Using Fictitious Play to Find Pseudo-optimal Solutions for Full-scale Poker

A pseudo-optimal solution to the poker variant, Two-Player Limit Texas Hold’em was developed and tested against existing world-class poker algorithms. Techniques used in creating the pseudo-optimal solution were able to simplify the problem from complexity from O(10^18) to O(10^7). To achieve this reduction, bucketing/grouping techniques were employed, as were methods replacing the chance nodes in the game tree; reducing it from a tree with millions of billions of terminal nodes, to a game tree with only a few thousand. When played in competition against several world-class algorithms, our algorithm displayed strong results, gaining and maintaining leads against each of the opponents it faced. Using proper abstraction techniques it is shown that we are able to succeed in approaching Nash Equilibria in complex game theoretical problems such as full-scale poker.