Skip to main content
SpringerLink
Log in

A New Family of k-in-a-Row Games

  • Conference paper
Advances in Computer Games (ACG 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4250))

Included in the following conference series:

Abstract

This paper contains three contributions. First, it introduces a new family of k-in-a-row games, Connect(m,n,k,p,q). In Connect(m,n,k, p,q), two players alternately place p stones on an m ×n board in each turn, except for the start when the first player places q stones at her first move. The player who first obtains k consecutive stones of her own first wins. The traditional game five-in-a-row, also called Go-Moku, in the free style is Connect(15,15,5,1,1). For brevity, Connect(k,p,q) denotes the game Connect(∞,∞,k,p,q), played on infinite boards.

Second, this paper analyzes the characteristics of these games, especially for the fairness. In the analysis of fairness, we first exclude the ones which are apparently unfair or solved. Then, for the rest of games, we argue that p=2q is a necessary condition for fairness in the sense that one player always has q more stones than the other after making a move. Among these games, Connect(6,2,1) is most interesting to this paper and is named Connect6.

Third, this paper proposes a threat-based strategy to play Connect(k,p,q) games and implements a computer program for Connect6, based on the strategy. In addition, this paper also illustrates a new null-move search approach by solving Connect(6,2,3) where the first player wins. The result also hints that for Connect6 the second player usually should not place the initial two stones far away from the first stone played by the first player.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allis, L.V.: Searching for Solutions in Games and Artificial Intelligence. Ph.D. Thesis, University of Limburg, Maastricht (1994)

    Google Scholar 

  2. Allis, L.V., van der Meulen, M., van den Herik, H.J.: Proof-Number Search. Artificial Intelligence 66(1), 91–124 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. Avetisyan, H., Lorentz, R.: Selective Search in an Amazons Program. In: Schaeffer, J., Müller, M., Björnsson, Y. (eds.) CG 2002. LNCS, vol. 2883, pp. 123–141. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Beal, D.F.: Experiments with the Null Move. In: Beal, D.F. (ed.) Advances in Computer Chess 5, pp. 65–79. Elsevier Science Publishers B.V., Amsterdam, The Netherlands (1989)

    Google Scholar 

  6. Beck, J.: On Positional Games. J. of Combinatorial Theory A–30, 117–133 (1981)

    Article  Google Scholar 

  7. Csirmaz, L.: On a Combinatorial Game with an Application to Go-Moku. Discrete Math. 29, 19–23 (1980)

    Article  MathSciNet  Google Scholar 

  8. Cazenave, T.: Iterative Widening. In: Proceedings of IJCAI 2001, vol. 1, pp. 523–528 (2001)

    Google Scholar 

  9. Cazenave, T.: Abstract Proof Search. In: Marsland, T., Frank, I. (eds.) CG 2001. LNCS, vol. 2063, pp. 39–54. Springer, Berlin (2002)

    Chapter  Google Scholar 

  10. Cazenave, T.: A Generalized Threats Search Algorithm. In: Schaeffer, J., Müller, M., Björnsson, Y. (eds.) CG 2002. LNCS, vol. 2883, pp. 75–87. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. van den Herik, H.J., Uiterwijk, J.W.H.M., van Rijswijck, J.: Games Solved: Now and in the Future. Artificial Intelligence 134, 277–311 (2002)

    Article  MATH  Google Scholar 

  12. Internet Application Technology Lab. Connect6 Homepage. National Chiao Tung University (2005), http://connect6.csie.nctu.edu.tw

  13. Japanese Professional Renju Association. History of Renju Rules (2003), http://www.renjusha.net/database/oldrule.htm

  14. Pluhar, A.: Generalizations of the Game k-In-A-Row. Rutcor Res. Rep., 15–94 (1994)

    Google Scholar 

  15. Pluhar, A.: The Accelerated k-In-A-Row Game. Theoretical Computer Science 271(1–2), 865–875 (2002)

    Article  MathSciNet  Google Scholar 

  16. Renju International Federation. The International Rules of Renju (1998), http://www.renju.nu/rifrules.htm

  17. Renju International Federation. MOM for the RIF General Assembly (2003), http://www.renju.nu/wc2003/MOM_RIF_030805.htm

  18. Sakata, G., Ikawa, W.: Five-In-A-Row. Renju. Ishi Press, Tokyo, Japan (1981)

    Google Scholar 

  19. Thomsen, T.: Lambda-Search in Game Trees - with Application to Go. ICGA Journal 23(4), 203–217 (2000)

    Google Scholar 

  20. Uiterwijk, J.W.H.M., van den Herik, H.J.: The Advantage of the Initiative. Information Sciences 122(1), 43–58 (2000)

    Article  MathSciNet  Google Scholar 

  21. Wagner, J., Virag, I.: Solving Renju. ICGA Journal 24(1), 30–34 (2001)

    Google Scholar 

  22. Wu, I.-C., Chang, H.-C.: Threat-based proof search for Connect6. Technical report, Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, Taiwan (2006), http://java.csie.nctu.edu.tw/~icwu/technical-reports/tr1-2006.pdf

  23. Zetters, T.G.L.: Problem S.10 Proposed by R.K. Guy and J.L. Selfridge. Amer. Math. Monthly 86, 87, 575–576 (1980)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, Taiwan

    I-Chen Wu & Dei-Yen Huang

Authors
  1. I-Chen Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dei-Yen Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Games and AI Group, MICC, Faculty of Humanities and Sciences, Universiteit Maastricht, Maastricht, The Netherlands

    H. Jaap van den Herik

  2. Department of Information Management, Chang Jung Christian University, Tainan

    Shun-Chin Hsu

  3. Institute of Information Science, Academia Sinica, Taipei,  

    Tsan-sheng Hsu

  4. Institute for Knowledge and Agent Technology, MICC, Universiteit Maastricht, Maastricht, The Netherlands

    H. H. L. M. (Jeroen) Donkers

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wu, IC., Huang, DY. (2006). A New Family of k-in-a-Row Games. In: van den Herik, H.J., Hsu, SC., Hsu, Ts., Donkers, H.H.L.M.(. (eds) Advances in Computer Games. ACG 2005. Lecture Notes in Computer Science, vol 4250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11922155_14

Download citation

  • DOI: https://doi.org/10.1007/11922155_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-48887-3

  • Online ISBN: 978-3-540-48889-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation