Naive_Poker_Calculator

A naive, brute-force/Monte-Carlo Texas Hold 'Em poker odds calculator written in Cython. Written so that I could learn Cython. Surprisingly fun way to learn about code optimisation.

Comes with a little GUI to calculate your hand odds like so:

Exhaustively calculates Turn and River cards. Uses Monte-Carlo to calculate the Preflop and Flop odds.

Calculating flop odds on a Intel Core i7-4790 @ 3.60GHz for different numbers of samples:

Exhaustive flop-odds calculation (1,070,190 hands) takes 1.94s.

Files

• Cython_compiler.py: Used to compile the cython code. Run it like this:

python cython_test_compiler.py build_ext --inplace

• Cython_Poker_Calculator.pyx: cython file which contains the functions.

• Poker_GUI.py: file which generates the GUI in wxPython.

How It Works

Every combination of 7 cards is made into a 4*13 (4 suits, 13 cards) matrix, 1's for cards, 0's otherwise.

For example, for a 7 card hand (2 pocket and 5 table cards):

>>> hand = ["2s", "th", "js", "qh", "kh", "ah", "td"]

would give a matrix:

array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1],
       [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]], dtype=int8)

A number of tests are then performed to give a score tuple. The above matrix would give a score tuple of:

>>> SCOREpyx(hand)
(5, 12)

where the 5 refers to a straight, and 12 indicates that the straight is to the ace.

When calculating flop odds, there are 2 known hole cards, and 3 known table cards. There are therefore 47C2 (1081) combinations of river and turn cards, and a further 45C2 (980) combinations of opponents cards, to give 1,070,190 total possible combinations.

For every possible combination of opponents and table cards, a score matirx is calculated, and compared to your hand.

Monte-Carlo Simulation

50,000 random hand + flop scenarios were exhaustively calculated to get a true win percentage. For these same trial hands, 75, 50, 25, 10, 5 and 1 thousand random combination of remaining board and opponent hands were calculated. The ratio of true win % to calculated win % gave distributions which are plotted above.

What I found nice was that a random selection of 1,000 combinations of the hole and opponent hands gave fairly accurate results (95% of the values were within 8.3% of the true value).

Out of 50,000 trials, the worst errors were as follows:

# Hands	Max % Error
75k	3 %
50k	4.3 %
25k	5.7 %
10k	8.8 %
5k	12.5 %
1k	35 %

There is diminishing returns for increasing the number of random combinations.