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Poker analysis tools

This code consists of two parts: an exact win probability calculator written in C++ and OpenCL, and Python code analyzing Nash equilibria. Here are details about each one:

Exact win/loss probabilities

The exact program computes the exact rational number probability of a win, loss, or tie given any pair of preflop hold'em hands. The code is written in a combination of C++ and OpenCL (with a bit of OpenMP to take advantage of multiple OpenCL devices). The core routine is a vectorized, branch free function that takes a 7 card hand represented as a bit set and uses bit twiddling to check for the various poker hands (straights, flushes, pairs, etc.).

Computing the entire table of win probabilities for all pairs of preflop hands takes around 5 minutes on a recent machine. For convenience (and regression testing) the results are included as exact.txt.


To build exact, run


Currently the Makefile is specific to Mac OS X, but this can easily be fixed. The only dependencies are OpenCL and OpenMP. On Mac this means 10.6 or later is required.

To rebuild the table of exact probabilities from scratch, run

make exact.txt

which does

time ./exact all > exact.txt

Other ways to invoke exact include

./exact           # print usage information
./exact hands     # print the list of two card hold'em hands
./exact test      # run regression tests
./exact some 100  # compute win/loss/tie probabilities for 100 random pairs of hands

Nash equilibria

The heads-up Python script computes Nash equilibria for an extremely simplified hold'em game with the following rules:

  1. There are two players, Alice and Bob.
  2. Bob posts a $1 blind.
  3. Alice either folds or raises a fixed amount b, for a total bet of $1+b.
  4. Bob either calls or folds.

To emphasize, the bet amount b is frozen in advance; Alice does not get to choose it.


heads-up has the following dependencies

On a Mac, these can be obtained through MacPorts via

sudo port install py26-numpy py26-scipy py26-matplotlib py26-cvxopt

cvxopt is GPL, so we isolate the LP solver interface inside the cvxopt script. Thus, the cvxopt script is GPL, but the rest of the code is BSD.

Update: In order to take advantage of the exact probabilities provided by exact, heads-up uses a fixed precision rational number dtype that I wrote for numpy. Unfortunately, this uncovered several bugs in numpy. Therefore, in order to use heads-up, you'll need to get numpy from my temporary fork here:

These changes should be incorporated in the main numpy git repo fairly soon.


Here are some example ways to use heads-up:

./heads-up -h                    # print usage information
./heads-up -b 2                  # determine the Nash equilibrium for bet level 2
./heads-up --plot -b 10 -n 100   # plot Alice's equity for b = 0 to 10
./heads-up --max -b 10           # find the bet level that maximizes Alice's equity


Want to contribute? Great! The Nash equilibrium computation could be generalized in many different ways, and exact (which is already almost entirely an exercise in pointless optimization) could always be optimized further. If you have changes you want to push back, either send pull requests or email to ask for commit access.


Investigations into simplified holdem poker







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