This repo serves as a didactic example of Counterfactual Regret Minimization in action. the CFR algorithm is used to find a nash equilibrium in 2 player zero sum imperfect information games.

The game that was used in this example is Kuhn Poker. Kuhn Poker has a long history in game theory literature, and has well known theoretical results, which makes it easy to verify that the code works. For more information on Kuhn Poker, see here.

The details of CFR, and a description of how it applies to Kuhn Poker, were adopted from this very excellent paper, although all the code is original.

This repo contains two seperate algorithms that converge to a Nash Equilibrium. The first algorithm considers a modifed version of Kuhn Poker in normal form. The normal form version is of course strategically identical to the standard sequential form, but allows us to calculate a Nash Equilibrium with simple regret matching. The second algorithm considers the standard version of Kuhn Poker, and finds a Nash Equilibrium using the CFR algorithm.

It is a well known theoretical result that in an equilibrium strategy, player one has an expected value of -1/18 per hand (or about -.055). In a small number of iterations, both the normal form and sequential form algorithms converge to this value, confirming the correctness of the implementation

To run the code, invoke one of:

python normal_form.py <num_iterations>

python sequential_form.py <num_iterations>