Monte Carlo Tree Search in Simultaneous Move Games with Applications to Goofspiel

  • Marc LanctotEmail author
  • Viliam Lisý
  • Mark H. M. Winands
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 408)


Monte Carlo Tree Search (MCTS) has become a widely popular sampled-based search algorithm for two-player games with perfect information. When actions are chosen simultaneously, players may need to mix between their strategies. In this paper, we discuss the adaptation of MCTS to simultaneous move games. We introduce a new algorithm, Online Outcome Sampling (OOS), that approaches a Nash equilibrium strategy over time. We compare both head-to-head performance and exploitability of several MCTS variants in Goofspiel. We show that regret matching and OOS perform best and that all variants produce less exploitable strategies than UCT.


Nash Equilibrium Decision Node Selection Policy Matrix Game Nash Equilibrium Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to thank Laurent Bartholdi for sharing his code for solving Goofspiel. We would also like to thank Olivier Teytaud for advice in optimizing Exp3. This work is partially funded by the Netherlands Organisation for Scientific Research (NWO) in the framework of the project Go4Nature, grant number 612.000.938 and the Czech Science Foundation, grant no. P202/12/2054.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Marc Lanctot
    • 1
    Email author
  • Viliam Lisý
    • 2
  • Mark H. M. Winands
    • 1
  1. 1.Department of Knowledge EngineeringMaastricht UniversityMaastrichtThe Netherlands
  2. 2.Department of Computer ScienceCzech Technical University in PraguePrahaCzech Republic

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