Skip to main content
SpringerLink
Log in

First Player’s Cannot-Lose Strategies for Cylinder-Infinite-Connect-Four with Widths 2 and 6

  • Conference paper
  • First Online:
Advances in Computer Games (ACG 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9525))

Included in the following conference series:

Abstract

Cylinder-Infinite-Connect-Four is Connect-Four played on a cylindrical square grid board with infinite row height and columns that cycle about its width. In previous work, the first player’s cannot-lose strategies have been discovered for all widths except 2 and 6, and the second player’s cannot-lose strategies have been discovered with all widths except 6 and 11. In this paper, we show the first player’s cannot-lose strategies for widths 2 and 6.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Yamaguchi, Y., Tanaka, T., Yamaguchi, K.: Cylinder-infinite-connect-four except for widths 2, 6, and 11 is solved: draw. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2013. LNCS, vol. 8427, pp. 163–174. Springer, Heidelberg (2014)

    Google Scholar 

  2. Allen, J.D.: A note on the computer solution of connect-four. In: Levy, D.N.L., Beal, D.F. (eds.) Heuristic Programming in Artificial Intelligence, The first Computer Olympiad, pp. 134–135. Ellis Horwood, Chinchester (1989)

    Google Scholar 

  3. Allen, J.D.: The Complete Book of Connect 4: History, Strategy, Puzzles. Sterling Publishing Co., Inc., New York (2010)

    Google Scholar 

  4. Allis, L.V.: A Knowledge-Based Approach to Connect-Four. The game is solved: White wins, Master’s thesis, Vrije Universiteit (1988)

    Google Scholar 

  5. Mahalko, E.M.: A Possible Win Strategy for the Game of Qubic, Computer Science Master’s thesis, Brigham Young University (1976)

    Google Scholar 

  6. Patashnik, O.: Qubic: \(4 \times 4 \times 4\) Tic-Tac-Toe. Math. Mag. 53, 202–216 (1980)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  8. God’s Number is 20. http://www.cube20.org

  9. Tromp, J.: Solving connect-4 on medium board sizes. ACG 31(2), 110–112 (2008)

    Google Scholar 

  10. Yamaguchi, Y., Yamaguchi, K., Tanaka, T., Kaneko, T.: Infinite connect-four is solved: draw. In: van den Herik, H.J., Plaat, A. (eds.) ACG 2011. LNCS, vol. 7168, pp. 208–219. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. Allis, L.V., van den Herik, H.J., Huntjens, M.P.H.: Go-Moku and Threat-Space Search, Report CS 93–02. Faculty of General Sciences, University of Limburg, Department of Computer Science (1993)

    Google Scholar 

  12. Wagner, J., Virag, I.: Note solving renju. ICGA J. 24, 30–35 (2001)

    Google Scholar 

  13. Harary, F., Harborth, H.: Achievement and avoidance games with triangular animals. J. Recreational Math. 18(2), 110–115 (1985–1986)

    Google Scholar 

  14. Gardner, M.: Mathematical games. Sci. Amer. 240, 18–26 (1979)

    Article  Google Scholar 

  15. Halupczok, I., Puchta, J.C.S.: Achieving snaky integers. Electron. J. Comb. Number Theor. 7, G02 (2007)

    Google Scholar 

  16. Harary, F.: Is snaky a winner? Geombinatorics 2, 79–82 (1993)

    MathSciNet  MATH  Google Scholar 

  17. Zetters, T.G.L.: 8 (or More) in a row. Am. Math. Mon. 87, 575–576 (1980)

    Article  MathSciNet  Google Scholar 

  18. Bode, J.P., Harborth, H.: Hexagonal polyomino achievement. Discrete Math. 212, 5–18 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  19. Inagaki, K., Matsuura, A.: Winning strategies for hexagonal polyomino achievement. In: 12th WSEAS International Conference on Applied Mathematics, pp. 252–259 (2007)

    Google Scholar 

  20. Wu, I.C.: Relevance-zone-oriented proof search for connect 6. IEEE Trans. Intell. AI Games (SCI) 2(3), 191–207 (2010)

    Article  Google Scholar 

  21. Geselowitz, L.: Freed Go. http://www.leweyg.com/lc/freedgo.html

  22. TetroSpin Free APK 1.2. http://m.downloadatoz.com/apps/emre.android.tetrominofree,158809.html

Download references

Acknowledgement

We thank I-Chen Wu for giving us important advice on Black’s cannot-lose strategy for Cylinder-Infinite-Connect-Four for width 2.

Author information

Authors and Affiliations

  1. The University of Tokyo, Tokyo, Japan

    Yoshiaki Yamaguchi

  2. Gettysburg College, Gettysburg, USA

    Todd W. Neller

Authors
  1. Yoshiaki Yamaguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Todd W. Neller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoshiaki Yamaguchi .

Editor information

Editors and Affiliations

  1. Leiden University , Leiden, The Netherlands

    Aske Plaat

  2. Leiden University , Leiden, The Netherlands

    Jaap van den Herik

  3. Leiden University , Leiden, The Netherlands

    Walter Kosters

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Yamaguchi, Y., Neller, T.W. (2015). First Player’s Cannot-Lose Strategies for Cylinder-Infinite-Connect-Four with Widths 2 and 6. In: Plaat, A., van den Herik, J., Kosters, W. (eds) Advances in Computer Games. ACG 2015. Lecture Notes in Computer Science(), vol 9525. Springer, Cham. https://doi.org/10.1007/978-3-319-27992-3_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27992-3_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27991-6

  • Online ISBN: 978-3-319-27992-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation