Abstract
In this paper, we present the newly obtained solution for variants of Connect-Four played on an infinite board. We proved this result by introducing never-losing strategies for both players. The strategies consist of a combination of paving patterns, which are follow-up, follow-in-CUP, and a few others. By employing the strategies, both players can block their opponents to achieve the winning condition. This means that optimal play by both players leads to a draw in these games.
By rearrangement of the same paving patterns, the solution for a semi-infinite board, where either the height or the width is finite, are also presented. Moreover, it is confirmed that these results are effective under various placement restrictions.
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© 2012 Springer-Verlag Berlin Heidelberg
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Yamaguchi, Y., Yamaguchi, K., Tanaka, T., Kaneko, T. (2012). Infinite Connect-Four Is Solved: Draw. In: van den Herik, H.J., Plaat, A. (eds) Advances in Computer Games. ACG 2011. Lecture Notes in Computer Science, vol 7168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31866-5_18
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DOI: https://doi.org/10.1007/978-3-642-31866-5_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31865-8
Online ISBN: 978-3-642-31866-5
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