Toward Solving “EinStein würfelt nicht!”
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“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.
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.
- 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
- 8.Allis, V.: A knowledge-based approach of connect-four. Master’s thesis, Vrije Universiteit (1988)Google Scholar
- 11.Nash, J.F.: Non-cooperative games. Ph.D. thesis, Princeton University (1950)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
- 16.MPI: A Message-Passing Interface Standard. http://mpi-forum.org/