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MCS 2020: Monte Carlo Search pp 1–16Cite as

The \(\alpha \mu \) Search Algorithm for the Game of Bridge

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Part of the Communications in Computer and Information Science book series (CCIS,volume 1379)

Abstract

\(\alpha \mu \) is an anytime heuristic search algorithm for incomplete information games that assumes perfect information for the opponents. \(\alpha \mu \) addresses and if given enough time solves the strategy fusion and the non-locality problems encountered by Perfect Information Monte Carlo search (PIMC). Strategy fusion is due to PIMC playing different strategies in different worlds when it has to find a unique strategy for all the worlds. Non-locality is due to choosing locally optimal moves that are globally inferior. In this paper \(\alpha \mu \) is applied to the game of Bridge and outperforms PIMC.

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Notes

  1. 1.

    It is an acceptable simplification of the real scoring of Bridge. At Bridge, the declarer has to make six more tricks than the number in his contract.

References

  1. Brown, N., Sandholm, T.: Superhuman AI for multiplayer poker. Science 365(6456), 885–890 (2019)

    MathSciNet  CrossRef  Google Scholar 

  2. Buro, M., Long, J.R., Furtak, T., Sturtevant, N.: Improving state evaluation, inference, and search in trick-based card games. In: Twenty-First International Joint Conference on Artificial Intelligence (2009)

    Google Scholar 

  3. Cowling, P.I., Powley, E.J., Whitehouse, D.: Information set Monte Carlo tree search. IEEE Trans. Comput. Intell. AI Games 4(2), 120–143 (2012)

    CrossRef  Google Scholar 

  4. Frank, I., Basin, D.: Search in games with incomplete information: a case study using bridge card play. Artif. Intell. 100(1–2), 87–123 (1998)

    MathSciNet  CrossRef  Google Scholar 

  5. Frank, I., Basin, D.: A theoretical and empirical investigation of search in imperfect information games. Theoret. Comput. Sci. 252(1–2), 217–256 (2001)

    MathSciNet  CrossRef  Google Scholar 

  6. Frank, I., Basin, D.A., Matsubara, H.: Finding optimal strategies for imperfect information games. In: AAAI/IAAI, pp. 500–507 (1998)

    Google Scholar 

  7. Furtak, T., Buro, M.: Recursive Monte Carlo search for imperfect information games. In: 2013 IEEE Conference on Computational Intelligence in Games (CIG), pp. 1–8. IEEE (2013)

    Google Scholar 

  8. Ginsberg, M.L.: Partition search. In: Proceedings of the Thirteenth National Conference on Artificial Intelligence and Eighth Innovative Applications of Artificial Intelligence Conference, AAAI 1996, IAAI 1996, Portland, Oregon, USA, 4–8 August 1996, vol. 1, pp. 228–233 (1996). http://www.aaai.org/Library/AAAI/1996/aaai96-034.php

  9. Ginsberg, M.L.: GIB: imperfect information in a computationally challenging game. J. Artif. Intell. Res. 14, 303–358 (2001). https://doi.org/10.1613/jair.820

    CrossRef  MATH  Google Scholar 

  10. Haglund, B.: Search algorithms for a bridge double dummy solver. Technical report (2010)

    Google Scholar 

  11. Kupferschmid, S., Helmert, M.: A Skat player based on Monte-Carlo simulation. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M.J. (eds.) CG 2006. LNCS, vol. 4630, pp. 135–147. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75538-8_12

    CrossRef  Google Scholar 

  12. Levy, D.N.: The million pound bridge program. In: Heuristic Programming in Artificial Intelligence The First Computer Olympiad, pp. 95–103 (1989)

    Google Scholar 

  13. Lockhart, E., et al.: Computing approximate equilibria in sequential adversarial games by exploitability descent. arXiv preprint arXiv:1903.05614 (2019)

  14. Long, J.R., Sturtevant, N.R., Buro, M., Furtak, T.: Understanding the success of perfect information Monte Carlo sampling in game tree search. In: Twenty-Fourth AAAI Conference on Artificial Intelligence (2010)

    Google Scholar 

  15. Mahmood, Z., Grant, A., Sharif, O.: Bridge for Beginners: A Complete Course. Pavilion Books (2014)

    Google Scholar 

  16. Müller, M.: Partial order bounding: a new approach to evaluation in game tree search. Artif. Intell. 129(1–2), 279–311 (2001)

    MathSciNet  CrossRef  Google Scholar 

  17. Silver, D., et al.: A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science 362(6419), 1140–1144 (2018)

    MathSciNet  CrossRef  Google Scholar 

  18. Silver, D., et al.: Mastering the game of go without human knowledge. Nature 550(7676), 354 (2017)

    CrossRef  Google Scholar 

  19. Sturtevant, N., Zinkevich, M., Bowling, M.: Prob-max\(\hat{\,}\) n: Playing n-player games with opponent models. In: AAAI, vol. 6, pp. 1057–1063 (2006)

    Google Scholar 

  20. Sturtevant, N.R., White, A.M.: Feature construction for reinforcement learning in hearts. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M.J. (eds.) CG 2006. LNCS, vol. 4630, pp. 122–134. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75538-8_11

    CrossRef  Google Scholar 

  21. Ventos, V., Costel, Y., Teytaud, O., Ventos, S.T.: Boosting a bridge artificial intelligence. In: 2017 IEEE 29th International Conference on Tools with Artificial Intelligence (ICTAI), pp. 1280–1287. IEEE (2017)

    Google Scholar 

  22. Zinkevich, M., Johanson, M., Bowling, M., Piccione, C.: Regret minimization in games with incomplete information. In: Advances in Neural Information Processing Systems, pp. 1729–1736 (2008)

    Google Scholar 

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Acknowledgment

Thanks to Alexis Rimbaud for explaining me how to use the solver of Bo Haglund and to Bo Haglund for his Double Dummy Solver.

Author information

Authors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, PSL, CNRS, Paris, France

    Tristan Cazenave

  2. NUKKAI, Paris, France

    Véronique Ventos

Authors
  1. Tristan Cazenave
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  2. Véronique Ventos
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Corresponding author

Correspondence to Tristan Cazenave .

Editor information

Editors and Affiliations

  1. Université Paris-Dauphine, Paris, France

    Tristan Cazenave

  2. Facebook FAIR, Paris, France

    Olivier Teytaud

  3. Maastricht University, Maastricht, Limburg, The Netherlands

    Prof. Mark H. M. Winands

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Cazenave, T., Ventos, V. (2021). The \(\alpha \mu \) Search Algorithm for the Game of Bridge. In: Cazenave, T., Teytaud, O., Winands, M.H.M. (eds) Monte Carlo Search. MCS 2020. Communications in Computer and Information Science, vol 1379. Springer, Cham. https://doi.org/10.1007/978-3-030-89453-5_1

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  • DOI: https://doi.org/10.1007/978-3-030-89453-5_1

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