| From the 40 s of last century,Turing,Shannon and other pioneers of computing science have come to explore the chess machine game to recent years,Deep blue,Alpha Go has induced national attention,machine games have long been touchstone to validate computational theory and artificial intelligence theory.Imperfect information game refers to only part of the information can be seen for the game participants,compared to perfect information game,no doubt increasing the complexity of the study.And the study of the imperfect information game can be applied to a wide range of fields,such as military game,commercial competition,financial regulation and so on.Texas Hold’em is a poker game that is popular all over the world.It is regarded as a very strategic with incompletely information,random events and partial information observable.This makes it a testbed of artificial intelligence research.2015 Canadian Bowling and other scientists improve the CFR algorithm to solve the heads-up limit Texas Hold’em poker,becoming a milestone of imperfect information machine game field.But CFR algorithm still has two problems,firstly CFR algorithm is an offline self-play algorithm,cannot be calculated in the actual game.Secondly CFR algorithm only guarantees the approximation Nash equilibrium strategy in the two player zero-sum game,whether it is applicable to multiplayer game is still unknown.In this paper,the online CFR algorithm and the application of CFR algorithm to the multi-player game are discussed.Aiming at the problem that CFR is not suitable for real-time scenes,an online CFR algorithm is proposed.The calculation and iteration of the CFR algorithm are analyzed,and the difference between offline and online is compared.The strategy of CFR algorithm is used to estimate the opponent’s strategy,and the counterfactual regret value of the CFR algorithm is obtained.As a result,in Annual Computer Poker Competition 2016,our agent got a eighth place in heads-up no-limit Texas Hold’em poker.Aiming at the problem that CFR algorithm is only used in two player zero-sum game,this paper puts forward the solution of CFR algorithm applied to 3-player Kuhn poker.The CFR algorithm converges to the approximate Nash equilibrium in a 3-player zero-sum game is proved by analyzing the proof that the CFR algorithm converges to the approximate Nash equilibrium in the two player zero-sum game.By analyzing the difference between Nash equilibrium and Minimax theorem in game theory,this paper proposes the solution of CFR algorithm in three-player game,namely,after calculating the approximate Nash equilibrium strategy offline with the original CFR algorithm,according to the opponent’s action for real-time changes use online CFR algorithm in order to better use the opponent’s weaknesses and increase our gains.The experiments have been carried out on the ACPC platform and have verified the effectiveness of the algorithm. |
