Abstract
In this paper we look at multi-player trick-taking card games that rely on obeying suits, which include Bridge, Hearts, Tarot, Skat, and many more. We propose mini-game solving in the suit factors of the game, and exemplify its application as a single-dummy or double-dummy analysis tool that restricts game play to either trump or non-trump suit cards. Such factored solvers are applicable to improve card selections of the declarer and the opponents, mainly in the middle game, and can be adjusted for optimizing the number of points or tricks to be made. While on the first glance projecting the game to one suit is an over-simplification, the partitioning approach into suit factors is a flexible and strong weapon, as it solves apparent problems arising in the phase transition of accessing static table information to dynamic play. Experimental results show that by using mini-game play, the strength of trick-taking Skat AIs can be improved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, Vol. 1–4. A K Peters (2001)
Bowling, M., Burch, N., Johanson, M., Tammelin, O.: Heads-up limit hold’em poker is solved. Commun. ACM 60(11), 81–88 (2017)
Cazenave, T.: Nested Monte-Carlo search. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 456–461 (2009)
Cazenave, T., Ventos, V.: The \(\alpha \)\(\mu \) search algorithm for the game of Bridge. CoRR, abs/1911.07960 (2019)
Edelkamp, S.: Challenging human supremacy in Skat. In: Symposium on Combinatorial Search (SOCS), pp. 52–60 (2019)
Edelkamp, S.: Representing and reducing uncertainty for enumerating the belief space to improve endgame play in Skat. In: European Conference on Artificial Intelligence (ECAI) (2020)
Furtak, T.M.: Symmetries and search in trick-taking card games. Ph.D. thesis, University of Alberta (2013)
Ginsberg, M.: Step toward an expert-level Bridge-playing program. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 584–589 (1999)
Gößl, R.: Der Skatfuchs - Gewinnen im Skatspiel mit Mathematische Methoden. Selfpublisher. Dämmig, Chemnitz, Available from the Author or via DSKV Altenburg (2019)
Keller, T., Kupferschmid, S.: Automatic bidding for the game of Skat. In: German Conference on Artificial Intelligence (KI), pp. 95–102 (2008)
Knorr, F.: Ein selbstkalibrierender Spieler für Skat. Master’s thesis, Universität Passau (2018)
Kupferschmid, S.: Entwicklung eines Double-Dummy Skat Solvers mit einer Anwendung für verdeckte Skatspiele. Master’s thesis, Albert-Ludwigs-Universität Freiburg (2003)
Kupferschmid, S., Helmert, M.: A Skat player based on Monte-Carlo simulation. In: Computers and Games, pp. 135–147 (2006)
Lasker, E.: Das verständige Kartenspiel. August Scherl Verlag, Berlin (1929)
Levy, D.N.L.: The million pound bridge program. In: Heuristic Programming in Artificial Intelligence (1989)
Long, J.R.: Search, inference and opponent modelling in an expert-caliber Skat player. Ph.D. thesis, University of Alberta (2011)
Müller, M.: Computer go as a sum of local games an application of combinatorial game theory. Ph.D. thesis, ETH Zürich (1995)
Müller, M.: Decomposition search: a combinatorial games approach to game tree search, with applications to solving Go endgames. In International Joint Conference on Artificial Intelligence (IJCAI), pp. 578–583 (1999)
Rebstock, D.: Improving AI in Skat through Human Imitation and Policy Based Inference. Master’s thesis (2019)
Rebstock, D., Solinas, C., Buro, M.: Learning policies from human data for Skat. CoRR, abs/1905.10907 (2019)
Rebstock, D., Solinas, C., Buro, M., Sturtevant, N.R.: Policy based inference in trick-taking card games. CoRR, abs/1905.10911 (2019)
Reinefeld, A., Marsland, T.A.: Enhanced iterative-deepening search. IEEE Trans. Pattern Anal. Mach. Intell. 16(7), 701–710 (1994)
Rosin, C.D.: Nested rollout policy adaptation for Monte Carlo tree search. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 649–654 (2011)
Schettler, F., Kirschbach, G.: Das große Skatvergnügen. Urania Verlag, Leipzig, Jena, Berlin (1988)
Schubert, H.: Das Skatspiel im Lichte der Wahrscheinlichkeitsrechnung. J. F. Richter, Hamburg (1887)
Silver, D.A.H., et al.: Mastering the game of Go with deep neural networks and tree search. Nature, 529, 484 (2016)
Silver, D., et al.: Mastering Chess and Shogi by self-play with a general reinforcement learning algorithm. Technical Report 1712.018, arxiv (2017)
Solinas, C.: Improving Determinized Search with Supervised Learning in Trick-Taking Card Games. Master’s thesis (2019)
Sturtevant, N.R., White, A.M.: Feature construction for reinforcement learning in hearts. In: Computers and Games, pp. 122–134 (2006)
Winands, M.H., Björnsson, Y., Saito, J.-T.: Monte-carlo tree search solver. Comput. Games 5131, 25–36 (2008)
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)
Acknowledgments
Thanks to Rainer Gößl for his invaluable help as a skat expert.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Edelkamp, S. (2020). Dynamic Play via Suit Factorization Search in Skat. In: Schmid, U., Klügl, F., Wolter, D. (eds) KI 2020: Advances in Artificial Intelligence. KI 2020. Lecture Notes in Computer Science(), vol 12325. Springer, Cham. https://doi.org/10.1007/978-3-030-58285-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-58285-2_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58284-5
Online ISBN: 978-3-030-58285-2
eBook Packages: Computer ScienceComputer Science (R0)