The Feasibility of Deep Counterfactual Regret Minimisation for Trading Card Games

Counterfactual Regret Minimisation (CFR) is the leading technique for approximating Nash Equilibria in imperfect information games. It was an integral part of Libratus, the first AI to beat professionals at Heads-up No-limit Texas-holdem Poker. However, current implementations of CFR rely on a tabular game representation and hand-crafted abstractions to reduce the state space, limiting their ability to scale to larger and more complex games. More recently, techniques such as Deep CFR (DCFR), Variance-Reduction Monte-carlo CFR (VR-MCCFR) and Double Neural CFR (DN-CFR) have been proposed to alleviate CFR's shortcomings by both learning the game state and reducing the overall computation through aggressive sampling. To properly test potential performance improvements, a class of game harder than Poker is required, especially considering current agents are already at superhuman levels. The trading card game Yu-Gi-Oh was selected as its game interactions are highly sophisticated, the overall state space is many orders of magnitude higher than Poker and there are existing simulator implementations. It also introduces the concept of a meta-strategy, where a player strategically chooses a specific set of cards from a large pool to play. Overall, this work seeks to evaluate whether newer CFR methods scale to harder games by comparing the relative performance of existing techniques such as regular CFR and Heuristic agents to the newer DCFR whilst also seeing if these agents can provide automated evaluation of meta-strategies.