Optimal heads-up preflop holdem

These pages describe a computer program that finds the (or a) perfect strategy for two-player Texas Holdem if there is no betting after the flop.

The program followed a suggestion by Paul Hankin and was 'published' on my web pages in February 1999. Exactly-solved poker models go back quite a way (1950s and probably earlier), but the one presented here, though clearly still highly cut-down, is thought by some to capture enough of the game of Texas Holdem (the most popular version of poker played today) to be actually useful to serious players. As far as I know it is the first perfect play solution to two-player Texas Holdem with no betting after the flop.

This article by Nick Christenson, originally from twoplustwo magazine, has some very kind things to say about how influential this program may have been!

Things have moved on since 1999 in the field of academic poker studies, and there have been many academic papers (some even citing my program and notes) describing sophisticated exact and approximate solutions of versions of real-world poker. One interesting observation is that in no-limit poker, Jam/Fold strategies (either raise all-in or fold) can be very close to optimal. This is good news for theoreticians since Jam/Fold strategies are much more tractable to analyse than strategies that would involve many future betting rounds, but it is perhaps disappointing for poker players since it means that the game is (in some situations) nearly solved. This is an example of such a paper.

  • Edited version of original usenet article

    The program that produced these results can also be made to solve heads-up preflop holdem under different conditions, e.g. potlimit. To run it you need the following three files. After you've done that, follow the instructions in README. You will need gcc. It works under Linux/Unix, and will probably work under Windows (but I haven't tested this).

    README file (19k)
    Program file (17k)
    Data file (165k)

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