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Old 06-24-2019, 03:25 AM   #1
Bogdan314
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Which GTO strategies are EV-indifferent?

I have posted this on a private forum but did not get any answer, so hopefully I have more success here.


Regarding GTO, the simplest example of Nash equilibrium in poker is the river spot with Hero having nuts and air in his range and Villain only bluff catchers. We know that here Hero has an optimal bluff frequency and Villain has an optimal call frequency, both of which are computed based on the bet size and pot size.

What troubles me is that this equilibrium works on the principle of indifference, meaning that as long as, e.g., Hero bluffs with the optimal frequency, his EV will not change if Villain deviates. [of course, if Villain deviates then Hero can deviate and exploit to increase EV, but that’s another story]

In other words, if I know for sure that my opponent in this spot is playing at Nash, then I can play as bad as I want and my EV will not change. I could be the biggest loser in poker and still my EV is maximum as long as my opponent is playing ”GTO-perfect”.

My question is: are *all* poker equilibrium solutions (in all various spots, flops, turns, rivers, etc) in the same situation like the one above? If not, how to recognize the solutions that are indifferent to the opponent strategy and those that gain EV when opponent deviates from equilibrium?

Or a better way to rephrase that: if I play an unknown opponent for the very first time and I choose to play GTO until I observe his play and make the proper adjustments, will I be at 0 EV (and thus losing money due to rake) even if my opponent is the worst poker player that has ever existed?

If that were true, then GTO is only useful as a defensive play until you observe the opponents leaks, and you should deviate and exploit as soon as possible or else you are losing money. Is that correct?
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Old 06-24-2019, 03:41 AM   #2
plexiq
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Re: Which GTO strategies are EV-indifferent?

No, not all poker equilibrium solutions are like this. You picked a very specific example where, at least in a simplified form of the game, all bluff catchers end up with neutral EV and can be played with any frequency against the GTO strategy without changing the EV. In that toy game there is no room to make mistakes as the caller. (The bettor can certainly make mistakes though, failing to bet all nut hands will result in a loss of EV. And once you consider card removal the bluff catchers will also no longer be truly EV neutral for the caller.)

In real games, generally only a fairly small fraction of decisions is actually EV neutral and there are plenty of opportunities to make mistakes against a GTO strategy. For any complex poker variant, achieving 0EV against a GTO strategy would likely be impossible for human players.

Quote:
Or a better way to rephrase that: if I play an unknown opponent for the very first time and I choose to play GTO until I observe his play and make the proper adjustments, will I be at 0 EV (and thus losing money due to rake) even if my opponent is the worst poker player that has ever existed?
No, see above.

Last edited by plexiq; 06-24-2019 at 03:49 AM.
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Old 06-24-2019, 04:39 AM   #3
Bogdan314
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Re: Which GTO strategies are EV-indifferent?

So when various poker books tell you that in order to find equilibrium strategies you need to solve the equations for indifference (I.e., Hero’s EV does not depend on the opponent’s actions), they are wrong!! It just happens that they are right for some simple spots (like the basic river bluff), but for more complex spots indifference will lead to incorrect results and you need different mathematical approaches to solving the Nash.
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Old 06-24-2019, 04:57 AM   #4
plexiq
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Re: Which GTO strategies are EV-indifferent?

That's correct, solving for indifference only works for simple toy games. More complex games are solved via Fictitious Play, CFRM and similar algorithms.
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Old 06-24-2019, 08:29 AM   #5
pucmo
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Re: Which GTO strategies are EV-indifferent?

Betting, raising, floating should break even vs. a GTO player but one can't call him all the way with a 3-high or so, and check it after he checks and expect not to lose.

Vs a combined pool, one is better to fold to aggression when one thinks it is legit. It won't lose vs. GTO aggression and one sees no indications that the opponent in the situation is more aggro than that.

Not too many regs and GTO players bluff or call light often enough in situations they think it will lose money. Especially in PLO, there is still some ball play left compared to NLH.
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