Abstract
This paper deals with a nondeterministic game based on die rolls and on the ”stop or continue” principle: Pickomino. During his turn, each participant has to make the best decisions first to choose the dice to keep, then to choose between continuing or stopping depending on the previous rolls and on the available resources. Markov Decision Processes (MDPs) offer the formal framework to model this game. The two main problems are first to determine the set of states, then to compute the transition probabilities.
We provide in this paper original solutions to both problems: we provide (1) a compact representation of states and (2) a constructive method to compute the probability distributions, based on the partitioning of the space of roll results depending on a set of marked values. Finally, we show the efficiency of the proposed method through numerous experimental results: it turns out to be impressive compared to previous programs we developed.
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
Preview
Unable to display preview. Download preview PDF.
References
Campbell, M., Hoane Jr., A.J., Hsu, F.h.: Deep Blue. Deep Blue. Artificial Intelligence 134(1-2), 57–83 (2002)
Schaeffer, J., Björnsson, Y., Burch, N., Kishimoto, A., Müler, M., Lake, R., Lu, P., Sutphen, S.: Solving checkers. In: Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 292–297 (2005)
Berliner, H.J.: Backgammon computer program beats world champion. Artificial Intelligence 14(2) (1980)
Tesauro, G.: Programming backgammon using self-teaching neural nets. Artificial Intelligence 134(1-2) (2002)
Sheppard, B.: World-championship-caliber scrabble. Artificial Intelligence 134(1-2), 241–275 (2002)
Chetcuti-Sperandio, N., Delorme, F., Lagrue, S., Stackowiack, D.: Determination and evaluation of efficient strategies for a stop or roll dice game: Heckmeck am bratwurmeck (pickomino). In: IEEE Symposium on Computational Intelligence and Games (CIG 2008), pp. 175–182 (2008)
Bellman, R.E.: Dynamic Programming. Princeton University Press, Princeton (1957)
Bertsekas, D.P.: Dynamic Programming: Deterministic and Stochastic Models. Prentice-Hall, Englewood Cliffs (1987)
Putterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Chichester (1994)
Brettspielwelt website, http://www.zoch-verlag.com/nc/en/games/chicken-world/heckmeck-am-bratwurmeck.html
Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cardon, S., Chetcuti-Sperandio, N., Delorme, F., Lagrue, S. (2011). A Markovian Process Modeling for Pickomino. In: van den Herik, H.J., Iida, H., Plaat, A. (eds) Computers and Games. CG 2010. Lecture Notes in Computer Science, vol 6515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17928-0_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-17928-0_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17927-3
Online ISBN: 978-3-642-17928-0
eBook Packages: Computer ScienceComputer Science (R0)