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not sure if SO is the right place to ask this question, but I am gonna try anyway.

I am playing with neural networks and poker and I am facing a problem that is how to evaluate different players. Poker variant I am talking about is No-limit holdem for 6 players. Is there a better way to find out exact (or atleast somehow exact) winrate of players, than to simulate X (ranging from hundreds of thousands to milions) hands? Problem is that simulating milion of hands is kinda time-consuming, since each move means calculating neural network output. Generating all possible hand and board options doesn't seem like a good idea, since there is a LOT of them.

Is it possible to do it better?

user3048782
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  • Are these trials merely one-shot hands? In other words, the model doesn't take into account the playing style of the opponents, history, etc. ? Since virtually *all* of the advantage in poker programs is from inter-player strategy, I'm not yet sure what you mean by "winrate" [sic]. – Prune Mar 16 '18 at 18:35
  • Sorry, should have clarified it. What I mean by that is how much chips each player wins / loses each hand on average. So if player A wins 1000 chips after playing 100 hands, his winrate is 10chips per hand – user3048782 Mar 16 '18 at 18:39

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Summary:

  • No way will you want to directly compute this metric.
  • You will not be able to simulate all possible hands with current computing power.

The main problem is the quantity of variables: not only do you have six two-card hands and five sequential up-cards, but you have to deal with five foreign betting strategies. Unless you know all the details of those strategies, you have no way of directly computing the probability-averaged outcome.

Assuming that you also have adaptive strategies, those adaptations add even more complexity to the computations, such that a 100-hand trial must consider the sequence of hands played -- a "big bang" of combinatorial explosion.

Thus, we seem to be stuck with Monte Carlo methods (e.g. random sampling). Experiment with a few trials to see how many you need to get a reasonable evaluation for your needs. Do you really need 10^6 hands played to do that, or will 100 or 1000 hands give you a good approximation? If you're just trying to train and tune your model, I'm guessing that 20 trials of 100 hands each will be more than you need to get 99% accuracy of your rate of return (win rate).

Prune
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