Abstract
In previous research an upper bound of 705 was proved on the number of moves in the 5T variant of the Morpion Solitaire game. We show a new upper bound of 485 moves. This is achieved in the following way: we encode Morpion 5T rules as a linear program and solve 126912 instances of this program on special octagonal boards. In order to show correctness of this method we analyze rules of the game and use a concept of a potential of a given position. By solving continuous-valued relaxations of linear programs on these boards, we obtain an upper bound of 586 moves. Further analysis of original, not relaxed, mixed-integer programs leads to an improvement of this bound to 485 moves. However, this is achieved at a significantly higher computational cost.
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
Notes
- 1.
- 2.
Regarding this and other records we refer to the webpage [1] for a detailed description and further references.
- 3.
This is a graph that plays a role in the proof of the 705 bound in [2].
- 4.
In fact, applying additional argumentation, in [2] is shown a bound of 141 moves.
- 5.
This proof does not rely on linear optimization. We just go over a finite list of octagons.
- 6.
In fact, a half of the instances required less than 100 s to reach the limit of 485 and 9 instances required the computation time longer than 18000 s.
References
Boyer, C.: Morpion solitaire (2008). http://www.morpionsolitaire.com
Demaine, E.D., Demaine, M.L., Langerman, A., Langerman, S.: Morpion solitaire. Theory Comput. Syst. 39(3), 439–453 (2006)
Gurobi Optimization, I.: Gurobi optimizer reference manual (2015). http://www.gurobi.com
Kawamura, A., Okamoto, T., Tatsu, Y., Uno, Y., Yamato, M.: Morpion solitaire 5d: a new upper bound 121 on the maximum score. In: CCCG (2013)
Michalewski, H., Nagrko, A., Pawlewicz, J.: Linear programs giving a new upper bound in the Morpion 5T game (2015). https://github.com/anagorko/morpion-lpp
Rosin, C.D.: Nested rollout policy adaptation for monte carlo tree search. In: IJCAI, pp. 649–654 (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Michalewski, H., Nagórko, A., Pawlewicz, J. (2016). 485 – A New Upper Bound for Morpion Solitaire. In: Cazenave, T., Winands, M., Edelkamp, S., Schiffel, S., Thielscher, M., Togelius, J. (eds) Computer Games. CGW GIGA 2015 2015. Communications in Computer and Information Science, vol 614. Springer, Cham. https://doi.org/10.1007/978-3-319-39402-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-39402-2_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-39401-5
Online ISBN: 978-3-319-39402-2
eBook Packages: Computer ScienceComputer Science (R0)