# Has the game of texas hold em poker been beaten?

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

• 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")
– dlev
Aug 5 at 19:36
• "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. Aug 5 at 19:46
• 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. Aug 5 at 19:49
• @GregMartin: Lying and intentionally being inconsistent are perfectly logical $-$ indeed, essential $-$ strategies in poker. So your comment doesn't make much sense. Aug 5 at 22:49
• 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. Aug 5 at 22:52

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.
• No.${}{}{}{}{}{}$ Aug 5 at 23:42