Tauros Earthquake vs 30% or 31% Rhydon?

[Lutra]

Is 30%(or 31%) and less HP Rhydon the right percentage to Earthquake with Tauros?

According to the Showdown Calculator, the possible damage riolls for Tauros Earthquake are: 129, 129, 130, 131, 131, 132, 132, 133, 134, 134, 135, 135, 136, 137, 137, 138, 138, 139, 140, 140, 141, 141, 142, 143, 143, 144, 144, 145, 146, 146, 147, 147, 148, 149, 149, 150, 150, 151, 152 (31.2% to 36.8%)


On PO, I've tested that HP percentages are floored, which means the first 7 damages: 129, 129, 130, 131, 131, 132, 132 could correspond to a Rhydon's 31% HP.

Blizzard always KOs when Rhydon is 31% HP, providing it hits. As Blizzard = 229/256 accuracy and Earthquake 255/256 accuracy, 229/255 is the accuracy of Blizzard compared to Earthquake.

Now, we want to find x where x/39 = 229/255, so that the chance of getting a low damage roll = .the chance of Blizzard missing

229/255 * 39 = x = ~35.024

39-~35.024 = ~3.976 to look at the low rolls.

Given that 129, 129, 130, 131, 131 are the first 5 damage rolls, would that mean 129, 129, 130 but not 131 qualify as being lower damage rolls than the chance of Blizzard missing? Therefore does this mean it's 3 Earthquake vs 4 Blizzard for 31%? So you have to make sure Rhydon is 30% and less HP on PO?

I just thought about this as I saw someone Blizzard Rhydon at 30% when they should have used Earthquake.


Note: Doesn't take into account low damage critical hits. They might even be enough to swing it the other way because it's that close.

Edit: Looks like it does swing to Earthquake for 31% when taking into account critical hits but would be nice if someone could produce a 4.x number for it.

[marcoasd]

If I'm right:
31,9% scenario is:
Blizzard 229/256= 89,45% EQ 32/39+ 7/39X110/512 for the CH rate= 3,86%=  85,86%

31,7%
EQ= 34/39 + CH rate 2,75%= 90%

31,2% or below, EQ= 100%

I'd use EQ vs 31% and Blizzard vs 32%

[Actaeon]

Ok let's use conditional probability.

First, as Lutra pointed out, the HP values Rhydon can be at when 31% is shown is 129, 130, 131 and 132. Let us assume that it is uniformly random which of these values it's actually at.

Tauros' Crit Rate is 55/256. Hence,

P(KO | 129 HP) = (39/39)*(255/256) (Rhydon is KOed whether EQ crits or not)
P(KO | 130 HP) = (37/39)*(255/256)*(201/256) + (255/256)*(55/256)
P(KO | 131 HP) = (36/39)*(255/256)*(201/256) + (255/256)*(55/256)
P(KO | 132 HP) = (34/39)*(255/256)*(201/256) + (255/256)*(55/256)

Since the HP "density" is uniform, the ultimate chance for Tauros KOing Rhydon with EQ (factoring in Crits and Misses) is the sum of these probabilities divided by four, i.e.,

P(Tauros KOes Rhydon with EQ) = 94.8%

So it's actually better than Blizzard on average.

[jorgen]

Sorry for the mess cbf to clean it up BUT TL;DR use EQ if Rhydon is 31% or below, use Blizz if 32% or above.

Blizzard accuracy = BA = 229/255 and will always KO if it hits
Crit Rate = CR = 110/512
Earthquake Accuracy = EA = 254/255

Damage rolls for Tauros EQ:
129, 129, 130, 131, 131, 132, 132, 133, 134, 134, 135, 135, 136, 137, 137, 138, 138, 139, 140, 140, 141, 141, 142, 143, 143, 144, 144, 145, 146, 146, 147, 147, 148, 149, 149, 150, 150, 151, 152

corresponding to 31.2% to 36.8

assuming the probability of crits, find the point where EQ KO is just as likely as a Blizzard KO
A crit will always KO, so a high enough roll occurs with probability 1

I will evaluate the point where
Blizz noKO = EQ noKO

P(~Blizz Hit) = P(~EQ Hit) + P(EQ Hit,~EQ Crit,EQ Lo) =independent= P(~EQ Hit) + P(EQ Hit)P(~EQ Crit)P(EQ Lo)
P(EQ Lo) is our target, x/39
(1-BA) = (1-EA) + EA*(1-CR)*(x/39)
(EA-BA)/(EA*(1-CR))*39 = x
note that my x is equivalent to lutra's 1-x.

x = 4.8889, or the number of rolls that need to be below current rhydon HP for a EQ KO to be less likely
obviously you can't have noninteger rolls, so X = floor(x) = 4
lowest 4 rolls for EQ are 129, 129, 130, 131
5th lowest is also 131
all rolls beyond the 5th are 132 or greater

Therefore, we are guaranteed a more likely KO with EQ than Blizzard if Rhydon is at 131 or less HP, as at this point there are only 3 rolls below Rhydon's current HP, whereas at 132 HP, this number jumps to 5.

HOWEVER, this assumes information that you just do not have. You get information in percentages on PO, not single-HP units.
Because PO floors percentages, Rhydon's HP display will give
31% for 124..132 HP ({124 125 126 127 128 129} are guaranteed KOs, {130 131 132} are not)
32% or more for 133+ (outside of kill range)

The question is, assuming that Rhydon is showing 31% HP, is it worth it to go for EQ over Blizzard?
To answer this, I will evaluate the following statement
P(~Blizz Hit) > P(~EQ Hit) + P(EQ Hit)P(~EQ Crit)P(EQ Lo|31%)

assuming a uniform prior for Rhydon's HP, solve for the union of conditional probabilities comprising 31%, then divide by the total number of instances comprising 31% (works because of uniform prior)
P(EQ Lo|31%) = sum(P(EQ Lo|n),n=124..132)/9
P(EQ Lo|n) = 0 for n=124..129
P(EQ Lo|n) = 2/39 for n = 130
P(EQ Lo|n) = 3/39 for n = 131
P(EQ Lo|n) = 5/39 for n = 132
therefore, P(EQ Lo|31%) = (10/9)/39 = LR

(1-BA) > (1-EA) + EA*(1-CR)*LR
0.1020 > 0.0285 (approximate values ofc)

Therefore, if Rhydon is at 31%, use EQ, as it is the more likely KO. If Rhydon is below 31%, use EQ, as it is a guaranteed KO (besides 255s of course). If Rhydon is 32% or above, use Blizzard, as EQ is no longer the more likely KO.

Theoretically you could keep track of what attacks you're using against Rhydon and come up with a better prior (and, therefore, maybe identify cases where Blizzard would actually be the better choice at 31%), but holy shit that's too much effort.

[Lutra]

Well done guys.

I guess I made a mistake in basing the HP values from the damage rolls.

[Actaeon]

I used the same method to calculate the probability that Earthquake KO's a 32% Rhydon.
In this case it has either 133, 134, 135 or 136 HP.

The probability is

P(EQ KOes 32% Rhydon) = 81.3%.

So that's it I guess, I'm coming up with the same conclusion as Jorgen. Good to know tho, I never really thought about it and use EQ/Blizzard depending on whether Eggy might switch in, one of the classic reasons to use Blizzard.