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)


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.


Logarithmic Function Gray Zone Winning Strategy Tight Bound Active Line 
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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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