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I am no mathematician, I guess this is obvious. I hope this question is appropriate.

So, I know that in poker the opponents psychology matter, but imagine that you are playing against a perfectly logical foe - is there an algorithm that can be followed in order to play the absolute optimal game against a mindless foe?

I know that in math, a beaten game means a game that has all the odds of all the different situations figured out, as I understand it

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    $\begingroup$ While it hasn't been solved in the same way Checkers has, there is some very strong poker playing software: en.wikipedia.org/wiki/Libratus As well, it is possible to apply game theory to heads up NL holdem such that you can play an "unexploitable" strategy (though only if certain inputs hold): en.everybodywiki.com/Poker_solver You can also find out more just be searching "GTO poker" (GTO => "game-theory optimal") $\endgroup$
    – dlev
    Commented Aug 5, 2022 at 19:36
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    $\begingroup$ "Perfectly logical" and "mindless" don't mean the same thing; and neither one is a good model for even a mediocre poker player, because lying and intentionally being inconsistent is an integral part of the game. $\endgroup$
    – Greg Martin
    Commented Aug 5, 2022 at 19:46
  • $\begingroup$ ok, I mean betting according to chance of winning and ignoring opponents actions. Perfectly logical as in logic riddles, when an "actor" always does the thing that has a slightly bigger chance of success. $\endgroup$
    – Nikolai Frolov
    Commented Aug 5, 2022 at 19:49
  • $\begingroup$ @GregMartin: Lying and intentionally being inconsistent are perfectly logical $-$ indeed, essential $-$ strategies in poker. So your comment doesn't make much sense. $\endgroup$
    – TonyK
    Commented Aug 5, 2022 at 22:49
  • $\begingroup$ Here’s my impression: No one has figured out an optimal poker strategy. So poker has not been “solved” in that sense. I’m sure that some simplified versions of poker have been solved. I believe AI algorithms have learned to play poker at a superhuman level, but they couldn’t explain why they make the moves they make. $\endgroup$
    – littleO
    Commented Aug 5, 2022 at 22:52

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If you are playing against a single opponent ("heads-up"), then there is indeed an algorithm that will guarantee you non-negative expected winnings. This is simply because of the symmetry of the game $-$ you are playing by the same rules as your opponent. Of course, your opponent can follow the same strategy, which means that your expected winnings will be zero.

But:

  1. Such a strategy will inevitably involve making random choices about whether to bluff, call etc. So it might not agree with your idea of what constitutes a strategy.
  2. Computing such a perfect strategy is beyond current technology. There are programs that play excellent heads-up poker, but I don't think any of them claim to play the perfect game.
  3. As soon as a third player joins the table, there can be no such guaranteed strategy, because the other two players may (consciously or unconsciously) collude against you; and then you will have almost no chance of coming out ahead.
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  • $\begingroup$ is there a way, if for example playing against 5 players, to always have an exact percentage of chance to win, so you can know what amount to bet, regarding that exact percentage to win? $\endgroup$
    – Nikolai Frolov
    Commented Aug 5, 2022 at 23:15
  • $\begingroup$ No.${}{}{}{}{}{}$ $\endgroup$
    – TonyK
    Commented Aug 5, 2022 at 23:42

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