Abstract
Quixo is a two-player game played on a \(5\times 5\) grid where the players try to align five identical symbols. Using a combination of value iteration and backward induction, we propose the first complete analysis of the game. We describe memory-efficient data structures and algorithmic optimizations that make the game solvable within reasonable time and space constraints. Our main conclusion is that Quixo is a Draw game. The paper also contains the analysis of smaller boards and presents some interesting states extracted from our computations.
A Japanese version of this paper was published and presented at the 25th Game Programming Workshop (GPW’20) [6]. S. Tanaka received the GPW Research Encouragement Award and the IPSJ Yamashita SIG Research Award for his work.
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Notes
- 1.
As d’Or Festival International des Jeux (1995), Oscar du Jouet (1995), Mensa Select Top 5 Best Games (1995), Games Magazine “Games 100 Selection” (1995), Games Magazine “Best New Strategy Game” (1995), Parent’s Choice Gold Award (1995) [4].
- 2.
In practice, this amount of space is likely much higher due to memory alignment. So, a more realistic estimation for full storage is in the order of 15 TB.
- 3.
Some implementation details are omitted. For example, since we only consider states with active player X, we need to swap the tiles/players after each move.
- 4.
We used a Ubuntu 18.04LTS server equipped with 32GB of RAM and powered by a 16-core Intel Core i9-9960X CPU.
- 5.
The \(3\times 3\) version is not discussed here and left to the reader (Win in 7 moves).
References
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Mishiba, S., Takenaga, Y.:
IEICE general conference p. 26 (2017), (in Japanese)Quixo page on BoardGameGeek website. https://boardgamegeek.com/boardgame/3190/quixo, (accessed 17 September 2021)
Quixo page on Gigamic website. https://en.gigamic.com/game/quixo, (accessed: September 17 2021)
Quixo source code repository. https://github.com/st34-satoshi/quixo-cpp
Tanaka, S., Bonnet, F., Tixeuil, S., Tamura, Y.: Quixo
. In: Proceedings of the 26th Game Programming Workshop, pp. 181–188 (2020), (in Japanese)Tanaka, S., Bonnet, F., Tixeuil, S., Tamura, Y.: Quixo is solved (2020). https://arxiv.org/abs/2007.15895
IEICE general conference p. 26 (2017), (in Japanese)
. In: Proceedings of the 26th Game Programming Workshop, pp. 181–188 (2020), (in Japanese)Author information
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Tanaka, S., Bonnet, F., Tixeuil, S., Tamura, Y. (2022). Quixo is Solved. In: Browne, C., Kishimoto, A., Schaeffer, J. (eds) Advances in Computer Games. ACG 2021. Lecture Notes in Computer Science, vol 13262. Springer, Cham. https://doi.org/10.1007/978-3-031-11488-5_8
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DOI: https://doi.org/10.1007/978-3-031-11488-5_8
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