Infinite connect-four is solved: Draw

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. © 2012 Springer-Verlag.