# Morpion Solitaire

@article{Demaine2005MorpionS,
title={Morpion Solitaire},
author={Erik D. Demaine and Martin L. Demaine and Arthur Langerman and Stefan Langerman},
journal={Theory of Computing Systems},
year={2005},
volume={39},
pages={439-453}
}
• Published 1 June 2006
• Computer Science
• Theory of Computing Systems
We study a popular pencil-and-paper game called morpion solitaire. We present upper and lower bounds for the maximum score attainable for many versions of the game. We also show that, in its most general form, the game is NP-hard and the high score is inapproximable within $n^{1-\epsilon}$ for any $\epsilon>0$ unless P = NP.
18 Citations
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Knowl. Based Syst.
• 2012
Tackling Morpion Solitaire with AlphaZero-like Ranked Reward Reinforcement Learning
• Computer Science
2020 22nd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)
• 2020
The recent impressive performance of deep self-learning reinforcement learning approaches from AlphaGo/AlphaZero is taken as inspiration to design a searcher for Morpion Solitaire, which is very close to the human best without any other adaptation to the problem than using ranked reward.
Games, puzzles and computation
• Philosophy
• 2006
This thesis develops the idea of game as computation to a greater degree than has been done previously, and presents a general family of games, called Constraint Logic, which is both mathematically simple and ideally suited for reductions to many actual board games.
Nested Monte-Carlo Search
Nested Monte-Carlo Search addresses the problem of guiding the search toward better states when there is no available heuristic, and uses nested levels of random games to guide the search.
Nested Monte-Carlo Search with AMAF Heuristic
• Computer Science
2010 International Conference on Technologies and Applications of Artificial Intelligence
• 2010
In the present study, All-Move-As-First heuristic is incorporated in Nested Monte-Carlo Search and the number of search is reduced to maintain a pseudo number of searches in order to achieve the higher level search.
Monte Carlo Beam Search
• T. Cazenave
• Computer Science
IEEE Transactions on Computational Intelligence and AI in Games
• 2012
The proposed Monte Carlo beam search achieves better scores in less time than NMC search alone and is able to match the record score of 82 moves on Morpion Solitaire.
Monte Carlo Search Algorithm Discovery for Single-Player Games
• Computer Science
IEEE Transactions on Computational Intelligence and AI in Games
• 2013
This work proposes an MCS algorithm discovery scheme that introduces a grammar over MCS algorithms that enables inducing a rich space of candidate algorithms and relies on multiarmed bandits to approximately solve this optimization problem.
Monte Carlo Search Algorithm Discovery for One Player Games
• Computer Science
ArXiv
• 2012
This work proposes an MCS algorithm discovery scheme that introduces a grammar over MCS algorithms that enables inducing a rich space of candidate algorithms and relies on multi-armed bandits to approximately solve this optimization problem.
Finding the Needle in the Haystack with Heuristically Guided Swarm Tree Search
• Computer Science
MKWI
• 2010
This paper considers the search in large state spaces with high branching factors and an objective function to be maximized and shows that UCT, which trades exploration for exploitation, can be more successful on several runs than on only one.

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