Evaluating the performance of a team consisting of an advanced agent and a less advanced agent in the game Manille : A comparison of agents trained using the CFR algorithm with and without abstractions.

Abstract: Making artificial intelligence (AI) algorithms solve games has always been an interesting benchmark of AI research. Perfect information games like Chess can be played on a level beyond human capabilities. However less progress has been made in solving imperfect information games like Poker or Manille where some of the information about the game is private. Counterfactual regret minimization (CFR) is an algorithm that can be applied to zero sum imperfect information games. An example of a successful implementation of CFR is the agent Libratus that was able to beat top professional players in the game Texas Hold’em Poker. The CFR algorithm stores a large amount of information states that holds information about different points in the game. These information states are traversed by the CFR algorithm to solve the game, but these states can become large in terms of computer memory and storage space. Abstractions can be applied that limits the amount of information stored in each state. An example of an abstraction could be removing part of the game history. This results in less memory needed to store all information sets, but gives the agents less information to base their decisions on, which may impact performance. In this study teams of two players in a 12 card version of the game Manille have been evaluated. This was done by comparing the performance of different combinations of an advanced agent and a less advanced agent. The advanced agent has no abstractions applied and remembers all the cards played, while the less advanced agent only remembers the cards in the current trick, which are the cards visible on the table. The results of this study confirm that a team of two advanced players perform better than a team of less advanced players. But when evaluating a team of an advanced player and a less advanced player, it was found that the team would perform better when the less advanced player plays first and the advanced player plays second in the team.