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Backgammon Is Hard

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Combinatorial Optimization and Applications (COCOA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13135))

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Abstract

We study the computational complexity of the popular board game backgammon. We show that deciding whether a player can win from a given board configuration is NP-Hard, PSPACE-Hard, and EXPTIME-Hard under different settings of known and unknown opponents’ strategies and dice rolls. Our work answers an open question posed by Erik Demaine in 2001. In particular, for the real life setting where the opponent’s strategy and dice rolls are unknown, we prove that determining whether a player can win is EXPTIME-Hard. Interestingly, it is not clear what complexity class strictly contains each problem we consider because backgammon games can theoretically continue indefinitely as a result of the capture rule.

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Authors and Affiliations

  1. NYU Tandon, Brooklyn, NY, 11201, USA

    R. Teal Witter

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  1. R. Teal Witter
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Correspondence to R. Teal Witter .

Editor information

Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. University of New Brunswick, Fredericton, NB, Canada

    Donglei Du

  3. Tianjin University of Technology, Tianjin, China

    Chenchen Wu

  4. Beijing University of Technology, Beijing, China

    Dachuan Xu

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Witter, R.T. (2021). Backgammon Is Hard. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_38

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  • DOI: https://doi.org/10.1007/978-3-030-92681-6_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92680-9

  • Online ISBN: 978-3-030-92681-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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