Monte-Carlo Tree Search for the Game of "7 Wonders"

Monte-Carlo Tree Search, and in particular with the Upper Confidence Bounds formula, has provided large improvements for AI in numerous games, particularly in Go, Hex, Havannah, Amazons and Breakthrough. In this work we study this algorithm on a more complex game, the game of "7 Wonders". This card game gathers together several known challenging properties, such as hidden information, multi-player and stochasticity. It also includes an inter-player trading system that induces a combinatorial search to decide which decisions are legal. Moreover, it is difficult to hand-craft an efficient evaluation function since the card values are heavily dependent upon the stage of the game and upon the other player decisions. We show that, in spite of the fact that "7 Wonders" is apparently not so related to classic abstract games, many known results still hold.

[1]  Mark H. M. Winands,et al.  Evaluation Function Based Monte-Carlo LOA , 2009, ACG.

[2]  Richard J. Lorentz Amazons Discover Monte-Carlo , 2008, Computers and Games.

[3]  H. Jaap van den Herik,et al.  Progressive Strategies for Monte-Carlo Tree Search , 2008 .

[4]  Rémi Coulom,et al.  Efficient Selectivity and Backup Operators in Monte-Carlo Tree Search , 2006, Computers and Games.

[5]  Matthew L. Ginsberg,et al.  GIB: Imperfect Information in a Computationally Challenging Game , 2011, J. Artif. Intell. Res..

[6]  Bruno Bouzy,et al.  Monte-Carlo strategies for computer Go , 2006 .

[7]  Peter I. Cowling,et al.  Determinization and information set Monte Carlo Tree Search for the card game Dou Di Zhu , 2011, 2011 IEEE Conference on Computational Intelligence and Games (CIG'11).

[8]  David Silver,et al.  Combining online and offline knowledge in UCT , 2007, ICML '07.

[9]  Martin Müller,et al.  Fuego—An Open-Source Framework for Board Games and Go Engine Based on Monte Carlo Tree Search , 2010, IEEE Transactions on Computational Intelligence and AI in Games.

[10]  Neil D. Lawrence,et al.  Missing Data in Kernel PCA , 2006, ECML.

[11]  Ryan B. Hayward,et al.  Monte Carlo Tree Search in Hex , 2010, IEEE Transactions on Computational Intelligence and AI in Games.

[12]  Simon M. Lucas,et al.  A Survey of Monte Carlo Tree Search Methods , 2012, IEEE Transactions on Computational Intelligence and AI in Games.

[13]  Rémi Coulom,et al.  Computing "Elo Ratings" of Move Patterns in the Game of Go , 2007, J. Int. Comput. Games Assoc..

[14]  Olivier Teytaud,et al.  On the Parallelization of Monte-Carlo planning , 2008, ICINCO 2008.

[15]  Pieter Spronck,et al.  Monte-Carlo Tree Search in Settlers of Catan , 2009, ACG.

[16]  Michael Pfeiffer,et al.  Reinforcement Learning of Strategies for Settlers of Catan , 2004 .

[17]  Alan Fern,et al.  Lower Bounding Klondike Solitaire with Monte-Carlo Planning , 2009, ICAPS.

[18]  Tristan Cazenave Monte-Carlo Kakuro , 2009, ACG.

[19]  Olivier Teytaud,et al.  Adding Expert Knowledge and Exploration in Monte-Carlo Tree Search , 2009, ACG.

[20]  Ransom K. Winder Methods for approximating value functions for the Dominion card game , 2014, Evol. Intell..

[21]  Jean-Yves Audibert,et al.  Infinitely many-armed bandits , 2008, NIPS 2008.

[22]  Olivier Teytaud,et al.  Creating an Upper-Confidence-Tree Program for Havannah , 2009, ACG.

[23]  Rémi Munos,et al.  Algorithms for Infinitely Many-Armed Bandits , 2008, NIPS.

[24]  Zongmin Ma,et al.  Computers and Games , 2008, Lecture Notes in Computer Science.

[25]  Csaba Szepesvári,et al.  Bandit Based Monte-Carlo Planning , 2006, ECML.