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Cylinder-Infinite-Connect-Four Except for Widths 2, 6, and 11 Is Solved: Draw

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8427))

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Abstract

Cylinder-Infinite-Connect-Four is a variant of the Connect-Four game played on cylindrical boards of differing cyclic widths and infinite height. In this paper, we show strategies to avoid losing at Cylinder-Infinite-Connect-Four except for Widths 2, 6, and 11. If both players use the strategies, the game will be drawn. This result can also be used to show that Width-Limited-Infinite-Connect-Four is drawn for any width. We also show that Connect-Four of any size with passes allowed is drawn.

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Acknowledgement

We are grateful to the reviewers for their valuable suggestions regarding Cylinder-Infinite-Connect-Four and passing.

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Authors and Affiliations

  1. The University of Tokyo, Tokyo, Japan

    Yoshiaki Yamaguchi, Tetsuro Tanaka & Kazunori Yamaguchi

Authors
  1. Yoshiaki Yamaguchi
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  2. Tetsuro Tanaka
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  3. Kazunori Yamaguchi
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Corresponding author

Correspondence to Yoshiaki Yamaguchi .

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Editors and Affiliations

  1. Tilburg University, Tilburg, The Netherlands

    H. Jaap van den Herik

  2. JAIST, Ishikawa, Japan

    Hiroyuki Iida

  3. Tilburg University, Tilburg, The Netherlands

    Aske Plaat

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Yamaguchi, Y., Tanaka, T., Yamaguchi, K. (2014). Cylinder-Infinite-Connect-Four Except for Widths 2, 6, and 11 Is Solved: Draw. In: van den Herik, H., Iida, H., Plaat, A. (eds) Computers and Games. CG 2013. Lecture Notes in Computer Science(), vol 8427. Springer, Cham. https://doi.org/10.1007/978-3-319-09165-5_14

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  • DOI: https://doi.org/10.1007/978-3-319-09165-5_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09164-8

  • Online ISBN: 978-3-319-09165-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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