Skip to main content
SpringerLink
Log in

New Hex Patterns for Fill and Prune

  • Conference paper
  • First Online:
Advances in Computer Games (ACG 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12516))

Included in the following conference series:

Abstract

For a position in the game of Hex, a fill pattern is a sub-position with one or more empty cells that can be filled without changing the position’s minimax value. A cell is prunable if it can be ignored when searching for a winning move. We introduce two new kinds of Hex fill – mutual and near-dead – and some resulting fill patterns; we show four new permanently-inferior fill patterns; and we present three new prune results, based on strong-reversing, reversing, and game-history respectively. Experiments show these results slightly reducing solving time on 8\(\,\times \,\)8 openings.

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. Arneson, B., Hayward, R.B., Henderson, P.: Solving hex: beyond humans. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2010. LNCS, vol. 6515, pp. 1–10. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-17928-0_1

    Chapter  Google Scholar 

  2. Beck, A., Bleicher, M.N., Crowe, D.W.: Excursions into Mathematics. Worth, New York (1969)

    MATH  Google Scholar 

  3. Gale, D.: Game of hex and the brouwer fixed point theorem. Am. Math. Monthly 86(10), 818–827 (1979)

    Article  MathSciNet  Google Scholar 

  4. Gao, C., Müller, M., Hayward, R.: Focused depth-first proof number search using convolutional neural networks for the game of hex. In: Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (IJCAI-17), pp. 3668–3674 (2017)

    Google Scholar 

  5. Hayward, R., van Rijswijck, J.: Hex and combinatorics. Discrete Math. 306(19–20), 2515–2528 (2006)

    Article  MathSciNet  Google Scholar 

  6. Hayward, R.B., Toft, B.: Hex, the full story. CRC Press, London (2019)

    Book  Google Scholar 

  7. Henderson, P.: Playing and Solving Hex. PhD thesis, University of Alberta, Edmonton, Alberta, Canada, Fall (2010). https://webdocs.cs.ualberta.ca/~hayward/theses/ph.pdf

  8. Henderson, P., Arneson, B., Hayward, R.B.: Hex, Braids, the Crossing Rule, and XH-Search. In: van den Herik, H.J., Spronck, P. (eds.) ACG 2009. LNCS, vol. 6048, pp. 88–98. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12993-3_9

    Chapter  Google Scholar 

  9. Henderson, P., Hayward, R.B.: Captured-reversible moves and star-decomposition domination in Hex. Integers 13(CG1), 1–15 (2013)

    MathSciNet  Google Scholar 

  10. Henderson, P., Hayward, R.B.: A Handicap Strategy for Hex, pp. 129–136. MSRI and Cambridge University Press (2015)

    Google Scholar 

  11. Huang, S.-C., Arneson, B., Hayward, R.B., Müller, M., Pawlewicz, J.: MoHex 2.0: a pattern-based MCTS hex player. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2013. LNCS, vol. 8427, pp. 60–71. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09165-5_6

    Chapter  Google Scholar 

  12. Pawlewicz, J., Hayward, R.B.: Scalable parallel DFPN search. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2013. LNCS, vol. 8427, pp. 138–150. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09165-5_12

    Chapter  Google Scholar 

  13. Pawlewicz, J., Hayward, R.B., Henderson, P., Arneson, B.: Stronger virtual connections in hex. IEEE Tran. Comput. Intel. AI Games 7(2), 156–166 (2015)

    Article  Google Scholar 

  14. Yamasaki, Y.: Theory of division games. Pub. Res. Inst. Math. Sci. 14, 337–358 (1978)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We thank Chao Gao for many helpful comments and suggestions.

Author information

Authors and Affiliations

  1. Dèpartement d’Informatique, ENS Ulm, Paris, France

    Nicolas Fabiano

  2. Department of Computing Science, University of Alberta, Edmonton, Canada

    Ryan Hayward

Authors
  1. Nicolas Fabiano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ryan Hayward
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Université Paris-Dauphine, Paris, France

    Tristan Cazenave

  2. Leiden University, The Hague, The Netherlands

    Jaap van den Herik

  3. The University of New South Wales, Sydney, NSW, Australia

    Abdallah Saffidine

  4. National Chiao-Tung University, Hsin-Chu, Taiwan

    I-Chen Wu

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Fabiano, N., Hayward, R. (2020). New Hex Patterns for Fill and Prune. In: Cazenave, T., van den Herik, J., Saffidine, A., Wu, IC. (eds) Advances in Computer Games. ACG 2019. Lecture Notes in Computer Science(), vol 12516. Springer, Cham. https://doi.org/10.1007/978-3-030-65883-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-65883-0_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-65882-3

  • Online ISBN: 978-3-030-65883-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation