15/128*5/8*1/2*b+3/4*113/128*5/8*1/2*x119+1/4*5/8*1/2*x114+3/4*15/128*3/8*1/2*b+3/4*113/128*3/8*1/2*x109+1/4*3/8*1/2*x104+3/4*15/128*3/4*1/2*b+3/4*113/128*3/4*1/2*x105+1/4*3/4*1/2*x100+3/4*15/128*1/4*1/2*b+3/4*113/128*1/4*1/2*x115+1/4*1/4*1/2*x110 && x114 == 3/4*15/128*3/4*b+3/4*113/128*3/4*x105+1/4*3/4*x100+3/4*15/128*1/4*b+3/4*113/128*1/4*x115+1/4*1/4*x110 && x115 == 3/4*3/4*b+1/4*3/4*x105+3/4*1/4*b+1/4*1/4*x115 && x117 == 3/4*5/8*2/3*b+1/4*5/8*2/3*x118+3/4*3/8*2/3*b+1/4*3/8*2/3*x108+3/4*3/4*1/3*b+1/4*3/4*1/3*x105+3/4*1/4*1/3*b+1/4*1/4*1/3*x115 && x118 == 3/4*5/8*1/2*b+1/4*5/8*1/2*x119+3/4*3/8*1/2*b+1/4*3/8*1/2*x109+3/4*3/4*1/2*b+1/4*3/4*1/2*x105+3/4*1/4*1/2*b+1/4*1/4*1/2*x115 && x119 == 3/4*3/4*b+1/4*3/4*x105+3/4*1/4*b+1/4*1/4*x115 && x120 == 5/8*3/4*x121+3/8*3/4*c+3/4*1/4*c+1/4*1/4*x120 && x121 == 3/4*15/128*5/8*3/4*x132+3/4*113/128*5/8*3/4*x127+1/4*5/8*3/4*x122+3/8*3/4*c+3/4*1/4*c+3/4*15/128*1/4*1/4*x130+3/4*113/128*1/4*1/4*x125+1/4*1/4*1/4*x120 && x122 == 3/4*15/128*5/8*2/3*x133+3/4*113/128*5/8*2/3*x128+1/4*5/8*2/3*x123+3/8*2/3*c+3/4*1/3*c+3/4*15/128*1/4*1/3*x130+3/4*113/128*1/4*1/3*x125+1/4*1/4*1/3*x120 && x123 == 3/4*15/128*5/8*1/2*x134+3/4*113/128*5/8*1/2*x129+1/4*5/8*1/2*x124+3/8*1/2*c+3/4*1/2*c+3/4*15/128*1/4*1/2*x130+3/4*113/128*1/4*1/2*x125+1/4*1/4*1/2*x120 && x124 == 3/4*c+3/4*15/128*1/4*x130+3/4*113/128*1/4*x125+1/4*1/4*x120 && x125 == 5/8*3/4*x126+3/8*3/4*c+3/4*1/4*c+1/4*1/4*x125 && x126 == 3/4*15/128*5/8*3/4*x137+3/4*113/128*5/8*3/4*x132+1/4*5/8*3/4*x127+3/8*3/4*c+3/4*1/4*c+3/4*15/128*1/4*1/4*x135+3/4*113/128*1/4*1/4*x130+1/4*1/4*1/4*x125 && x127 == 3/4*15/128*5/8*2/3*x138+3/4*113/128*5/8*2/3*x133+1/4*5/8*2/3*x128+3/8*2/3*c+3/4*1/3*c+3/4*15/128*1/4*1/3*x135+3/4*113/128*1/4*1/3*x130+1/4*1/4*1/3*x125 && x128 == 3/4*15/128*5/8*1/2*x139+3/4*113/128*5/8*1/2*x134+1/4*5/8*1/2*x129+3/8*1/2*c+3/4*1/2*c+3/4*15/128*1/4*1/2*x135+3/4*113/128*1/4*1/2*x130+1/4*1/4*1/2*x125 && x129 == 3/4*c+3/4*15/128*1/4*x135+3/4*113/128*1/4*x130+1/4*1/4*x125 && x130 == 5/8*3/4*x131+3/8*3/4*c+3/4*1/4*c+1/4*1/4*x130 && x131 == 3/4*15/128*5/8*3/4*x142+3/4*113/128*5/8*3/4*x137+1/4*5/8*3/4*x132+3/8*3/4*c+3/4*1/4*c+3/4*15/128*1/4*1/4*x140+3/4*113/128*1/4*1/4*x135+1/4*1/4*1/4*x130 && x132 == 3/4*15/128*5/8*2/3*x143+3/4*113/128*5/8*2/3*x138+1/4*5/8*2/3*x133+3/8*2/3*c+3/4*1/3*c+3/4*15/128*1/4*1/3*x140+3/4*113/128*1/4*1/3*x135+1/4*1/4*1/3*x130 && x133 == 3/4*15/128*5/8*1/2*x144+3/4*113/128*5/8*1/2*x139+1/4*5/8*1/2*x134+3/8*1/2*c+3/4*1/2*c+3/4*15/128*1/4*1/2*x140+3/4*113/128*1/4*1/2*x135+1/4*1/4*1/2*x130 && x134 == 3/4*c+3/4*15/128*1/4*x140+3/4*113/128*1/4*x135+1/4*1/4*x130 && x135 == 5/8*3/4*x136+3/8*3/4*c+3/4*1/4*c+1/4*1/4*x135 && x136 == 3/4*15/128*5/8*3/4*b+3/4*113/128*5/8*3/4*x142+1/4*5/8*3/4*x137+3/4*15/128*3/8*3/4*b+3/4*113/128*3/8*3/4*c+1/4*3/8*3/4*c+3/4*15/128*3/4*1/4*b+3/4*113/128*3/4*1/4*c+1/4*3/4*1/4*c+3/4*15/128*1/4*1/4*b+3/4*113/128*1/4*1/4*x140+1/4*1/4*1/4*x135 && x137 == 3/4*15/128*5/8*2/3*b+3/4*113/128*5/8*2/3*x143+1/4*5/8*2/3*x138+3/4*15/128*3/8*2/3*b+3/4*113/128*3/8*2/3*c+1/4*3/8*2/3*c+3/4*15/128*3/4*1/3*b+3/4*113/128*3/4*1/3*c+1/4*3/4*1/3*c+3/4*15/128*1/4*1/3*b+3/4*113/128*1/4*1/3*x140+1/4*1/4*1/3*x135 && x138 == 3/4*15/128*5/8*1/2*b+3/4*113/128*5/8*1/2*x144+1/4*5/8*1/2*x139+3/4*15/128*3/8*1/2*b+3/4*113/128*3/8*1/2*c+1/4*3/8*1/2*c+3/4*15/128*3/4*1/2*b+3/4*113/128*3/4*1/2*c+1/4*3/4*1/2*c+3/4*15/128*1/4*1/2*b+3/4*113/128*1/4*1/2*x140+1/4*1/4*1/2*x135 && x139 == 3/4*15/128*3/4*b+3/4*113/128*3/4*c+1/4*3/4*c+3/4*15/128*1/4*b+3/4*113/128*1/4*x140+1/4*1/4*x135 && x140 == 3/4*3/4*b+1/4*3/4*c+3/4*1/4*b+1/4*1/4*x140 && x142 == 3/4*5/8*2/3*b+1/4*5/8*2/3*x143+3/4*3/8*2/3*b+1/4*3/8*2/3*c+3/4*3/4*1/3*b+1/4*3/4*1/3*c+3/4*1/4*1/3*b+1/4*1/4*1/3*x140 && x143 == 3/4*5/8*1/2*b+1/4*5/8*1/2*x144+3/4*3/8*1/2*b+1/4*3/8*1/2*c+3/4*3/4*1/2*b+1/4*3/4*1/2*c+3/4*1/4*1/2*b+1/4*1/4*1/2*x140 && x144 == 3/4*3/4*b+1/4*3/4*c+3/4*1/4*b+1/4*1/4*x140, {x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x142, x143, x144}]

Here's what Mathematica spat out:

SPOILER: Click to show

x0 == (5142175855881592750910450278590166654571522441385625 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (1840561346815806553411760798027890691825539863251417120654787757846530678768289976080210618586\

> 9388311061619282625178579085441866497510333781680016986203046864744380048553570431978458346\

> 4980559941217294655104992420291469408486706961794372764837949227087115938808888409721181483

> b) / 104187228975551907725009192969949798568335253390023767910516238520914446232151988149128\

> 584486453840636983234683103122922646252115682463665146830035872881815581229069032900735497966\

> 988643531117454420134145152156172877845652091537786330759703973030839381877296598089728000000\

> 0000 + (7602516728223144429136722882455799788483616554650953383124700099178703224163642153944\

> 0273668655871539318943478991848025614795312843650680493623454856991951533448517739622070696\

> 6081894747421412777148409553881209216599963064463833611275070255865524985327578809546408870\

> 278818517 c) /

> 1041872289755519077250091929699497985683352533900237679105162385209144462321519881491285844864\

> 538406369832346831031229226462521156824636651468300358728818155812290690329007354979669886435\

> 311174544201341451521561728778456520915377863307597039730308393818772965980897280000000000 &&

> x1 == (8227481369410548401456720445744266647314435906217000 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (7662821486767818657675725392094776286655925733858414446419514004517095061100364856440305490954\

> 8662191571298443615278188034091309457663005940206906630492867578792921517819794045006058678\

> 9866255760367114702248857651906897686310528649496782506951811600408334576898170184767640765\

> 43 b) / 42675088988386061404163765440491437493590119788553735336147451298166557176689454345\

> 883068205651493124908332926199039149115904866583537117244141582693532391662071426675876141259\

> 967278548390345709330486945854323168410765579096693877281079174747353431810816940686577552588\

> 8000000000 + (2861828159277581365905575799202827514894408989337431968546126683638354353914067\

> 2943356699647115912201443276011372383247383395386957134711374957243027987552395117549337151\

> 1240095495725191951057008688514765050372329097885942261650141330636878868927108942359248472\

> 845291411235923457 c) /

> 4267508898838606140416376544049143749359011978855373533614745129816655717668945434588306820565\

> 149312490833292619903914911590486658353711724414158269353239166207142667587614125996727854839\

> 03457093304869458543231684107655790966938772810791747473534318108169406865775525888000000000\

> && x2 == (6421942165113021318195682082620438102429602863273625 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (9390413663790963627604422831449869256181546120440778007411337003974302386231872649125668089037\

> 3230664437398255171931303221469325368180595070661986390270237409544573234497365226415447765\

> 58497914585178373989802421901642587185532507893155634402000774023355699446912337112399727 b)

> / 520936144877759538625045964849748992841676266950118839552581192604572231160759940745642922\

> 432269203184916173415515614613231260578412318325734150179364409077906145345164503677489834943\

> 21765558727210067072576078086438922826045768893165379851986515419690938648299044864000000000\

> + (3661090176664648442137988900026344400272156387764320389470353911747950997253222057475454007\

> 7403721043346972827546104543157144050568924837208595322054144442697802962951282955084525500\

> 0393001373858529401529731927872421743421001837061113830994320593230599413090717805268876002\

> 73 c) / 52093614487775953862504596484974899284167626695011883955258119260457223116075994074\

> 564292243226920318491617341551561461323126057841231832573415017936440907790614534516450367748\

> 983494321765558727210067072576078086438922826045768893165379851986515419690938648299044864000\

> 000000 && x3 == (4906402211664663449231710521519438427239268425897625 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (7577669863904692145722807672660476719707288415893472043897399709397415696004458587634124953887\

> 9170311460300763948228688009285287039898937323271234590471546420277263519049954897873534774\

> 88992036769280685199833374925728088938176460868324376938110339968179325067510872492253561 b)

> / 416748915902207630900036771879799194273341013560095071642064954083657784928607952596514337\

> 945815362547932938732412491690585008462729854660587320143491527262324916276131602941991867954\

> 57412446981768053658060862469151138260836615114532303881589212335752750918639235891200000000\

> + (3037357940123485458312336025913287474092426602753927747135527597851924187804594354750478976\

> 8988838920755334925264452288969758743779383023090981314267298321528963886403179562114753569\

> 5282747329790993284770591039826033751227285293653264944317724938117625394938406786187077464\

> 39 c) / 41674891590220763090003677187979919427334101356009507164206495408365778492860795259\

> 651433794581536254793293873241249169058500846272985466058732014349152726232491627613160294199\

> 186795457412446981768053658060862469151138260836615114532303881589212335752750918639235891200\

> 000000 && x4 == (3014733370581001964280550642928245948543575204009625 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (4708201770700076389074476961448175492232071679326586187434468917418585227577372960333527353876\

> 4494564214176841791333587731620059817747080381353431926969840459986269121891109417877953000\

> 87845038600147498385516597907705323260605418857425744153185706836770334124466995360116329 b)

> / 239855491166738204834553537772546298862354540178471983678886304508580020102795943940439906\

> 731404525207443417975489203850696407748333729301057450442297281877597074115759195937837046304\

> 79086300421161469731258050341957489646524670569514995039763575445037554485547761664000000000\

> + (1796051979115258698933018371020389045374565000969485941313648184070923315936049445638085278\

> 3702361309895571769781779574571677833825487346222057245945473420714925154044633759570389855\

> 1466634339939154373984323878667371011007645966696487063733183494140281288040553586686398836\

> 71 c) / 23985549116673820483455353777254629886235454017847198367888630450858002010279594394\

> 043990673140452520744341797548920385069640774833372930105745044229728187759707411575919593783\

> 704630479086300421161469731258050341957489646524670569514995039763575445037554485547761664000\

> 000000 && x5 == (10878616670728096299781969929094919790803654975001625 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (5864583955078102644470561651610950819983309328526890552639972967045679437060359062691810989561\

> 5374739725735904597692250097773253249877347713167942364906722175582321983521480403494044651\

> 15293558444123385793337603993193475589934309745886318500126348512334354153215037716941143389

> b) / 3333991327217661047200294175038393554186728108480760573136519632669262279428863620772\

> 114703566522900383463509859299933524680067701838837284698561147932218098599330209052823535934\

> 943636592995758541444292644868997532091060866929209162584310527136986860220073491138871296000\

> 0000000 + (2087039548152313053972167505294774357063627758442427693536395773076280325149115063\

> 9538682156859101002962737872317599686031787296948660486394468311283516236342304020455392968\

> 3998108207537834465425968962240859691078077236570036581000104322375537879066457593353102479\

> 15243058856611 c) /

> 3333991327217661047200294175038393554186728108480760573136519632669262279428863620772114703566\

> 522900383463509859299933524680067701838837284698561147932218098599330209052823535934943636592\

> 9957585414442926448689975320910608669292091625843105271369868602200734911388712960000000000\

> && x6 == (17405786673164954079651151886551871665285847960002600 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (1463631743219342193285108240167120274190515196257634671643133051923517172819993984167201789539\

> 7733398376372461960323841009717761649450761990066229112967371218816653809748287064926328878\

> 1855589299542890825365028863977674032683488380168920697492856230040402474520494612798711229

> b) / 104187228975551907725009192969949798568335253390023767910516238520914446232151988149128\

> 584486453840636983234683103122922646252115682463665146830035872881815581229069032900735497966\

> 988643531117454420134145152156172877845652091537786330759703973030839381877296598089728000000\

> 0000 + (5652624236548159935310458533915239007019163056816522997727857985725857397526641578000\

> 3297144833154604110244042064646960610354080309312144750761276963338082231757168039236853837\

> 0946040301894711025987284797687369688801108684446905389662448881364671491573018219064114667\

> 201288771 c) /

> 1041872289755519077250091929699497985683352533900237679105162385209144462321519881491285844864\

> 538406369832346831031229226462521156824636651468300358728818155812290690329007354979669886435\

> 311174544201341451521561728778456520915377863307597039730308393818772965980897280000000000 &&

> x7 == (14648442894099974859364644033925439060939050991654425 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (2493045614096616157145751403281527782457022557563836641763453050016388165545215907922693141609\

> 8727620596247652219729956697946513132843377787554858692991294756936487730906624192822093076\

> 68704102358418745986871255174188376197640563461421166443743950547069886723760945199856943037

> b) / 1666995663608830523600147087519196777093364054240380286568259816334631139714431810386\

> 057351783261450191731754929649966762340033850919418642349280573966109049299665104526411767967\

> 471818296497879270722146322434498766045530433464604581292155263568493430110036745569435648000\

> 0000000 + (9730022275094649058416773777843480446478807116885110309961077018490016680071680150\

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> 8303276664060643408998265233845201410151965413812119268325952027451864260104712729772818710\

> 7280143056963 c) /

> 1666995663608830523600147087519196777093364054240380286568259816334631139714431810386057351783\

> 261450191731754929649966762340033850919418642349280573966109049299665104526411767967471818296\

> 4978792707221463224344987660455304334646045812921552635684934301100367455694356480000000000\

> && x8 == (11813975973069953410774626929208868158686980698969625 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (5512921130349145298810438636533184395917778376467637926928775013165322857770505940745761580295\

> 3140864723746013355087337456389932943813704525100514188133901837127311409579865513264222638\

> 5464867639186900633576405993468466105612083680558796973393364162083586793269189720352021161\

> 4919 b) /

> 3414007119070884912333101235239314999487209583084298826891796103853324574135156347670645456452\

> 119449992666634095923131929272389326682969379531326615482591332965714134070091300797382283871\

> 2276567464389556683458534728612463277355101824863339797882745448653552549262042071040000000000

> + (212821663398193122904505694385161541415286911935715263079138699411204538626982127130946611\

> 6436962472034439317196849610968039198749504664141627768263837429359921126237734415842397151\

> 8212808302671882392662538770679843291063963228740088182178560343410431058118222914193507519\

> 788385081 c) /

> 3414007119070884912333101235239314999487209583084298826891796103853324574135156347670645456452\

> 119449992666634095923131929272389326682969379531326615482591332965714134070091300797382283871\

> 2276567464389556683458534728612463277355101824863339797882745448653552549262042071040000000000

> && x9 == (9945664064726094955957716396951164330595672303244825 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (8730995853633993649436500193310759282079160546504835858795765632153204737392426550103411617371\

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> 4322509474818696051491316112605747921090592664155214072680722355680465094902769200826318486\

> 47 b) / 53343861235482576755204706800614296866987649735692169170184314122708196470861817932\

> 353835257064366406135416157748798936394881083229421396555176978366915489577589283344845176574\

> 959098185487932136663108682317903960513456973870867346601348968434191789763521175858221940736\

> 0000000000 + (3495127621672854116994284550603309951897950372785596318072523631306458297745048\

> 6273847699733570715589462706460801236288282856516356306126100506806661459722866572938980211\

> 1493920272296542512090250410352635681468412121199955264140574169800627531346138324900164926\

> 978135277368151353 c) /

> 5334386123548257675520470680061429686698764973569216917018431412270819647086181793235383525706\

> 436640613541615774879893639488108322942139655517697836691548957758928334484517657495909818548\

> 79321366631086823179039605134569738708673466013489684341917897635211758582219407360000000000\

> && x10 == (20950653463013208255751955146102399286233166151849625 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (2718521756983800667152633851060499716205106734199380563335405769619587221471277612219444511855\

> 8895921070522147665376720727954232487644506175850359776899354293944813539185613054320081649\

> 352939840446688513401678366484306319151241127218034179267163287732141988574171199367694929 b

> ) / 2083744579511038154500183859398995971366705067800475358210324770418288924643039762982571\

> 689729076812739664693662062458452925042313649273302936600717457636311624581380658014709959339\

> 772870622349088402682903043123457556913041830755726615194079460616787637545931961794560000000\

> 00 + (101688277549972702528547214422219410428105480121831143544002057821337499786447466798773\

> 8336610694210815482201195629919127667769766993865817065121844033571016928776359256726996033\

> 0544155535077584451587802605983848421674623842030756497211419733440939602692032162322425663\

> 2305071 c) /

> 2083744579511038154500183859398995971366705067800475358210324770418288924643039762982571689729\

> 076812739664693662062458452925042313649273302936600717457636311624581380658014709959339772870\

> 62234908840268290304312345755691304183075572661519407946061678763754593196179456000000000 &&

> x11 == (28584556719174804168329095966317278869584404299229200 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (2155179600611913415760157683949089849033669153154740781042874611589603185328431782928246240938\

> 2296419610553953650369762830452821670457857136451157469324041801561306047255770214696204170\

> 6038689617768410192898441060906805427080776033491237241027659826080913967729769875010021487\

> 107 b) / 2133754449419303070208188272024571874679505989427686766807372564908327858834472717\

> 294153410282574656245416646309951957455795243329176855862207079134676619583103571333793807062\

> 998363927419517285466524347292716158420538278954834693864053958737367671590540847034328877629\

> 440000000000 + (80751229159547834845604482133279456598575748951485186526109171025328729032693\

> 5107730409501289484028956787758097748562077269012377528708413430778338424976182282580706891\

> 6877900140691788670139404104826012838132767381135125434933687205112083725201822176779848040\

> 56370346429978512893 c) /

> 2133754449419303070208188272024571874679505989427686766807372564908327858834472717294153410282\

> 574656245416646309951957455795243329176855862207079134676619583103571333793807062998363927419\

> 517285466524347292716158420538278954834693864053958737367671590540847034328877629440000000000\

> && x12 == (25704737831694234908090539777361658345776075698243225 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (5885228277716641291847471832857210785929163070413834609694122997330706312602965940698333278082\

> 9935196367652870942632977170424911037361742605170254558729628142184119914452368576713965852\

> 268448016201956696451229735447043188032664906578116162456418490966635075030689934448229241 b

> ) / 5209361448777595386250459648497489928416762669501188395525811926045722311607599407456429\

> 224322692031849161734155156146132312605784123183257341501793644090779061453451645036774898349\

> 432176555872721006707257607808643892282604576889316537985198651541969093864829904486400000000\

> 00 + (218230918497498317828076653555803473302488206641618073563542597749374746309918357424989\

> 6232759559728408599631057454488142313465385771126944518238817079765441599621158332638921128\

> 0486335662935010581333837553751197383749924650095463346701499039927025252608205985761470555\

> 1770759 c) /

> 5209361448777595386250459648497489928416762669501188395525811926045722311607599407456429224322\

> 692031849161734155156146132312605784123183257341501793644090779061453451645036774898349432176\

> 55587272100670725760780864389228260457688931653798519865154196909386482990448640000000000 &&

> x13 == (21942176734554720825990153796302939866925538648233625 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (1326764633012177186512122302605756460317654160453926717005260283336860821645498749767217302119\

> 4241490432016277598483536435507931900560707288879297227851521844382590265719414243950609316\

> 8179816165339517982204366742485163615064360563938152743527071498981425921654010539776808203

> b) / 104187228975551907725009192969949798568335253390023767910516238520914446232151988149128\

> 584486453840636983234683103122922646252115682463665146830035872881815581229069032900735497966\

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> 0000 + (4928784595303655604036636268496839641883341499941697306542340282282722909135468903524\

> 6699489601397532405790351318861209452128374164930137847837681358682682450307512873285255247\

> 0685460232595823570126409164140210549156362581180905587289654431987670570721127455555046740\

> 223191797 c) /

> 1041872289755519077250091929699497985683352533900237679105162385209144462321519881491285844864\

> 538406369832346831031229226462521156824636651468300358728818155812290690329007354979669886435\

> 311174544201341451521561728778456520915377863307597039730308393818772965980897280000000000 &&

> x14 == (17892327485920547766495327005811709345211278346655385 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (4881236903795826651173397665414303904933865921762064707074999297756049538633633408905392561208\

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> 1442406352262126926393931919597345732644942731925981124316448986666866356403779680159828113

> b) / 333399132721766104720029417503839355418672810848076057313651963266926227942886362077211\

> 470356652290038346350985929993352468006770183883728469856114793221809859933020905282353593494\

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> 0000 + (1759537979438334514766717091617651024214629539003625841407468303076184046512044655421\

> 9422263325150053019707298241731923426505080044153123837864845352127400108087444636233933525\

> 9549596515097196821844607450651667332033923533214825511675400379449571326667595222120744745\

> 5840171887 c) /

> 3333991327217661047200294175038393554186728108480760573136519632669262279428863620772114703566\

> 522900383463509859299933524680067701838837284698561147932218098599330209052823535934943636592\

> 995758541444292644868997532091060866929209162584310527136986860220073491138871296000000000 &&

> x15 == (32801386299509587233436571498539142095648390839836185 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (2790847499727015937082031570970400812256900926630140107232739727522139421867491991391478416139\

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> 15570242122195617546047782619104570161641059005625799064016026498952100611623199477237777353

> b) / 3333991327217661047200294175038393554186728108480760573136519632669262279428863620772\

> 114703566522900383463509859299933524680067701838837284698561147932218098599330209052823535934\

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> 0000000 + (1063375918697458411003897099374432228717562550178363003009770995316674351702430803\

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> 2974271851932908187013945288470848761306810441792896704055437588378431522470891560565196537\

> 43882762222647 c) /

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> 522900383463509859299933524680067701838837284698561147932218098599330209052823535934943636592\

> 9957585414442926448689975320910608669292091625843105271369868602200734911388712960000000000\

> && x16 == (42038746075316367125707823265731504353865916567736336 a) /

> 54912304248954538795489937340192423398464989015152281 +

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> 6660634105536185528333487250274496353887839688719750138820350347693454183475452824730648521

> b) / 416748915902207630900036771879799194273341013560095071642064954083657784928607952596514\

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> 269351479 c) /

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> 153625479329387324124916905850084627298546605873201434915272623249162761316029419918679545741\

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> x17 == (40140251616262058753412071073802414875523282228013593 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (9485027587498773742812301024355272311921357831673710026563901187517873464345891994190442814354\

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> 1522819891742016939407553717639267463210124393850017853265823029798792271603434957422717557

> b) / 166699566360883052360014708751919677709336405424038028656825981633463113971443181038605\

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> 82577282443 c) /

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> 261450191731754929649966762340033850919418642349280573966109049299665104526411767967471818296\

> 4978792707221463224344987660455304334646045812921552635684934301100367455694356480000000000\

> && x18 == (37541322141758862494331966231331047220659235197798937 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (4603791712362812198474959010205879115911880332736827970804672940822629011448843679354581484710\

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> 958061423477063679901 c) /

> 6828014238141769824666202470478629998974419166168597653783592207706649148270312695341290912904\

> 238899985333268191846263858544778653365938759062653230965182665931428268140182601594764567742\

> 455313492877911336691706945722492655471020364972667959576549089730710509852408414208000000000\

> && x19 == (32425976873106665645155609285902348839780246924020249 a) /

> 54912304248954538795489937340192423398464989015152281 +

> (9215788756175084261647428755095094037935311828935900109707025559010400680787631105423916895191\

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> 30646605911427406043168966238179842192270742126913586771568354541196134126644036585648580931

> b) / 1066877224709651535104094136012285937339752994713843383403686282454163929417236358647\

> 076705141287328122708323154975978727897621664588427931103539567338309791551785666896903531499\

> 181963709758642733262173646358079210269139477417346932026979368683835795270423517164438814720\

> 00000000 + (344723260894407461571775056891323801351277577613007576614166976014334124276056912\

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> 022998351419069 c) /

> 1066877224709651535104094136012285937339752994713843383403686282454163929417236358647076705141\

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> && x20 == (1008521482969540273440048110181881776100356717439346468723545311606433422580781952462\

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> (7916414652313797571776797595800379517276936828399881578075534989115270615504213683624221679178\

> 33578496999833543357511607392858394811375215140160890136147490526660833 c) /

> 1483981537287077565728635074842270325820989230282735873495363364926292539705564064682878541801\

> 262604922556769164458899644520364512845405087234227484114708070400000000 &&

> x64 == (44058857384919286063650430898854439434018824216580820624836330700885194617067180547911033\

> 766218743853021294995193070611335585833364426376684793050346647160872400763 b) /

> 1159360576005529348225496152220523692047647836158387401168252628848666046644971925533498860782\

> 23641009574747590973351534728153477566047272440174022196461568000000000 +

> (7187720021563364875889918432319792977074595939925791949198893218398141004743001200543885231200\

> 4897156553452595780280923392567644201620895755380971849814407127599237 c) /

> 1159360576005529348225496152220523692047647836158387401168252628848666046644971925533498860782\

> 23641009574747590973351534728153477566047272440174022196461568000000000 &&

> x65 == (76254362338088484791499600474969162390677738167430456967443454363308505444099023684907837\

> 5931362457205706662116024084087965601568542955744129440483610872092558009 b) /

> 9057504500043198033011688689222841344122248719987401571626973662880203489413843168230459849861\

> 22195387302715554479308865063699043484744315938859548409856000000000 +

> (1432068266234349553861728641725925105054474903244355874882628226549352945003940799739676090547\

> 59738181596053438455224777098097474941788571809419064798983907441991 c) /

> 9057504500043198033011688689222841344122248719987401571626973662880203489413843168230459849861\

> 22195387302715554479308865063699043484744315938859548409856000000000 &&

> x67 == (50143819931289928532867952546579607571810572556037098488274255815540891236387833634806381\

> 572180051435773453906739486291218314865582195002949897424793540937196679 b) /

> 5660940312526998770632305430764275840076405449992125982266858539300127180883651980144037406163\

> 2637211706419722154956804066481190217796519746178721775616000000000 +

> (6465583193980059173455101761063150828953481943884161334394329577460380572448686166633992489452\

> 585775932965815415470512848166324635601516796281296982075062803321 c) /

> 5660940312526998770632305430764275840076405449992125982266858539300127180883651980144037406163\

> 2637211706419722154956804066481190217796519746178721775616000000000 &&

> x68 == (50465019772910996870526718991568897228554413512097453174145949601160846279441991900697580\

> 579339655558898935807158143733685552573735575170707672101513192819747766809 b) /

> 5796802880027646741127480761102618460238239180791937005841263144243330233224859627667494303911\

> 1820504787373795486675767364076738783023636220087011098230784000000000 +

> (7503009027365470540748088619457287373827978295821916884266681841272456052806604375977362459772\

> 164945888437988328532033678524165047448465512414909585037964252233191 c) /

> 5796802880027646741127480761102618460238239180791937005841263144243330233224859627667494303911\

> 1820504787373795486675767364076738783023636220087011098230784000000000 &&

> x69 == (76254362338088484791499600474969162390677738167430456967443454363308505444099023684907837\

> 5931362457205706662116024084087965601568542955744129440483610872092558009 b) /

> 9057504500043198033011688689222841344122248719987401571626973662880203489413843168230459849861\

> 22195387302715554479308865063699043484744315938859548409856000000000 +

> (1432068266234349553861728641725925105054474903244355874882628226549352945003940799739676090547\

> 59738181596053438455224777098097474941788571809419064798983907441991 c) /

> 9057504500043198033011688689222841344122248719987401571626973662880203489413843168230459849861\

> 22195387302715554479308865063699043484744315938859548409856000000000 &&

> x70 == (14322541261266398069773632760784104910232781756855490732877362465312715051718312783396468\

> 53369 b) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> + (418064129688956866257273301322134344398682309221661016757566071816867112768485388873633499\

> 33831 c) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> && x71 == (132115324848331684284312803942953736085340031954613090483241330638000953786633723891\

> 8822277671311 b) /

> 2213819755265143113354480302504542460461645265810004518351070383524760718439442952483993435504\

> 6400 + (2081704430416811429070167498561588724376305233855391427867829052886759764652809228592\

> 1112077375089 c) /

> 2213819755265143113354480302504542460461645265810004518351070383524760718439442952483993435504\

> 6400 && x72 == (12079354718813182845585625332931403593958256269922067976136649532007636978628\

> 0829053248844569 b) /

> 2702416693438895402044043338018240308180719318615728171815271464263623923876273135356437299200\

> + (2581623146250763573588187084688926272241136755916507492053904968943547554089992306303188454\

> 631 c) / 2702416693438895402044043338018240308180719318615728171815271464263623923876273135\

> 356437299200 && x73 == (479045551724653021496388659557090069826323398148395856313798276195305\

> 61046816999823990157332017 b) /

> 1383637347040714445846550189065339037788528291131252823969418989702975449024651845302495897190\

> 400 + (13357327918682491436969113231096300308058959513164132383380391620834448879778348454785\

> 05739858383 c) /

> 1383637347040714445846550189065339037788528291131252823969418989702975449024651845302495897190\

> 400 && x74 == (117142513725830293364397138828324824437282316491679805755405740221289830736149\

> 9707893189541907 b) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> + (420672419577640234990607220200085966865186859329348526914902860260050844746588704578098072\

> 45293 c) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> && x75 == (207402735736548896029724639309999500166944249897875974733798913736051998214383236856\

> 1689703481 b) /

> 26608410520013739343202888251256519957471697906370246614796519032749527865858689332740305715200

> + (245343831626482503829056418581565249558022554073914868674585298953890078837148569641786160\

> 11719 c) /

> 26608410520013739343202888251256519957471697906370246614796519032749527865858689332740305715200

> && x76 == (593238953929030265178061391358174901342333618737906298705163357470816037332836720443\

> 5163875767 b) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> + (373062775557320237809240794947100959174681729104725877619927098535098224086920029612678329\

> 11433 c) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> && x77 == (186209897309203306926947870948178147173538598782993873463694014237635118577794504710\

> 30755916489 b) /

> 1729546683800893057308187736331673797235660363914066029961773737128719311280814806628119871488\

> 00 + (154333678649168975038123986538349565006212176513107215649807972289108419270302030191781\

> 231232311 c) /

> 1729546683800893057308187736331673797235660363914066029961773737128719311280814806628119871488\

> 00 && x78 == (2919528757685313625331606390936223427898716106004281498117873675786461854407926\

> 8518770229357390763 b) /

> 3542111608424228981367168484007267936738632425296007229361712613639617149503108723974389496807\

> 42400 + (325015873265569761883400784491364559394876081469557907954992524606097096406231603878\

> 668720323351637 c) /

> 3542111608424228981367168484007267936738632425296007229361712613639617149503108723974389496807\

> 42400 && x79 == (3709423751289312587451165602308104821158613014958602288357152356112383531334\

> 63973485243520139019 b) /

> 5534549388162857783386200756261356151154113164525011295877675958811901796098607381209983588761\

> 600 + (51636070130339265246410841960305456690382518630291510670419607232006634429651434077247\

> 40068622581 c) /

> 5534549388162857783386200756261356151154113164525011295877675958811901796098607381209983588761\

> 600 && x80 == (711663937471580606003715799996550120560465742136796491638147431106234222357220\

> 1367038981829829 b) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> + (361220277203065203726675354083263437252868516764836858326628691171556405584481687986640149\

> 57371 c) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> && x81 == (310071056279412973365160448468304617473278081868635854063292666370511415497947040534\

> 63321757860691 b) /

> 1106909877632571556677240151252271230230822632905002259175535191762380359219721476241996717752\

> 32000 + (796838821353158583312079702783966612757544551036366405112242525391868943721774435707\

> 36350017371309 c) /

> 1106909877632571556677240151252271230230822632905002259175535191762380359219721476241996717752\

> 32000 && x82 == (3197141114981250984779335466206794653834378923563918579994536588391553735027\

> 145051791930605689 b) /

> 13512083467194477010220216690091201540903596593078640859076357321318119619381365676782186496000

> + (103149423522132260254408812238844068870692176695147222790818207329265658843542206249902558\

> 90311 c) /

> 13512083467194477010220216690091201540903596593078640859076357321318119619381365676782186496000

> && x83 == (256391473403237074953586145312986503556443167060258734802867756407376038601515564437\

> 4451851449069 b) /

> 1383637347040714445846550189065339037788528291131252823969418989702975449024651845302495897190\

> 4000 + (1127245873637477370892964043752352534232085124070994089166551233295599410423136280865\

> 0507120454931 c) /

> 1383637347040714445846550189065339037788528291131252823969418989702975449024651845302495897190\

> 4000 && x84 == (74539744415489153267942419186992065432786176116878057075102639115404924435465\

> 94839108665786713 b) /

> 54048333868777908040880866760364806163614386372314563436305429285272478477525462707128745984000

> + (465943594272289927140866248416655996203357687606267577287951653737319860339788678680200801\

> 97287 c) /

> 54048333868777908040880866760364806163614386372314563436305429285272478477525462707128745984000

> && x85 == (559610472423772152521730466371288305237076663069797205354162123875480915759992295884\

> 252536281877 b) /

> 1729546683800893057308187736331673797235660363914066029961773737128719311280814806628119871488\

> 000 + (11699362113771209047864572699603854919985837008442688246076116132532383955208225107438\

> 67335206123 c) /

> 1729546683800893057308187736331673797235660363914066029961773737128719311280814806628119871488\

> 000 && x86 == (230729721153268582108249448149003691027146938167262286397074331096648115756091\

> 03431986430181371 b) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> + (201656949796954682218797485933914758281768152811254221093369103185531712064112667337165666\

> 05829 c) /

> 43238667095022326432704693408291844930891509097851650749044343428217982782020370165702996787200

> && x87 == (850705732872691610516873209118098530826689503482088672934541566062487282800432477909\

> 34117358881 b) /

> 1729546683800893057308187736331673797235660363914066029961773737128719311280814806628119871488\

> 00 + (878840950928201446791314527213575266408970860431977357027232171066232028480382328718778\

> 69789919 c) /

> 1729546683800893057308187736331673797235660363914066029961773737128719311280814806628119871488\

> 00 && x88 == (1538894399690906426794520190136792102715042927037988910179678619711586762268786\

> 04626953582048316467 b) /

> 3542111608424228981367168484007267936738632425296007229361712613639617149503108723974389496807\

> 42400 + (200321720873332255457264829387047583402358949825801831918203399392803038723432267770\

> 485367632425933 c) /

> 3542111608424228981367168484007267936738632425296007229361712613639617149503108723974389496807\

> 42400 && x89 == (9473238615536848781143651845583242374518299599011478218353642220489651898333\

> 888064544119415767903 b) /

> 2767274694081428891693100378130678075577056582262505647938837979405950898049303690604991794380\

> 8000 + (1819950832527744013578735193572353838125226622361357826103473757356985708215914884150\

> 5798528040097 c) /

> 2767274694081428891693100378130678075577056582262505647938837979405950898049303690604991794380\

> 8000 && x90 == (18007130775480511179085593163313288092917069381277456791255884802393427335165\

> 3682029850968978629 b) /

> 2161933354751116321635234670414592246544575454892582537452217171410899139101018508285149839360\

> 00 + (361220277203065203726675354083263437252868516764836858326628691171556405584481687986640\

> 14957371 c) /

> 2161933354751116321635234670414592246544575454892582537452217171410899139101018508285149839360\

> 00 && x92 == (1187868972352975036999826907632701978699623771603119204091201699571726775353874\

> 1641633718066299 b) /

> 13512083467194477010220216690091201540903596593078640859076357321318119619381365676782186496000

> + (163339374366472664022194761376418175390735887704744881816434032560085186584262403514846842\

> 9701 c) /

> 13512083467194477010220216690091201540903596593078640859076357321318119619381365676782186496000

> && x93 == (119407261316290552921077635824453284646056401741551107711401217552102119571761897930\

> 58149456113829 b) /

> 1383637347040714445846550189065339037788528291131252823969418989702975449024651845302495897190\

> 4000 + (1895647338778089166357738308208061913279642737157417468554068141819542533070328659966\

> 809515790171 c) /

> 1383637347040714445846550189065339037788528291131252823969418989702975449024651845302495897190\

> 4000 && x94 == (18007130775480511179085593163313288092917069381277456791255884802393427335165\

> 3682029850968978629 b) /

> 2161933354751116321635234670414592246544575454892582537452217171410899139101018508285149839360\

> 00 + (361220277203065203726675354083263437252868516764836858326628691171556405584481687986640\

> 14957371 c) /

> 2161933354751116321635234670414592246544575454892582537452217171410899139101018508285149839360\

> 00 && x95 == (6628101178761046048967035316265737724923024082568344576183252000516948921420943\

> 0064284501148469 b) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 + (24922199997521721686644535171504695417384330194022248825839866177592081901952799288530\

> 52586851531 c) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 && x96 == (658436637486968839107223832032601583783175631838327008687769604508159711569493\

> 11465007838838249011 b) /

> 1309952517908368706126911421600320982521683589236689064113059398535361371857658551765676589056\

> 000000 + (12441088541596718222161890383970608241433660260528563632442824380845454007007092403\

> 00668750217750989 c) /

> 1309952517908368706126911421600320982521683589236689064113059398535361371857658551765676589056\

> 000000 && x97 == (581811986445321951761592537731998385529093603968895793930764376298992042492\

> 7348203989078982869 b) /

> 1599063132212364143221327418945704324367289537642442705216136961102736049630930849323335680000\

> 00 + (154088193356783194804516816517250448581438017724555312582306052347283684538165736728344\

> 489017131 c) /

> 1599063132212364143221327418945704324367289537642442705216136961102736049630930849323335680000\

> 00 && x98 == (2177677778240772610610002614237406623223299998109722384190744545616551788980620\

> 191427409067915917 b) /

> 8187203236927304413293196385002006140760522432729306650706621240846008574110365948535478681600\

> 0000 + (7969435459103227152232196123578265478438192432918334412287546786284353395212303929392\

> 7377748084083 c) /

> 8187203236927304413293196385002006140760522432729306650706621240846008574110365948535478681600\

> 0000 && x99 == (46434698874556068642673906889603993814851122076652549254115517054965604307620\

> 001276666960256807 b) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 + (25120663126652265605114499634235229251728121381512557790917036207094120751018693576406\

> 70127743193 c) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 && x100 == (13701321008065302684455434040230969547449667089297493850733559318374363537884\

> 21313352187260621553 b) /

> 2046800809231826103323299096250501535190130608182326662676655310211502143527591487133869670400\

> 0000 + (1909787599151173076478744755848191839715633937289351724169319717027758508148749355798\

> 6509443378447 c) /

> 2046800809231826103323299096250501535190130608182326662676655310211502143527591487133869670400\

> 0000 && x101 == (3312657751311051469233300547253979661065618296777578305356419843801763526960\

> 78042783134600123067 b) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 + (22272352364086774822307938155877289528811014305501504978101771533842013267134113161342\

> 02487876933 c) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 && x102 == (10209350379139873520282082080946902105475436839268723393987444095347956565809\

> 32647475040891547589 b) /

> 1023400404615913051661649548125250767595065304091163331338327655105751071763795743566934835200\

> 0000 + (9213069008245143164588287273157817465403109356984760973984532141522715061057024788194\

> 307460452411 c) /

> 1023400404615913051661649548125250767595065304091163331338327655105751071763795743566934835200\

> 0000 && x103 == (1555781611988674742734196061415679803348418901479109932663261978253030842753\

> 010761901463895579162463 b) /

> 2095924028653389929803058274560513572034693742778702502580895037656578194972253682825082542489\

> 6000000 + (1940345867454522455529638668418945591699851852630791509314568839831275110696952606\

> 6349361529316837537 c) /

> 2095924028653389929803058274560513572034693742778702502580895037656578194972253682825082542489\

> 6000000 && x104 == (1940046856109440164463891949986438646262106879293904197511616448776287022\

> 5981859889809166517913919 b) /

> 3274881294770921765317278554000802456304208973091722660282648496338403429644146379414191472640\

> 00000 + (308087660915997774887088935900215859167799828516233224053148685146077472738432778051\

> 609980746086081 c) /

> 3274881294770921765317278554000802456304208973091722660282648496338403429644146379414191472640\

> 00000 && x105 == (401280813573412298102780076834120285062695060471525758805931533405371475227\

> 169655585276013397329 b) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 + (21572201979663703310513437934790066339249681997563825695398876043590062041823197033320\

> 61074602671 c) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 && x106 == (17891550181792672030126444021423542300828342534572139340199220691977604827369\

> 10245815762342903545191 b) /

> 6549762589541843530634557108001604912608417946183445320565296992676806859288292758828382945280\

> 000000 + (47606075713625763276219127058592506825255836927262313865453749234790463765513825130\

> 12620602376454809 c) /

> 6549762589541843530634557108001604912608417946183445320565296992676806859288292758828382945280\

> 000000 && x107 == (18320792232494833631384581743817974470086955299789669198987843732526503758\

> 5505641567992884651189 b) /

> 7995315661061820716106637094728521621836447688212213526080684805513680248154654246616678400000\

> 00 + (616323643781233735296817892034672417482775215823324660618190043226102987229959783093674\

> 955348811 c) /

> 7995315661061820716106637094728521621836447688212213526080684805513680248154654246616678400000\

> 00 && x108 == (145057656480572458770625214087832986807770704259557845232914871789390410415220\

> 872793647724903876569 b) /

> 8187203236927304413293196385002006140760522432729306650706621240846008574110365948535478681600\

> 00000 + (673662667212157982558694424412367627268281539013372819837747252295210446995815722059\

> 900143256123431 c) /

> 8187203236927304413293196385002006140760522432729306650706621240846008574110365948535478681600\

> 00000 && x109 == (412371145386532908596041495582105879644801675007017930181831265677558504928\

> 028735910463253192213 b) /

> 3198126264424728286442654837891408648734579075284885410432273922205472099261861698646671360000\

> 000 + (27857551190381953778466133423093027690897774002778674802504426565279135943338329627362\

> 08106807787 c) /

> 3198126264424728286442654837891408648734579075284885410432273922205472099261861698646671360000\

> 000 && x110 == (32418231864592639587737654900374318979796557541626151840030137949677172438931\

> 095819575425282657377 b) /

> 1023400404615913051661649548125250767595065304091163331338327655105751071763795743566934835200\

> 00000 + (699218085969986655784272999121507577797099728674901812938026275608979347374484785371\

> 18058237342623 c) /

> 1023400404615913051661649548125250767595065304091163331338327655105751071763795743566934835200\

> 00000 && x111 == (135364552311064237781060754198232232158864244382816542442645391026388099263\

> 9486899641281141027951 b) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 + (12048554884291402513435163283308045973990208163997429039193652275004966867700024592760\

> 55946972049 c) /

> 2558501011539782629154123870313126918987663260227908328345819137764377679409489358917337088000\

> 000 && x112 == (49825703009729854315701527735830882662644196539559252708436056918757847681575\

> 93620882243787537341 b) /

> 1023400404615913051661649548125250767595065304091163331338327655105751071763795743566934835200\

> 0000 + (5251433745186145085046342707669419409686233386955708042539670859181725949480363814787\

> 104564462659 c) /

> 1023400404615913051661649548125250767595065304091163331338327655105751071763795743566934835200\

> 0000 && x113 == (8988301084531801819079736037949411569493148134135369611293875903752276303025\

> 427882294263271749017287 b) /

> 2095924028653389929803058274560513572034693742778702502580895037656578194972253682825082542489\

> 6000000 + (1197093920200209747895084670765572415085378929365165541451507447281350564669710894\

> 5956562153146982713 c) /

> 2095924028653389929803058274560513572034693742778702502580895037656578194972253682825082542489\

> 6000000 && x114 == (5497530518051867133819947177216384455144852033675546991481017651764369006\

> 44505928370611332141675203 b) /

> 1637440647385460882658639277000401228152104486545861330141324248169201714822073189707095736320\

> 000000 + (10876875955802741692766445592787627826376192831783066309932224829927648141775672613\

> 36484404178324797 c) /

> 1637440647385460882658639277000401228152104486545861330141324248169201714822073189707095736320\

> 000000 && x115 == (10635284859732542814719275558086627961013348101383159072189208084462882192\

> 865127091254624365397329 b) /

> 1279250505769891314577061935156563459493831630113954164172909568882188839704744679458668544000\

> 0000 + (2157220197966370331051343793479006633924968199756382569539887604359006204182319703332\

> 061074602671 c) /

> 1279250505769891314577061935156563459493831630113954164172909568882188839704744679458668544000\

> 0000 && x117 == (7019523724188426469567746567366098919125364148465660581154335434186502380010\

> 14300286823789801199 b) /

> 7995315661061820716106637094728521621836447688212213526080684805513680248154654246616678400000\

> 00 + (975791936873394246538890527362422702711083539746552944926349371327177868144511243748440\

> 50198801 c) /

> 7995315661061820716106637094728521621836447688212213526080684805513680248154654246616678400000\

> 00 && x118 == (705474114939516394546260558033765735391751091078610100234680970844982664724284\

> 770277427111118007729 b) /

> 8187203236927304413293196385002006140760522432729306650706621240846008574110365948535478681600\

> 00000 + (113246208753214046783059080466434878684301152194320564835981153239618192686751824576\

> 120757041992271 c) /

> 8187203236927304413293196385002006140760522432729306650706621240846008574110365948535478681600\

> 00000 && x119 == (106352848597325428147192755580866279610133481013831590721892080844628821928\

> 65127091254624365397329 b) /

> 1279250505769891314577061935156563459493831630113954164172909568882188839704744679458668544000\

> 0000 + (2157220197966370331051343793479006633924968199756382569539887604359006204182319703332\

> 061074602671 c) /

> 1279250505769891314577061935156563459493831630113954164172909568882188839704744679458668544000\

339541108998569457275113377670359 b
> 0000 && x120 == ----------------------------------- +
25013777616939010195430294033530880

24674236507940440738155180655860521 c
> ------------------------------------- &&
25013777616939010195430294033530880

339541108998569457275113377670359 b 12167347699470935640440033639095081 c
> x121 == ----------------------------------- + ------------------------------------- &&
12506888808469505097715147016765440 12506888808469505097715147016765440

1751390855433838310185650211976149029 b 100705042263548347450296834149366335451 c
> x122 == --------------------------------------- + ----------------------------------------- &&
102456433118982185760482484361342484480 102456433118982185760482484361342484480

75991262226516031657787180650596591 b 6327535807709870578372368091933308689 c
> x123 == ------------------------------------- + --------------------------------------- &&
6403527069936386610030155272583905280 6403527069936386610030155272583905280

937305937045764022543356130943553 b 99117804530710276759177820003179967 c
> x124 == ------------------------------------ + ------------------------------------- &&
100055110467756040781721176134123520 100055110467756040781721176134123520

1815767425115854611531957 b 45211199456135005311350603 c
> x125 == --------------------------- + ---------------------------- &&
47026966881250859922882560 47026966881250859922882560

1815767425115854611531957 b 21697716015509575349909323 c
> x126 == --------------------------- + ---------------------------- &&
23513483440625429961441280 23513483440625429961441280

10147472941671735133607070867 b 182474983403931787110519894893 c
> x127 == ------------------------------- + -------------------------------- &&
192622456345603522244126965760 192622456345603522244126965760

97010509871643654974137317 b 2912715370528411380090346523 c
> x128 == ---------------------------- + ------------------------------ &&
3009725880400055035064483840 3009725880400055035064483840

2186222958706959436219497 b 91867710803794760409545623 c
> x129 == --------------------------- + ---------------------------- &&
94053933762501719845765120 94053933762501719845765120

8563780035865611 b 79848919873669109 c
> x130 == ------------------ + ------------------- &&
88412699909534720 88412699909534720

8563780035865611 b 35642569918901749 c
> x131 == ------------------ + ------------------- &&
44206349954767360 44206349954767360

56722023335254871541 b 305416395494199341579 c
> x132 == ---------------------- + ----------------------- &&
362138418829454213120 362138418829454213120

2375161352766892089 b 20258489824073996231 c
> x133 == --------------------- + ---------------------- &&
22633651176840888320 22633651176840888320

10569994226931681 b 166255405592137759 c 36295653 b 129923987 c
> x134 == ------------------- + -------------------- && x135 == ---------- + ----------- &&
176825399819069440 176825399819069440 166219640 166219640

36295653 b 46814167 c 274743359043 b 406092286397 c
> x136 == ---------- + ---------- && x137 == -------------- + -------------- &&
83109820 83109820 680835645440 680835645440

7334531061 b 13941582859 c 155554971 b 509323589 c 4 b c
> x138 == ------------ + ------------- && x139 == ----------- + ----------- && x140 == --- + - &&
21276113920 21276113920 664878560 664878560 5 5

1093 b 187 c 67 b 13 c 4 b c
> x142 == ------ + ----- && x143 == ---- + ---- && x144 == --- + -
1280 1280 80 80 5 5

But most of you aren't maths majors like me, and don't give a crap about any of that. I just put it in so you could see why this took a few weeks. (If you do find any typos in that huge morass of maths, though, let me know.)

So here's the relevant shit.

Paralysed Chansey vs. healthy Lapras
9.4% Lapras wins without being paralysed.
17.7% Lapras wins but is paralysed.
73.0% Chansey wins.

Chansey switching into Lapras Body Slam, becomes paralysed or was already paralysed
19.8% Lapras wins without being paralysed.
17.6% Lapras wins but is paralysed.
62.6% Chansey wins.

Paralysed Chansey vs. paralysed Lapras
13.3% Lapras wins.
86.7% Chansey wins.

Chansey switching into paralysed Lapras Body Slam, becomes paralysed or was already paralysed
19.8% Lapras wins.
80.2% Chansey wins.

Honestly, Lapras does better than I thought (my initial estimate was "between 2 and 3 freeze chances" ie 17-25%). Oh well, now we know.

m9m out.

[marcoasd]

Congrats, the thread is great.

The most important/surprising line is obviously

"Chansey switching into Lapras Body Slam, becomes paralysed or was already paralysed
19.8% Lapras wins without being paralysed.
17.6% Lapras wins but is paralysed.
62.6% Chansey wins."

Once you have taken some rest (and maybe you wanto to do some more maths), I'd suggest to try those events with a beforehand damaged Chansey.

X% Chansey switching into Lapras Body Slam, becomes paralysed or was already paralysed- is the next level, as at that point you know what moves you need to use to cause that damage, before forcing the (still unsafe) switch out.

[Isa]

Thanks a lot for doing this massive work, Magic!

[magic9mushroom]

Apr 30, 2014 22:42:54 GMT -8 marcoasd said:

Congrats, the thread is great.

The most important/surprising line is obviously

"Chansey switching into Lapras Body Slam, becomes paralysed or was already paralysed
19.8% Lapras wins without being paralysed.
17.6% Lapras wins but is paralysed.
62.6% Chansey wins."

Once you have taken some rest (and maybe you wanto to do some more maths), I'd suggest to try those events with a beforehand damaged Chansey.

X% Chansey switching into Lapras Body Slam, becomes paralysed or was already paralysed- is the next level, as at that point you know what moves you need to use to cause that damage, before forcing the (still unsafe) switch out.

Nah, no need for rest. They're all in the data. I solved the full Markov chain; that means every single state has had its chances evaluated. They're listed as fractions above, but since you asked nicely:

Chansey chipped into 4HKO range (76-86%) switching into Body Slam and getting or already being paralysed:
38.2% Lapras wins without being paralysed.
13.0% Lapras wins but is paralysed.
48.8% Chansey wins.

Chansey chipped into 3HKO range (51-65%) switching into Body Slam and getting or already being paralysed:
59.7% Lapras wins without being paralysed.
8.4% Lapras wins but is paralysed.
31.9% Chansey wins.

Those are assuming it doesn't crit on the switch, obviously.

I think you know the chances when Chansey that's already in 2HKO range switches into Lapras.

[marcoasd]

May 1, 2014 3:44:27 GMT -8 magic9mushroom said:

Nah, no need for rest. They're all in the data. I solved the full Markov chain; that means every single state has had its chances evaluated. They're listed as fractions above, but since you asked nicely:

Chansey chipped into 4HKO range (76-86%) switching into Body Slam and getting or already being paralysed:
38.2% Lapras wins without being paralysed.
13.0% Lapras wins but is paralysed.
48.8% Chansey wins.

Chansey chipped into 3HKO range (51-65%) switching into Body Slam and getting or already being paralysed:
59.7% Lapras wins without being paralysed.
8.4% Lapras wins but is paralysed.
31.9% Chansey wins.

Those are assuming it doesn't crit on the switch, obviously.

I think you know the chances when Chansey that's already in 2HKO range switches into Lapras.

Thanks, didn't look at the fractions cause the spoiler scared me XD
Simply said: that 14% damage is very relevant, and makes the MU tied; under 65% Chansey is in a bad position (60% to not even paralyze).
If Chansey switches into Lapras when in 2HKO range, I don't know the exact % as I'm bad at maths, but I know I'd be an happy player.

[magic9mushroom]

May 1, 2014 6:52:52 GMT -8 marcoasd said:

If Chansey switches into Lapras when in 2HKO range, I don't know the exact % as I'm bad at maths, but I know I'd be an happy player.

No maths required. Switching into a faster 2HKO is a guaranteed loss.

[marcoasd]

May 1, 2014 14:31:18 GMT -8 magic9mushroom said:

May 1, 2014 6:52:52 GMT -8 marcoasd said:

If Chansey switches into Lapras when in 2HKO range, I don't know the exact % as I'm bad at maths, but I know I'd be an happy player.

No maths required. Switching into a faster 2HKO is a guaranteed loss.

Hehe, sure, it was just a joke!... but actually, looking closely, there's still the chance of a 255 miss.

[magic9mushroom]

Ran the Hyper Beam non-Confuse Ray Lapras vs. Chansey calcs for comparison.

Markov chain

SPOILER: Click to show

(0) Chansey at full
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 3/4 Thunder Wave (7|6), 1/4 nothing (2|1)

(1) Chansey hit once
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 3/4 Softboiled (1|0), 1/4 nothing (3|2)

(2) Chansey hit twice
Lapras: 15/128 critical Body Slam, 113/128 Body Slam
Chansey: 3/4 Softboiled (2|1), 1/4 nothing (Lapras win|3)

(3) Chansey hit thrice
Lapras: 0.9 Hyper Beam, 0.1 nothing
Chansey: 3/4 Softboiled (Lapras win|1), 1/4 nothing (Lapras win|3)

(4) Chansey hit four times
lol

(5) Chansey at full; Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4*25/256 critical Thunderbolt (17|16|15), 3/4*231/256 Thunderbolt (12|11|10), 1/4 nothing (7|6|5)

(6) Chansey hit once; Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (6|5|5), 1/4 nothing (8|7|6)

(7) Chansey hit twice; Lapras paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (7|6|5), 1/4 nothing (9}8}7)

(8) Chansey hit thrice; Lapras paralysed
Lapras: 0.675 Hyper Beam, 0.325 nothing
Chansey: 3/4 Softboiled (Lapras win|6), 1/4 nothing (Lapras win|8)

(9) Chansey hit four times; Lapras paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (Lapras win|7), 1/4 nothing (Lapras win|9)

(10) Chansey at full; Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4*25/256*1011/1521 fatal critical Thunderbolt (Chansey win), 3/4*25/256*510/1521 non-fatal critical Thunderbolt (27|26|25), 3/4*231/256 Thunderbolt (22|21|20), 1/4 nothing (12|11|10)

(11) Chansey hit once; Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (11|10|10), 1/4 nothing (13|12|11)

(12) Chansey hit twice; Lapras hit once, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (12|11|10), 1/4 nothing (14|13|12)

(13) Chansey hit thrice; Lapras hit once, paralysed
Lapras: 0.675 Hyper Beam, 0.325 nothing
Chansey: 3/4 Softboiled (Lapras win|11), 1/4 nothing (Lapras win|13)

(14) Chansey hit four times; Lapras hit once, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (Lapras win|12), 1/4 nothing (Lapras win|14)

(15) Chansey at full; Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4*25/256 critical Thunderbolt (Chansey win), 3/4*231/256*1011/1521 fatal Thunderbolt (Chansey win), 3/4*231/256*510/1521 non-fatal Thunderbolt (27|26|25), 1/4 nothing (17|16|15)

(16) Chansey hit once; Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (16|15|15), 1/4 nothing (18|17|16)

(17) Chansey hit twice; Lapras critted, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (17|16|15), 1/4 nothing (19|18|17)

(18) Chansey hit thrice; Lapras critted, paralysed
Lapras: 0.675 Hyper Beam, 0.325 nothing
Chansey: 3/4 Softboiled (Lapras win|16), 1/4 nothing (Lapras win|18)

(19) Chansey hit four times; Lapras critted, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (Lapras win|17), 1/4 nothing (Lapras win|19)

(20) Chansey at full; Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4*25/256 critical Thunderbolt (Chansey win), 3/4*231/256*0.921 fatal Thunderbolt (Chansey win), 3/4*231/256*0.079 non-fatal Thunderbolt (27|26|25), 1/4 nothing (22|21|20)

(21) Chansey hit once; Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (21|20|20), 1/4 nothing (23|22|21)

(22) Chansey hit twice; Lapras hit twice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (22|21|20), 1/4 nothing (24|23|22)

(23) Chansey hit thrice; Lapras hit twice, paralysed
Lapras: 0.675 Hyper Beam, 0.325 nothing
Chansey: 3/4 Softboiled (Lapras win|21), 1/4 nothing (Lapras win|23)

(24) Chansey hit four times; Lapras hit twice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Softboiled (Lapras win|22), 1/4 nothing (Lapras win|24)

(25) Chansey at full; Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt (Chansey win), 1/4 nothing (27|26|25)

(26) Chansey hit once; Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt (Chansey win), 1/4 nothing (28|27|26)

(27) Chansey hit twice; Lapras hit thrice, paralysed
Lapras: 3/4*15/128 critical Body Slam, 3/4*113/128 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt (Chansey win), 1/4 nothing (29|28|27)

(28) Chansey hit thrice; Lapras hit thrice, paralysed
Lapras: 0.675 Hyper Beam, 0.325 nothing
Chansey: 3/4 Thunderbolt (Lapras win|Chansey win), 1/4 nothing (Lapras win|28)

(29) Chansey hit four times; Lapras hit thrice, paralysed
Lapras: 3/4 Body Slam, 1/4 nothing
Chansey: 3/4 Thunderbolt (Lapras win|Chansey win), 1/4 nothing (Lapras win|29)

Equation form input

SPOILER: Click to show

Reduce[x0 == 15/128*3/4*x7+113/128*3/4*x6+15/128*1/4*x2+113/128*1/4*x1 && x1 == 15/128*3/4*x1+113/128*3/4*x0+15/128*1/4*x3+113/128*1/4*x2 && x2 == 15/128*3/4*x2+113/128*3/4*x1+15/128*1/4*a+113/128*1/4*x3 && x3 == 0.9*a+0.1*3/4*x1+0.1*1/4*x3 && x5 == 3/4*15/128*3/4*25/256*x17+3/4*113/128*3/4*25/256*x16+1/4*3/4*25/256*x15+3/4*15/128*3/4*231/256*x12+3/4*113/128*3/4*231/256*x11+1/4*3/4*231/256*x10+3/4*15/128*1/4*x7+3/4*113/128*1/4*x6+1/4*1/4*x5 && x6 == 3/4*15/128*3/4*x6+3/4*113/128*3/4*x5+1/4*3/4*x5+3/4*15/128*1/4*x8+3/4*113/128*1/4*x7+1/4*1/4*x6 && x7 == 3/4*15/128*3/4*x7+3/4*113/128*3/4*x6+1/4*3/4*x5+3/4*15/128*1/4*x9+3/4*113/128*1/4*x8+1/4*1/4*x7 && x8 == 0.675*b+0.325*3/4*x6+0.325*1/4*x8 && x9 == 3/4*b+1/4*3/4*x7+1/4*1/4*x9 && x10 == 3/4*25/256*1011/1521*c+3/4*15/128*3/4*25/256*510/1521*x27+3/4*113/128*3/4*25/256*510/1521*x26+1/4*3/4*25/256*510/1521*x25+3/4*15/128*3/4*231/256*x22+3/4*113/128*3/4*231/256*x21+1/4*3/4*231/256*x20+3/4*15/128*1/4*x12+3/4*113/128*1/4*x11+1/4*1/4*x10 && x11 == 3/4*15/128*3/4*x11+3/4*113/128*3/4*x10+1/4*3/4*x10+3/4*15/128*1/4*x13+3/4*113/128*1/4*x12+1/4*1/4*x11 && x12 == 3/4*15/128*3/4*x12+3/4*113/128*3/4*x11+1/4*3/4*x10+3/4*15/128*1/4*x14+3/4*113/128*1/4*x13+1/4*1/4*x12 && x13 == 0.675*b+0.325*3/4*x11+0.325*1/4*x13 && x14 == 3/4*b+1/4*3/4*x12+1/4*1/4*x14 && x15 == 3/4*25/256*c+3/4*231/256*1011/1521*c+3/4*15/128*3/4*231/256*510/1521*x27+3/4*113/128*3/4*231/256*510/1521*x26+1/4*3/4*231/256*510/1521*x25+3/4*15/128*1/4*x17+3/4*113/128*1/4*x16+1/4*1/4*x15 && x16 == 3/4*15/128*3/4*x16+3/4*113/128*3/4*x15+1/4*3/4*x15+3/4*15/128*1/4*x18+3/4*113/128*1/4*x17+1/4*1/4*x16 && x17 == 3/4*15/128*3/4*x17+3/4*113/128*3/4*x16+1/4*3/4*x15+3/4*15/128*1/4*x19+3/4*113/128*1/4*x18+1/4*1/4*x17 && x18 == 0.675*b+0.325*3/4*x16+0.325*1/4*x18 && x19 == 3/4*b+1/4*3/4*x17+1/4*1/4*x19 && x20 == 3/4*25/256*c+3/4*231/256*0.921*c+3/4*15/128*3/4*231/256*0.079*x27+3/4*113/128*3/4*231/256*0.079*x26+1/4*3/4*231/256*0.079*x25+3/4*15/128*1/4*x22+3/4*113/128*1/4*x21+1/4*1/4*x20 && x21 == 3/4*15/128*3/4*x21+3/4*113/128*3/4*x20+1/4*3/4*x20+3/4*15/128*1/4*x23+3/4*113/128*1/4*x22+1/4*1/4*x21 && x22 == 3/4*15/128*3/4*x22+3/4*113/128*3/4*x21+1/4*3/4*x20+3/4*15/128*1/4*x24+3/4*113/128*1/4*x23+1/4*1/4*x22 && x23 == 0.675*b+0.325*3/4*x21+0.325*1/4*x24 && x24 == 3/4*b+1/4*3/4*x22+1/4*1/4*x24 && x25 == 3/4*c+3/4*15/128*1/4*x27+3/4*113/128*1/4*x26+1/4*1/4*x25 && x26 == 3/4*c+3/4*15/128*1/4*x28+3/4*113/128*1/4*x27+1/4*1/4*x26 && x27 == 3/4*c+3/4*15/128*1/4*x29+3/4*113/128*1/4*x28+1/4*1/4*x27 && x28 == 0.675*b+0.325*3/4*c+0.325*1/4*x28 && x29 == 3/4*b+1/4*3/4*c+1/4*1/4*x29, {x0, x1, x2, x3, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29}]

Output

SPOILER: Click to show

x0 == 0. + 0.0441267 a + 0.198101 b + 0.757772 c &&

> x1 == 0. + 0.151092 a + 0.175933 b + 0.672975 c &&

> x2 == 0. + 0.367968 a + 0.130986 b + 0.501046 c &&

> x3 == 0. + 0.934699 a + 0.0135333 b + 0.0517673 c && x5 == 0. + 0.145421 b + 0.854579 c &&

> x6 == 0. + 0.193285 b + 0.806715 c && x7 == 0. + 0.31242 b + 0.68758 c &&

> x8 == 0. + 0.785974 b + 0.214026 c && x9 == 0. + 0.862484 b + 0.137516 c &&

> x10 == 0. + 0.0853549 b + 0.914645 c && x11 == 0. + 0.136583 b + 0.863417 c &&

> x12 == 0. + 0.264092 b + 0.735908 c && x13 == 0. + 0.77093 b + 0.22907 c &&

> x14 == 0. + 0.852818 b + 0.147182 c && x15 == 0. + 0.0310178 b + 0.968982 c &&

> x16 == 0. + 0.0852896 b + 0.91471 c && x17 == 0. + 0.220373 b + 0.779627 c &&

> x18 == 0. + 0.757322 b + 0.242678 c && x19 == 0. + 0.844075 b + 0.155925 c &&

> x20 == 0. + 0.0210445 b + 0.978956 c && x21 == 0. + 0.0763762 b + 0.923624 c &&

> x22 == 0. + 0.214023 b + 0.785977 c && x23 == 0. + 0.762095 b + 0.237905 c &&

> x24 == 0. + 0.842805 b + 0.157195 c && x25 == 0. + 0.0111485 b + 0.988852 c &&

> x26 == 0. + 0.0434335 b + 0.956566 c && x27 == 0. + 0.148469 b + 0.851531 c &&

> x28 == 0. + 0.734694 b + 0.265306 c && x29 == 0. + 0.8 b + 0.2 c

Relevant:

Paralysed Chansey vs. Hyper Beam Lapras
4.4% Lapras wins without being paralysed
19.8% Lapras wins but is paralysed
75.8% Chansey wins

Chansey switching into Hyper Beam Lapras Body Slam, becomes paralysed or was already paralysed
15.1% Lapras wins without being paralysed
17.6% Lapras wins but is paralysed
67.3% Chansey wins

Paralysed Chansey vs. paralysed Hyper Beam Lapras
14.5% Lapras wins
85.5% Chansey wins

Chansey switching into paralysed Hyper Beam Lapras Body Slam, becomes paralysed or was already paralysed
19.3% Lapras wins
80.7% Chansey wins

Chansey at 70-81% switching into Hyper Beam Lapras Body Slam, becomes paralysed or was already paralysed
36.8% Lapras wins without being paralysed
13.1% Lapras wins but is paralysed
50.1% Chansey wins

Chansey at 45-60% switching into Hyper Beam Lapras Body Slam, becomes paralysed or was already paralysed
93.5% Lapras wins without being paralysed
1.4% Lapras wins but is paralysed
5.2% Chansey wins


Notes:

- When Lapras is unparalysed and Chansey's at high health, Confuse Ray is slightly better.
- When Chansey is brought into KO range from Hyper Beam, Hyper Beam is obviously better.
- When Lapras is paralysed, Hyper Beam is slightly better than Confuse Ray.

[Mantishuffle]

This is the knowledge of the masterful. Truly impressive stuff. It would be fantastic to see calculations of other interesting 1v1 situations as well.

It seems more time consuming than hard for those who know how to do the math. I hope I speak for everyone who visits this page when I say that I appreciate these kinds of informative posts.

I should have tried harder in school! Math can be fun when applied like this.

[magic9mushroom]

May 2, 2014 19:06:26 GMT -8 Mantishuffle said:

It seems more time consuming than hard for those who know how to do the math.

Pretty much, yeah. Applied maths is, in my experience, 10% knowing what method to use and 90% knowing how to automate that method. (This is why I prefer pure. )

[Isa]

Maybe a dumb question, but what's up with the gap between 60% and 70%?

(Nice job!)

[magic9mushroom]

May 3, 2014 2:01:56 GMT -8 Isa said:

Maybe a dumb question, but what's up with the gap between 60% and 70%?

(Nice job!)

60% guarantees a Body Slam + Hyper Beam 2HKO according to your calcs, while 70% guarantees a 3HKO. The stuff in-between is more complex (because you have to consider what Body Slam rolls and whether to use Body Slam or Hyper Beam the next turn), and as such doesn't tie precisely to one of the artificial "states" I used.

[magic9mushroom]

From the chatbox:

Isa: Hey Magic, do you take requests on Markov chains? If so, could you math out Reflect Alakazam vs. Tauros?
magic9mushroom: I don't take requests, I take suggestions. ReflectZam vs. Tauros is kinda annoying because the damage calcs are right in the "ugly region" where simplifying assumptions have large errors associated with them. See, the states "Lapras hit Chansey twice" and "Lapras hit Chansey twice, then Chansey Softboiled, then Lapras hit Chansey twice more" are very similar collections of substates that both amount to "3HKO, but a 2HKO's very unlikely". But! "Tauros hit ReflectZam twice" and "Tauros hit ReflectZam twice, then Zam Recovered, then Tauros hit ReflectZam twice more" are NOT as similar, because on average Tauros does slightly over 25% and as such the probability that Hyper Beam will KO through Reflect is drastically different for those two collections of substates (and its optimal move even changes depending on the exact damage rolls!). As such you can't make the simplifying assumptions that "Recover heals 2 non-crit Body Slams" or that "Alakazam has been hit twice" is even a meaningful state, and you have to run through all the possible damage rolls which balloons to thousands of states in order to get an accurate result. Lapras vs. Chansey was a lucky case where a cheat like that was somewhat accurate. I could come up with upper-bound and lower-bound calcs for ReflectZam vs. Tauros, but they'd probably be 20-30% apart or even more. (Note, however, that any scenario NOT involving users of instant-recovery moves doesn't have this problem; Rest heals ALL your HP and as such "get hit X times" is identically equivalent with "get hit Y times, Rest, get hit X times".) So if anybody wants Slowbro vs. X/RestLax vs. X/Rest Lapras vs. X calcs, I can do those accurately. It's just Chansey/Alakazam/Starmie that create ugly situations.

To further elaborate on what I was saying, my cheat with Lapras vs Chansey is this logic:

Lapras 5HKO vs. Chansey is guaranteed.
Lapras 4HKO vs. Chansey is almost impossible (0.2%).
Lapras 7HKO vs. Chansey with 1 Softboiled factored in is guaranteed.
Lapras 6HKO vs. Chansey with 1 Softboiled factored in is almost impossible (<0.2%).
Lapras 9HKO vs. Chansey with 2 Softboileds factored in is almost guaranteed (666-909 damage, heavily biased toward the middle).
Lapras 8HKO vs. Chansey with 2 Softboileds factored in is almost impossible (<<0.2%).
etc.

Thus, without serious loss of accuracy, we can assume that "Chansey has been hit N times and used Softboiled k times" and "Chansey has been hit N-2k times" are the same thing.

That's the crucial criterion that allowed me to collapse the full 21,000-state Markov chain into something manageable that I could elucidate by hand. I'm sure there are ways to computer-generate the full chain from a set of parameters, but I don't have those skills - I'm majoring in pure maths and not applied maths specifically because I hate working with computer maths programs.

[jorgen]

So how long did it take you to run all that anyway? I mean, in hours. Every estimate I can come up with says "a fuckload of time". 21,000 states gets silly, especially when you need to invert the transient-states matrix to get the absorbing probabilities.

[magic9mushroom]

May 13, 2014 5:34:14 GMT -8 jorgen said:

So how long did it take you to run all that anyway? I mean, in hours. Every estimate I can come up with says "a fuckload of time". 21,000 states gets silly, especially when you need to invert the transient-states matrix to get the absorbing probabilities.

As I said, I didn't do the full 21k states. I used a simplifying assumption to reduce it to 140 states, and then solved that. Probably took me along the lines of 30-40 hours total, but most of that was in setting up the states; I used a computer to solve the system.

[jorgen]

I wouldn't have thought that one assumption about Chansey's health being equal after 2 Bslams + Soft would have collapsed so many states.

[magic9mushroom]

May 13, 2014 21:23:56 GMT -8 jorgen said:

I wouldn't have thought that one assumption about Chansey's health being equal after 2 Bslams + Soft would have collapsed so many states.

703 Chansey health values vs. "full health"/"hit once"/"hit twice"/"hit three times"/"hit four times". 703/5 = 140x, giving ~20k states vs. 140.

EDIT: Well, you could do it with about 2k states by using states defined as "Chansey hit X times and healed Y times", but then you have to actually do the damage calcs for e.g. Lapras Body Slam vs. Chansey 15HKO through 5 Softboileds (and remember, the order of the Body Slams and Softboileds matters, because Softboiled is truncated at full health!). Which boils down to the same amount of work anyway, as basically you're either handling the damage calcs integrated into the Markov chain or parametrising them.

That "Softboiled = 2 Body Slams" approximation is, indeed, enormously powerful (well, it's not so much that the approximation is THAT powerful; it's more that instant-recovery moves are THAT hard to model accurately). Which is, of course, the reason I used it; you'll note that I didn't ignore crits, the tiny chance of Thunderbolt not 3HKOing Lapras, or even the difference in damage between a Chansey Tbolt crit and 2 non-crits. I made this one approximation (and the complementary approximation that PP exhaustion doesn't happen - I say complementary because conflating "N Slams + k Softboileds" with "N-2k Slams" requires it) because it was absolutely necessary to render the problem tractable.

[Actaeon]

This is next-level Pokémon, wonderful work. It actually made me enthusiastic to look at Markov chains again.

I understand the way you used Markov chains in this calculation, and agree with the premises you made before. The damage variance may actually be important for the chance in the end, because if either Pokémon enters the fainted state as a consequence of two "high" rolls, that is a great influence to the (absorbing) chain. Note that the chain is not even absorbing a priori if the Pokémon have infinite PP, and theoretically it could be the case that no Pokémon wins if the match is "tight enough". In practice, however, most markov chains that will represent Pokémon matchups will be transient.

The most important tool we need in order to generalize your method is automatizing the presentation of all states (because that's very time-consuming), and ultimately the probabilities associated with them. If we can find an algorithm for that, that would make it possible to make a program that calculates all chances you'd like given two Pokémon and their movesets (provided they don't switch, of course). Also it would be more accurate if we can implement exact "current HP's" and stuff.

However, I can't think of a smart method to make a computer calculate these events, as most states require a "competitive" thought such as "if Chansey is low on HP, then it uses Softboiled". It would always require a person to actually point out which moves are used in which situations.

Do you agree on any of this?

[magic9mushroom]

Do you agree on any of this?

May 14, 2014 14:06:48 GMT -8 Actaeon said:

I understand the way you used Markov chains in this calculation, and agree with the premises you made before. The damage variance may actually be important for the chance in the end, because if either Pokémon enters the fainted state as a consequence of two "high" rolls, that is a great influence to the (absorbing) chain.

Four high rolls, not two. Lapras Body Slam vs. Chansey = 152-179 damage (21.6-25.4%); a single "average" roll of 165 or less will prevent the 4HKO even if the other three roll max. I know it matters, but my gut says it's outweighed by the inaccuracy the other way (that nine Body Slams don't guarantee a KO through two Softboileds, and so on for higher numbers). In any case, like I said, I used the approximation because otherwise the problem isn't tractable.

Note that the chain is not even absorbing a priori if the Pokémon have infinite PP, and theoretically it could be the case that no Pokémon wins if the match is "tight enough". In practice, however, most markov chains that will represent Pokémon matchups will be transient.

All Markov chains must have either a) no absorbing states, b) an absorbing subchain containing no absorbing states, or c) a set of absorbing states which together represent 100%. Paralysis and Ice moves prevent both a) and b) by guaranteeing that every state has a possibility of winning, so the only chains that won't result in 100% absorption (even ignoring PP) are stupid things like Seismic Toss/Reflect/Softboiled/Growl Chansey mirrors (I was going to say Withdraw Slowbro mirrors, but three crits plus the speed tie allows even that to resolve - albeit inaccurately to how it really plays out).

The most important tool we need in order to generalize your method is automatizing the presentation of all states (because that's very time-consuming), and ultimately the probabilities associated with them. If we can find an algorithm for that, that would make it possible to make a program that calculates all chances you'd like given two Pokémon and their movesets (provided they don't switch, of course). Also it would be more accurate if we can implement exact "current HP's" and stuff.

However, I can't think of a smart method to make a computer calculate these events, as most states require a "competitive" thought such as "if Chansey is low on HP, then it uses Softboiled". It would always require a person to actually point out which moves are used in which situations.

You can do it the way chess programs do it. Computer checks probability of winning for each possible strategy it can use, selects best one and returns that strategy along with its associated probability.

But that's halfway to writing a "solve RBY" program, and would involve serious programming as opposed to just maths work.

[Actaeon]

What would be harder in your opinion, solving chess or solving RBY? If we had all the programming skills and a full team of players to work on it, would it be possible to make something like an RBY Bot that wins all, say, best of 7 matches?

EDIT: That would practically mean "the end" of RBY...

[magic9mushroom]

May 15, 2014 0:41:03 GMT -8 Actaeon said:

What would be harder in your opinion, solving chess or solving RBY? If we had all the programming skills and a full team of players to work on it, would it be possible to make something like an RBY Bot that wins all, say, best of 7 matches?

EDIT: That would practically mean "the end" of RBY...

Well, the base complexity of the data is higher (more potential kinds of "pieces", taking into account sets, and damage levels are a lot more complex than "taken" or "not taken") but the amount of moves available to each side is lower (typically you have 2-5 decent choices out of a total of exactly 9; chess (IIRC, it's been years since I played chess competitively) has 3-7 decent options out of a total of 20+) and games are shorter on average (but so is the length for which you can run an "opening book" - RBY openings are only a few turns long). Random outcomes hurt, particularly calculations like this one; you don't need to run a Markov chain every time you want to know if an Arimaa elephant can drag a camel (then again, most of these chains can be done in advance). Incomplete information is bad news because it means you have to account for all possibilities; you don't know if your opponent has Zapdos when deciding whether to blow up Golem, but you sure know whether your opponent has a queen when deciding whether to sacrifice your knight for a bishop. Simultaneous turns preclude a deterministic solution; the optimal strategy is in almost all cases a mixed one (whereas the optimal strategy for chess or Arimaa is an (exceedingly complex, with a billion if/thens) pure strategy). There's also a lot of information that you'd have to feed into the Bot that changes game-to-game - a perfect RBY Bot would have to be fed full usage statistics, and potentially some data representing the opponent's known patterns (of course, you could just record the data it gets from playing, but it'll be total shit until it learns the meta).

Overall I think it'd be a bigger challenge to solve; this is, however, a much tougher challenge than merely designing a program that beats all human champions. I think the latter is doable with modern computer speed, but obviously it's already been done and by a huge margin for chess (to the point where accusations of cheating - with a chess program running on a mobile phone - are actually meaningful these days).

[piexplode]

Imagine getting RBY to that chess level though

[piexplode]

Actually, time for a totally mad thought now.. Imagine being able to have computers that could go on the ladder and play players, teambuild etc. would make playing at obsequious times when the ladders are deader still playable, and eventually the bots might become competitive enough. Imagine bidding for bots in SPL or whatever. Ok kinda mad thoughts and clarity is lost but I hope you understand what I mean. Cool ideas.

[Actaeon]

To calculate probabilities like the above, wouldn't it be easier to use Monte Carlo methods instead of exact approaches?

1) There is no need to make a configuration of all states and the transition probablities;
2) No "assumptions" have to be made;
3) Maybe we can use part of PO's code to implement all game mechanics correctly instead of designing a good program ourselves.

I think most computers can do a matchup like Chansey vs Lapras in less than a second, so if you'd leave the computer running for a day or two, your probability will be quite accurate already.

Any ideas?

[jorgen]

Monte Carlo probably works better for a single starting point. I think the bigger issue, though, is that setting up a Markov model, while tedious, allows you to get absorbing state probabilities for multiple starting points all in one handy matrix, whereas you'd need to set up a new simulation for each possible starting point (not to mention that you'd need to run it for sufficient time to not only get win probabilities, but also the probabilities of the victor emerging healthy or crippled). Plus m9m is a math person and I imagine it was more fun to try to find an exact solution rather than resorting to brutish approximations.

[Actaeon]

@ Jorgen: I agree with you on this point, but ultimately, if enough data is available, the (average) amount of HP remaining and status of the winner can be graphed as well.

From a mathematical point of view, the Markov chains are a more beautiful way to accomplish the same, but it's a hell of work. And most of the time you need to calculate "stupid" probabilities anyway. Both methods don't really use pure math anyway, and all we're REALLY interested in is that probability, because that knowledge helps us in becoming better players.

Therefore I think we should give this a shot as well, because it might be easier to use for many situations we'd like to know the probabilites of.

[magic9mushroom]

As jorgen said, I'm a pure mathematician. I find the Monte Carlo method deeply disgusting, and will have nothing to do with it.

(Also, please tell me I haven't just inspired a project to kill competitive Pokemon.)

[piexplode]

This wouldn't kill competitive pokemon.
But using repeated computer simulations to find the probabilities of outcomes in different situations to find probabilities sounds like an interesting way to move forward, when we find things where markov chains are not tractable (reflect zam vs tauros?). It's just moving forward, gaining yet more information about the game.

[Actaeon]

It won't kill Pokémon by far. The best it's going to do is provide us with better knowledge about certain matchups. Of course, the factor of switching would be too much work to implement anyway.

As I said before, I would be very interested in outcomes of these simulations. Sadly, I lack the programming skills to make such a setup. I don't really understand your point of view, m9m, of course it's not a "beautiful way" in any means, but if we can extract useful numbers from a method of this kind, I think it would benefit us all.

[piexplode]

I disagree slightly. You could calculate instead of when a mon gets KOed but when they go beneath a certain threshhold, at which point the player would switch. Still difficult to implement, but ultimately not much more difficult than stuff like Reflect Zam vs Tauros where we might have to do computer simulations (get the sim to play through the game 10million times through that one situation with certain initial conditions?) which hopefully we'll find solutions for eventually.