Scenario: What would you do?

[Zilch]

Isa and I were discussing mindgames after a NU match, and we eventually settled on what I believe to be the perfect scenario.

Player 1: Tauros (1%)
Player 2: Exeggutor (45%), Golem (49%)

No status effects are in play.

If you were player 1, would you elect to use Body Slam or Hyper Beam? Keep in mind that Eggy dies to HBeam and critical BSlam but not Blizzard, while Golem dies to Blizzard.

[t3h Icy]

It's really dependent on the player and how the rest of the match went.

So let's go over the possibilities:

Body Slam against Exeggutor has a 7.5% chance to cause a FP and a ~21.5% chance to CH. This means with Body Slam on Exeggutor, Tauros has a 27.39% chance to win. Anything else, Tauros loses.

Body Slam against Golem is mostly a safety move, and regardless of roll, it'd be best to follow-up with Blizzard. Tauros then has a 90% chance to win, but slightly more in the event of Paralysis and FPs covering for Blizzard misses. The chance of that is about ~0.2%.

Hyper Beam against the damaged Exeggutor is a guarantee KO, but has 90% accuracy.

Hyper Beam against Golem is death, unless on a miss. A CH can't finish Golem off either, so this gives Tauros a 9% chance for success when attacking with Blizzard the following turn.

So the percentages of each possibility are:

Body Slam against Exeggutor: ~27.39%
Body Slam against Golem: ~90%
Hyper Beam against Exeggutor: 90%
Hyper Beam against Golem: 9%

This means Body Slam is the best chance to win mathematically, but it's down to making the right choice for the most part.

[hipmonlee]

Against a perfect opponent, you should select your moves with the ratio so that whatever move your opponent selects, the expected return is the same.

So, the expected return assuming your opponent stays with eggy is 27.39*p[bodyslam] + 90*(1-p[bodyslam]). The return assuming the switch is 91.7*p[bodyslam] + 9*(1-p[bodyslam])

According to wolfram alpha, p[bodyslam] should be 55.7%

Of course opponents dont play perfectly, and calculating nash equilibriums mid battle takes too long to be practical, but this should give you some idea. Basically you can think of it, that because it doesnt matter what they do, your chance of winning should be the same if your opponent always takes option one or always takes option two. In this case, because Bodyslamming Exeggutor works a reasonable amount of time, if they always left Eggy in you still win more than half the time if you bodyslam more than half the time, and if they always switched to golem you win more than half the time because you are predicting it more than half the time. So you can see in your head that you should bodyslam slightly more than half the time.

But having done the maths and am now actually thinking about the scenario, using bodyslam is a terrible move. You should definitely either blizzard or hyperbeam. The chance of a freeze or a ch is better than the chance of a ch and a parfp slam even considering the miss chance, and the chance of killing golem goes from a little over 10% to 99%.

Actually the odds of blizzard killing eggy is 27.4 and bs killing it are 27.3 so its actually pretty damn close, but blizzard is definitely the superior move. With that, you get 58% blizzard and 42% hyperbeam.

[jorgen]

Your Choice\Opponent's Choice:	Exeggutor	Golem
Body Slam	25/75	81/19
Hyper Beam	81/19	8/92
Blizzard	24/76	89/11

Numbers shown in following format: Your winning percentage/opponent's winning percentage (both are approximate, rounded to nearest integer percent)

All percentages are basically those in Icy's post, but multiplied by 0.9 to account for the fact that if you do predict correctly, you still need your next attack to hit what remains on the following turn. Blizzard percentages I ran myself. EDIT: (Hit^2)*(Non-freeze*crit + Freeze) for the chance of winning with a switch to Egg. Hit^2 + Miss*Hit^2 for the chance of winning with a switch to Golem.

Blizz in this situation means you effectively get 2 shots with it against Golem, and has a 9% chance to freeze Eggy. So Blizz gets you comparable odds relative to BS in the worst-case, and (relevantly) better odds against a possible Golem switch-in, thus making it slightly better imo from a strict numbers POV. But if you're extremely risk-averse, go with Bslam, I guess.

If you tweak the HPs a bit lower, you can get it so that Golem is guaranteed to be 1-shotted by EQ after BS, and that Egg is guaranteed to be KO'd by Blizzard after an EQ. That way, the dichotomy is more between BS/Hbeam and no "third way" is relevant.

But, yeah. Blizz is probably the best option if you don't know anything about who you're up against, but against somebody you know even a little about, the math doesn't quite cut it. It all depends on the opponent, how they play (low-risk, high-risk), how I think they think I play (if I'm risk-averse or risk-prone in their eyes), and deeper and deeper ad infinitum. Or, I just pick one at random if that fails. There isn't a Nash Equilibrium here, hence why it's an issue to begin with, and also why it really isn't worth the effort in thinking, overthinking, etc.

[t3h Icy]

Blizzard hits, no CH, no Freeze - ~63.6%
Blizzard hits, CH - ~19.3%
Blizzard hits, no CH, Freeze - ~7.07%
Blizzard misses - 10%

Blizzard wins - 26.37%

Though with a 1.1x better chance to take out what it's intended for (Golem), Blizzard is definitely the route to go if a player predicts a Golem switch-in.

[t3h Icy]

jorgen: Since Tauros is the only Pokemon left, there is no realistic point in using Body Slam. The opponent can either attack with Exeggutor or switch to Golem, and the player selects a move based on that. If they predict Golem, use Blizzard, and if they predict Exeggutor, use Hyper Beam. Body Slam sacrifices 9% of success on what it's intended for, just for an extra 1% if the player is incorrect.

[jorgen]

I completely agree with that, but again, if you're extremely risk averse, you might decide to slam just to get that extra 1% in the worst-case scenario. It's a real tradeoff, though imo (and iyo), it's definitely not worth it.

But if the HPs are tweaked so that, after a slam, Golem is OHKO'd by EQ, while Egg is OHKO'd by Blizz after an EQ, slamming is a little better than going for the 90% move right off the bat.

[Consumptus]

You go with your gut and base it off choices during the battle before =d

[WaterWizard]

Blizzard is clearly the best option.

[garrinred]

I agree with Blizzard.

[hipmonlee]

There is a nash equilibrium.. Why wouldnt there be?

Since I did the blizzard maths wrong and there is a slightly better chance with bodyslam than blizzard it may involve selecting bodyslam some miniscule amount of the time. The maths here becomes pretty complicated.

Ok, I just tried it, but I used jorgen's calcs this time, I am not entirely sure this is right, in fact I am not confident at all. But I got you blizzard 53%, hyperbeam 47% and never bodyslam. If that is right, then being risk averse is irrelevant in this situation (actually risk aversion is irrelevant regardless) the decision is purely mathematical.

[jorgen]

Ack, I'm not terribly well-practiced with my game theory, and it shows. I mixed up the Nash Eq. concept with that of the existence of a dominant strategy. Silly me.

[Isa]

Clearly Zilch and I needs to improve...our original case of Primeape versus Abra and Rhyhorn was so much easier

[davidchansey]

Using these values:
Accuracy of hbeam and blizz = 229/256,
Chance of paralysing = 76/256,
Chance of full paralysis (don't know exact value) = 0.25,
Chance of freezing = 25/256,
Critical hit rate = 110/512
From this link: www.gamefaqs.com/gameboy/367023-pokemon-red-version/faqs/20844 , I get these results:

Bslam vs Eggy (crit or para then fp) then blizz vs Golem = 0.244...
Hbeam vs Eggy then blizz vs Golem = 0.800...
Blizz vs Eggy (crit or freeze) then blizz vs Golem = 0.233...

Bslam vs Golem, then blizz vs Golem, then hbeam vs Eggy = 0.800...
Hbeam vs Golem (miss) then blizz vs Golem, then hbeam vs Eggy = 0.084...
Blizz vs Golem then hbeam vs Eggy = 0.800...

Basically, bslam dominates blizz, so we can rule out blizz. Now we have:

Bslam vs Eggy (crit or para then fp) then blizz vs Golem = 0.244...
Hbeam vs Eggy then blizz vs Golem = 0.800...

Bslam vs Golem, then blizz vs Golem, then hbeam vs Eggy = 0.800...
Hbeam vs Golem (miss) then blizz vs Golem, then hbeam vs Eggy = 0.084...

So bslam has chances 0.244 and 0.8 to win, and hbeam has 0.8 and 0.084 chance to win. Bslam is clearly the play safe option, but there is no stable solution. We can formulate a game plan like this:

B vs E = 0.244
B vs G = 0.8
H vs E = 0.8
H vs G = 0.084

Where:
E = stay with Eggy
G = switch to Golem
B = use Bslam
H = use Hbeam.

So, for example, if Tauros uses Bslam and Eggy stays in, Tauros has a 0.244 chance of winning the game.

Making the assumption that player 2 will choose both of his options with equal probability, we can solve this problem by letting p = probability to use bslam, and 1-p = probability to use hbeam. So we get these simultaneous equations:

0.244p + 0.8(1-p) and 0.8p + 0.084(1-p)
Let 0.244p + 0.8(1-p) = 0.8p + 0.084(1-p)
-0.556p + 0.8 = 0.716p + 0.084
1.272p = 0.716
p = 0.563...

This means, in this very specific scenario (and if it were to occur many times) you should use bslam 56.3% of the time, and hbeam 43.7% of the time. This is the optimul solution. Putting this value of p back into either equation gives the value 0.487. This means you will win this scenario 48.7% of the time using this strategy. Of course, the assumption of player 2 choosing Eggy and Golem with equal probability was made.

So what should player 2 do? Well, let's presume Tauros chose bslam and hbeam with equal probability. Player 2 should stay with Eggy 56.3% of the time, and switch to Golem 43.7% of the time. Again, this is making the assumption that Tauros uses bslam and hbeam with equal probability.

Warning: just because bslam is the safe option, it doesn't mean you should use it every time. You will become predictable that way. Of course, this scenario is very obscure, but generally in gameplay you will have many times where you will have to make a win or lose choice, and determining how often to use each choice is the key to winning.

I must admit I enjoyed this, and it was fun to recap over maths before uni in 2 days. I am PRAYING I haven't made a simple arithmetic mistake, as that would ruin the whole thing.

To conclude: go bslam or hbeam, roughly equal amount of times. Bslam is safer. Blizz should not be considered.

[jorgen]

Nah. As described above, Bslamming throws away one of your Blizzard chances against Golem (throwing away 8-9% chance of winning if they go Golem) in favor of 1% chance of beating Egg on the mispredict. Neither really dominates the other, though realistically, the choice is more between Blizz and Hbeam than it is anything else.

[t3h Icy]

Body Slam is just the safe move, but ideally, you'd want to react perfectly to your opponent. Blizzard or Hyper Beam.

[davidchansey]

Actually, between 0.244 and 0.233, that makes 11% difference in defeating Eggy if he stays in using bslam rather than blizz.

[garrinred]

CONCLUSION:

If the opponent chooses at random:

Blizzard > Stomp > Body Slam >>> Earthquake > Hyper Beam.

Yes, that's right! Earthquake is actually superior to Hyper Beam!! Assuming the opponent chooses Golem(or goes at random).

If you think you can outpredict the opponent, you choose between Hyper Beam and Earthquake. Not Blizzard. You choose Blizzard only if you want to play it safe. And you never ever choose Stomp or Body Slam(but Stomp IS better than Body Slam).

Want to know how I arrived at my conclusions? Read on!

--------------

My turn to run the numbers myself. I will ignore 255s and assume 90% hit rate and 30% BS para rate and 25% fp rate and 21.48% Tauros crit rate. I also assume you don't have Stomp and Earthquake on the same set, as that would create even more of a mess than a paralyzed Golem.

Assuming Eggy stays in:

Hyper Beam- 90% chance of KO. Then Blizz vs. Golem, another 90% chance. So 81% chance of victory.

Body Slam- 100% chance of hit. 21.48% chance of crit, which KOs. Also 30% chance of para and 25% from there of fp. So chance of para-fp is 7.5%. Either of those scenarios mean Eggy is dead. This means a 27.3% chance of killing Eggy. Then the 90% chance of killing Golem gives a 24.6% chance of victory overall.

Blizzard- 90% chance of hit. 21.48% chance of crit, if it hits, which KOs. Also 10% chance to freeze, if it hits. Counting accuracy, crit rate, and freeze chance, I get a total kill chance of about 26.4%. Then the 90% chance of killing Golem gives a 23.8% chance of victory overall.

Earthquake- You are royally screwed.

Stomp- a crit might KO. Or Eggy might flinch. Either way Body Slam kills Eggy on the follow-up. So Tauros only needs to land one 90% move from there. So a little over 27% for total victory chances.

Assuming Golem comes in:

Hyper Beam- You are royally screwed.

Body Slam- You win if you can land two 90% moves in succession. That's an 81% chance of victory. Unless you paralyze Golem. If you paralyze Golem, the math gets complicated, especially when you consider the possibility of switching back to Eggy, the possibility of a crit body slam, and the possibility of missing a 90% attack. Suffice it to say the victory chance overall is greater than 81%, but not by a lot.

Blizzard- KOs Golem if it lands, and then you just need to land the Hyper Beam. If it does not land, that's ok, you still get ANOTHER shot on Golem.
(90%)First Blizz hits, you have a 90% of victory from there.
(10%)First Blizz misses, you have an 81% chance of victory from there.
Total victory chances: 89.1%.

Earthquake- Whether or not it crits, it basically means you only have to land one 90% attack. That is, a Hyper Beam on Eggy.

Stomp- Tauros still has to land two 90% moves, though bonus points if a critical Stomp knocks Golem into HB range. 81% chance of victory from there.

--------------------Eggy---------- Golem
Hyper Beam----------81%-------------0%
Body Slam-----------24.6%--------->81%
Blizzard-------------23.8%----------89.1%
Earthquake-----------0%--------------90%
Stomp-------------->27%------------81%

But wait, there's more. A Stomp knocks Golem into EQ range. And an EQ knocks Eggy into Maybe-Blizzard range. That kinda screws with things. But that would mean you're not packing BS+HB. And it may or may not make Stomp a better choice than Blizzard. Let's not explore this option for now, I'm too lazy

And that, as they say, is that.

[jorgen]

.244 - .233 = 0.011. 1.1%.

Stomp does mess with things, that's for sure. But it's only a marginally better "safe" option than Bslam for when you guess wrong, so even if you're running it, you probably don't want to be using it.

Also, Hbeam against Golem offers you some play in the event that it misses, whereas EQ just gives you absolutely no chance against Egg.

And EQ doesn't really give an advantage at all. You have the crit chance to kill a Golem switch-in, but otherwise, you still need to hit 2 Hyper beams for (.215 + .785*.9)*.9 = ~0.83. Of course, there's some extra play for if you EQ twice (once for golem, and once on the switch back to Egg), then have a possibility for Blizz to KO Egg the following turn (at best ~50%, I think). All of which probably doesn't bring it up above Blizzard's chances if they go Golem. Meaning EQ is dominated by Blizz.

[davidchansey]

... I have now embarrassed myself yet again. Yeah blizz or hbeam seem to be the way to go.

[garrinred]

Sept 13, 2011 13:31:34 GMT -8 jorgen said:

.244 - .233 = 0.011. 1.1%.

Stomp does mess with things, that's for sure. But it's only a marginally better "safe" option than Bslam for when you guess wrong, so even if you're running it, you probably don't want to be using it.

Also, Hbeam against Golem offers you some play in the event that it misses, whereas EQ just gives you absolutely no chance against Egg.

And EQ doesn't really give an advantage at all. You have the crit chance to kill a Golem switch-in, but otherwise, you still need to hit 2 Hyper beams for (.215 + .785*.9)*.9 = ~0.83. Of course, there's some extra play for if you EQ twice (once for golem, and once on the switch back to Egg), then have a possibility for Blizz to KO Egg the following turn (at best ~50%, I think). All of which probably doesn't bring it up above Blizzard's chances if they go Golem. Meaning EQ is dominated by Blizz.

Wrong. Well, right about Stomp. The point is it's irrelevant because the choice is HB vs. EQ vs. Blizz.

Here's the wrong part: EQ puts Golem into HB killing range.

Check this out:

Golem comes in, Tauros EQs. Then Tauros EQs again, but this time the opponent switched back to Eggy. Ok. HB time. Either Eggy is dead, Golem is dead, HB missed Eggy, or HB missed Golem. If Eggy died, EQ for the finish. If Golem died, HB for the finish. If Eggy is alive you're dead. If Golem is alive, EQ again.

This gives a solid 90% chance of winning.

Now that I think about it, that's actually BETTER THAN HYPER BEAM. Hyper Beam you need to land the HB, and then land a Blizz, even if Eggy did stay in. That's 81%. I'm going to go correct that now.

[garrinred]

Sept 13, 2011 14:00:13 GMT -8 @davidchansey said:

... I have now embarrassed myself yet again. Yeah blizz or hbeam seem to be the way to go.

No, EQ is slightly better than Blizzard if you predict Golem. Only slightly.

But Blizzard is best overall.

[jorgen]

Ah yep, you're right. Still, the benefit is barely better than Blizzard's, and again, if Egg stays in for the first EQ, you're boned, whereas Blizz gives you a shot. EQ really isn't worth it, but you may be selecting it a trivial number of times.

The odds for EQ vs. Golem are definitely better than those for Hbeam vs. Egg, though you can't really say EQ is better than Hbeam for that since they're for two totally different predictions.

[Nerd]

Use hyper beam if you think they will stay in and use blizzard if you think they will switch. Not that complicated.

[WaterWizard]

that, or just Bliz and hope for the best. This thread was a grand waste of time.

comes down to a 50/50 chance (yes, we do have players who honestly flip coins for the random factor).

at this point in the match, you should be thinking how to not get into this situation again. you've already screwed up.

[jorgen]

It's not complicated, but the fun comes from finding ways to make it complicated.

Plus, while the conclusion itself is pretty intuitive, it's always nice to work through the proof to validate what intuition holds true (or, hopefully, to find out a better solution that intuition alone wouldn't really see).

[Zilch]

Sept 13, 2011 18:39:54 GMT -8 WaterWizard said:

that, or just Bliz and hope for the best. This thread was a grand waste of time.

Agreed. Everything that needs to have been said has been said. No need to argue about this anymore.

Locked.