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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Allis, L.V.: Searching for solutions in games and artificial intelligence. Ph.D. Thesis, University of Limburg, Maastricht, The Netherlands (1994)
Allis, L.V., Van den Herik, H.J., Huntjens, M.P.H.: Go-Moku solved by new search Techniques. Computational Intelligence 12, 7–23 (1996)
Berge, C.: Graphs and Hypergraphs. North Holland, Amsterdam (1973)
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for your Mathematical Plays, 2nd edn., vol. 3. A K Peters. Ltd., Canada (2003)
Diestel, R.: Graph Theory, 2nd edn. Springer, New York (2000)
Van den Herik, H.J., Uiterwijk, J.W.H.M., Rijswijck, J.V.: Games solved: now and in the future. Artificial Intelligence 134, 277–311 (2002)
Hsieh, M.-Y., Tsai, S.-C.: On the fairness and complexity of generalized k-in-a-row games. Theoretical Computer Science 385, 88–100 (2007)
Pluhar, A.: The accelerated k-in-a-row game. Theoretical Computer Science 271, 865–875 (2002)
Wu, I.-C., Huang, D.-Y.: A New Family of k-in-a-row Games. In: The 11th Advances in Computer Games (ACG11) Conference, Taipei, Taiwan (2005)
Wu, I.-C., Huang, D.-Y., Chang, H.-C.: Connect6. ICGA Journal 28(4), 234–242 (2006)
Zetters, T.G.L.: 8(or more) in a row. American Mathematical Monthly 87, 575–576 (1980)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-12993-3_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12992-6
Online ISBN: 978-3-642-12993-3
eBook Packages: Computer ScienceComputer Science (R0)