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On Drawn K-In-A-Row Games

  • Sheng-Hao Chiang
  • I-Chen Wu
  • Ping-Hung Lin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6048)

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 p3, 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 2p < 1000, except for p = 3.

Keywords

Logarithmic Function Gray Zone Winning Strategy Tight Bound Active Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sheng-Hao Chiang
    • 1
  • I-Chen Wu
    • 2
  • Ping-Hung Lin
    • 2
  1. 1.National Experimental High School at Hsinchu Science ParkHsinchuTaiwan
  2. 2.Department of Computer ScienceNational Chiao Tung UniversityHsinchuTaiwan

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