Abstract
We propose doppelkopf, a trick-taking card game with similarities to skat, as a benchmark problem for AI research. While skat has been extensively studied by the AI community in recent years, this is not true for doppelkopf. However, it has a substantially larger state space than skat and a unique key feature which distinguishes it from skat and other card games: players usually do not know with whom they play at the start of a game, figuring out the parties only in the process of playing.
Since its introduction in 2006, the UCT algorithm has been the dominating approach for solving games in AI research. It has notably achieved a playing strength comparable to good human players at playing go, but it has also shown good performance in card games like Klondike solitaire and skat. In this work, we adapt UCT to play doppelkopf and present an algorithm that generates random card assignments, used by the UCT algorithm for sampling. In our experiments, we discuss and evaluate different variants of the UCT algorithm, and we show that players based on UCT improve over simple baseline players and exhibit good card play behavior also when competing with a human player.
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References
Deutscher Doppelkopf Verband. http://www.doko-verband.de (Online; in German; accessed April 28, 2015)
Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Machine Learning 47, 235–256 (2002)
Bezáková, I., Štefankovič, D., Vazirani, V.V., Vigoda, E.: Accelerating simulated annealing for the permanent and combinatorial counting problems. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 900–907. SODA 2006. ACM (2006)
Bjarnason, R., Fern, A., Tadepalli, P.: Lower bounding Klondike solitaire with Monte-Carlo planning. In: Gerevini, A., Howe, A., Cesta, A., Refanidis, I. (eds.) Proceedings of the Nineteenth International Conference on Automated Planning and Scheduling, ICAPS 2009, pp. 26–33. AAAI Press (2009)
Buro, M., Long, J.R., Furtak, T., Sturtevant, N.: Improving state evaluation, inference, and search in trick-based card games. In: Boutilier, C. (ed.) Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI 2009), pp. 1407–1413 (2009)
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. The MIT Press (1990)
Edelkamp, S., Federholzner, T., Kissmann, P.: Searching with partial belief states in general games with incomplete information. In: Glimm, B., Krüger, A. (eds.) KI 2012. LNCS, vol. 7526, pp. 25–36. Springer, Heidelberg (2012)
Eyerich, P., Keller, T., Helmert, M.: High-quality policies for the Canadian traveler’s problem. In: Fox, M., Poole, D. (eds.) Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2010, pp. 51–58. AAAI Press (2010)
Finnsson, H., Björnsson, Y.: Simulation-based approach to general game playing. In: Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, pp. 259–264. AAAI Press (2008)
Furtak, T., Buro, M.: Using payoff-similarity to speed up search. In: Walsh [25], pp. 534–539
Furtak, T., Buro, M.: Recursive Monte Carlo search for imperfect information games. In: 2013 IEEE Conference on Computational Intelligence in Games (CIG), Niagara Falls, ON, Canada, August 11–13, pp. 1–8. IEEE (2013)
Gelly, S., Wang, Y., Munos, R., Teytaud, O.: Modification of UCT with Patterns in Monte-Carlo Go. Tech. Rep. 6062, INRIA (November 2006)
Keller, T., Eyerich, P.: PROST: Probabilistic planning based on UCT. In: McCluskey, L., Williams, B., Silva, J.R., Bonet, B. (eds.) Proceedings of the Twenty-Second International Conference on Automated Planning and Scheduling (ICAPS 2012), pp. 119–127. AAAI Press (2012)
Keller, T., Kupferschmid, S.: Automatic bidding for the game of skat. In: Dengel, A.R., Berns, K., Breuel, T.M., Bomarius, F., Roth-Berghofer, T.R. (eds.) KI 2008. LNCS (LNAI), vol. 5243, pp. 95–102. Springer, Heidelberg (2008)
Kocsis, L., Szepesvári, C.: Bandit based Monte-Carlo planning. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) ECML 2006. LNCS (LNAI), vol. 4212, pp. 282–293. Springer, Heidelberg (2006)
Kupferschmid, S., Helmert, M.: A Skat player based on Monte Carlo simulation. In: Proceedings of the Fifth International Conference on Computers and Games, CG 2006, pp. 135–147 (2006)
Long, J.R., Buro, M.: Real-time opponent modeling in trick-taking card games. In: Walsh [25], pp. 617–622
Russell, S., Norvig, P.: Artificial Intelligence – A Modern Approach. Prentice Hall (2003)
Schäfer, J.: The UCT Algorithm Applied to Games with Imperfect Information. Master’s thesis, Otto-von-Guericke-Universität Magdeburg (July 2008)
Schofield, M.J., Cerexhe, T.J., Thielscher, M.: Hyperplay: A solution to general game playing with imperfect information. In: Hoffmann, J., Selman, B. (eds.) Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, AAAI 2012, pp. 1606–1612. AAAI Press (2012)
Schofield, M.J., Thielscher, M.: Lifting model sampling for general game playing to incomplete-information models. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, AAAI 2015, pp. 3585–3591. AAAI Press (2015)
Sievers, S.: Implementation of the UCT Algorithm for Doppelkopf. Master’s thesis, University of Freiburg, Germany (April 2012)
Sturtevant, N.R.: An analysis of UCT in multi-player games. In: van den Herik, H.J., Xu, X., Ma, Z., Winands, M.H.M. (eds.) CG 2008. LNCS, vol. 5131, pp. 37–49. Springer, Heidelberg (2008)
Valiant, L.G.: The complexity of computing the permanent. Theoretical Computer Science 8, 189–201 (1979)
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Sievers, S., Helmert, M. (2015). A Doppelkopf Player Based on UCT. In: Hölldobler, S., , Peñaloza, R., Rudolph, S. (eds) KI 2015: Advances in Artificial Intelligence. KI 2015. Lecture Notes in Computer Science(), vol 9324. Springer, Cham. https://doi.org/10.1007/978-3-319-24489-1_12
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DOI: https://doi.org/10.1007/978-3-319-24489-1_12
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