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Toward Solving “EinStein würfelt nicht!”

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Advances in Computer Games (ACG 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10664))

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Abstract

“EinStein würfelt nicht!” is a simple board game, played usually on a \(5\times 5\) board with 6 stones per player and a die. Many computer programs have been developed for this game, but in this research, we compute for the first time an exact solution to some instances of the game, with fewer stones on smaller (or larger) boards. When the rules allow the players to choose their initial configuration, a solution consists in computing the exact optimal winning chances of the players for any initial configuration, and then computing the resulting Nash Equilibrium between the two players. Our most difficult result is the solution for a \(4\times 4\) board with 6 stones per player.

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Notes

  1. 1.

    For brevity, we use “he” and “his” whenever “he or she” and “his or her” are meant.

  2. 2.

    For example, let us assume that a player still has stones 1, 5, and 6 on the board. Given a die value of 1, 5, or 6, the player must move the corresponding stone. With a die value of 2, 3, or 4, he can choose to move either stone 1 or stone 5.

  3. 3.

    After capturing the stone 2, a die value of 2 lets the player decide to move either stone 1 or stone 3. Such choice does not exist if stone 1 or 3 is captured.

References

  1. Althöfer, I.: On the origins of “EinStein würfelt nicht!” (2011). http://www.althofer.de/origins-of-ewn.html

  2. Bonnet, F., Viennot, S.: Analytical solution for “EinStein würfelt nicht!” with one stone. In: Winands, M., et al. (eds.) ACG 2017. LNCS, vol. 10664, pp. 1–12. Springer, Cham (2017)

    Google Scholar 

  3. Schäfer, A.: Rock’n’Roll, A Cross-Platform Engine for the Board Game “EinStein würfelt nicht!”. Student Research Project, Friedrich Schiller University Jena (2005)

    Google Scholar 

  4. Lorentz, R.J.: An MCTS program to play EinStein Würfelt Nicht!. In: van den Herik, H.J., Plaat, A. (eds.) ACG 2011. LNCS, vol. 7168, pp. 52–59. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31866-5_5

    Chapter  Google Scholar 

  5. Turner, W.: Einstein würfelt nicht – an analysis of endgame play. ICGA J. 35, 94–102 (2012)

    Article  Google Scholar 

  6. Hartisch, M.: Impact of rounding during retrograde analysis for a game with chance nodes: Karl’s race as a test case. ICGA J. 38, 81–93 (2015)

    Article  Google Scholar 

  7. Bouton, C.L.: Nim, a game with a complete mathematical theory. Ann. Math. 3, 35–39 (1901)

    Article  MathSciNet  MATH  Google Scholar 

  8. Allis, V.: A knowledge-based approach of connect-four. Master’s thesis, Vrije Universiteit (1988)

    Google Scholar 

  9. Schaeffer, J., Burch, N., Björnsson, Y., Kishimoto, A., Müller, M., Lake, R., Lu, P., Steve, S.: Checkers is solved. Science 317, 1518–1522 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. van den Herik, H., Uiterwijk, J.W., van Rijswijck, J.: Games solved: now and in the future. Artif. Intell. 134, 277–311 (2002)

    Article  MATH  Google Scholar 

  11. Nash, J.F.: Non-cooperative games. Ph.D. thesis, Princeton University (1950)

    Google Scholar 

  12. Bonnet, F., Viennot, S.: Nash equilibrium in mastermind. In: Plaat, A., Kosters, W., van den Herik, J. (eds.) CG 2016. LNCS, vol. 10068, pp. 115–128. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-50935-8_11

    Chapter  Google Scholar 

  13. Michie, D.: Game-playing and game-learning automata. In: Advances in Programming and Non-Numerical Computation, pp. 183–200. Pergamon Press Ltd. (1966)

    Google Scholar 

  14. Ballard, B.W.: The *-minimax search procedure for trees containing chance nodes. Artif. Intell. 21, 327–350 (1983)

    Article  MATH  Google Scholar 

  15. Hauk, T., Buro, M., Schaeffer, J.: Rediscovering *-Minimax search. In: van den Herik, H.J., Björnsson, Y., Netanyahu, N.S. (eds.) CG 2004. LNCS, vol. 3846, pp. 35–50. Springer, Heidelberg (2006). https://doi.org/10.1007/11674399_3

    Chapter  Google Scholar 

  16. MPI: A Message-Passing Interface Standard. http://mpi-forum.org/

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Acknowledgments

This work is partially supported by JSPS KAKENHI Grant (C)(JP15K00183) and (JP15K00189) and Japan Science and Technology Agency, CREST (JPMJCR1404) and Infrastructure Development for Promoting International S&T Cooperation and Project for Establishing a Nationwide Practical Education Network for IT Human Resources Development, Education Network for Practical Information Technologies. We would also like to thank the anonymous reviewers for their comments that helped us improve the paper.

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Authors and Affiliations

  1. Graduate School of Engineering, Osaka University, Suita, Japan

    François Bonnet

  2. Graduate School of Advanced Science and Technology, JAIST, Nomi, Japan

    Simon Viennot

Authors
  1. François Bonnet
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  2. Simon Viennot
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Corresponding authors

Correspondence to François Bonnet or Simon Viennot .

Editor information

Editors and Affiliations

  1. Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, Limburg, The Netherlands

    Mark H.M. Winands

  2. Leiden Centre of Data Science, Leiden University, Leiden, Zuid-Holland, The Netherlands

    H. Jaap van den Herik

  3. Leiden Institute of Advanced Computer Science, Leiden University, Leiden, Zuid-Holland, The Netherlands

    Walter A. Kosters

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Bonnet, F., Viennot, S. (2017). Toward Solving “EinStein würfelt nicht!”. In: Winands, M., van den Herik, H., Kosters, W. (eds) Advances in Computer Games. ACG 2017. Lecture Notes in Computer Science(), vol 10664. Springer, Cham. https://doi.org/10.1007/978-3-319-71649-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-71649-7_2

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