Abstract
In 2005, Wu and Huang [9] presented a generalized family of k-in-a-row games. The current paper simplifies the family to Connect(k, p). Two players alternately place p stones on empty squares of an infinite board in each turn. The player who first obtains k consecutive stones of his own horizontally, vertically, diagonally wins. A Connect(k, p)game is drawn if both have no winning strategy. Given p, this paper derives the value k draw(p), such that Connect(k draw(p), p) is drawn, as follows. (1) k draw(2) = 11. (2) For all p ≥ 3, k draw(p) = 3p+3d+8, where d is a logarithmic function of p. So, the ratio k draw(p)/p is approximate to 3 for sufficiently large p. To our knowledge, our k draw(p) are currently the smallest for all 2 ≤ p < 1000, except for p = 3.
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Chiang, SH., Wu, IC., Lin, PH. (2010). On Drawn K-In-A-Row Games. In: van den Herik, H.J., Spronck, P. (eds) Advances in Computer Games. ACG 2009. Lecture Notes in Computer Science, vol 6048. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12993-3_15
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DOI: https://doi.org/10.1007/978-3-642-12993-3_15
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