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International Conference on Computers and Games

CG 2013: Computers and Games pp 84–99Cite as

Anomalies of Pure Monte-Carlo Search in Monte-Carlo Perfect Games

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8427))

Abstract

A game is called “Monte-Carlo perfect” when in each position pure Monte-Carlo search converges to perfect play as the number of simulations tends toward infinity. We exhibit three families of Monte-Carlo perfect single-player and two-player games where this convergence is not monotonic. We for example give a class of MC-perfect games in which MC(1) performs arbitrarily well against MC(1,000).

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Notes

  1. 1.

    For Brevity, we use ‘he’ and ‘his’ whenever ‘he or she’ and ‘his or her’ are meant.

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Acknowledgments

This paper is dedicated to Prof. Bernd Brügmann. Twenty years ago in his report from 1993 [18] he introduced the approach of pure Monte-Carlo search to the game of Go and also created the name “Monte-Carlo Go”. Brügmann now holds a chair in theoretical physics for gravitational theory. His special topic is the understanding of mergers of black holes. This motivated us to call the jump-outs in our Double Step Races “black holes”.

Back in 2005, Jörg Sameith designed his beautiful tool McRandom, which allows one to design and test new board games with Monte-Carlo game search. With the help of McRandom we found the “DSR-3 with 16 Black Holes”. Also the graphic in the upper part of Fig. 1 is that of McRandom. In a workshop on search methodologies in September 2012, Soren Riis asked several questions on our preliminary anomaly result. This motivated us to do the research presented in this paper. Participants of the computer-go mailing list gave helpful feedback; here special thanks go to Jonas Kahn, Cameron Browne, and Stefan Kaitschick. Thanks to Matthias Beckmann and Michael Hartisch for proofreading an earlier version, and to the three anonymous referees for their constructive criticism and helpful proposals. Finally, thanks to Jaap van den Herik for his proposals in giving the paper a much clearer structure.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Friedrich-Schiller-University, Ernst-Abbe-Platz 2, 07743, Jena, Germany

    Ingo Althöfer & Wesley Michael Turner

Authors
  1. Ingo Althöfer
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  2. Wesley Michael Turner
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Corresponding author

Correspondence to Ingo Althöfer .

Editor information

Editors and Affiliations

  1. Tilburg University, Tilburg, The Netherlands

    H. Jaap van den Herik

  2. JAIST, Ishikawa, Japan

    Hiroyuki Iida

  3. Tilburg University, Tilburg, The Netherlands

    Aske Plaat

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Althöfer, I., Turner, W.M. (2014). Anomalies of Pure Monte-Carlo Search in Monte-Carlo Perfect Games. In: van den Herik, H., Iida, H., Plaat, A. (eds) Computers and Games. CG 2013. Lecture Notes in Computer Science(), vol 8427. Springer, Cham. https://doi.org/10.1007/978-3-319-09165-5_8

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  • DOI: https://doi.org/10.1007/978-3-319-09165-5_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09164-8

  • Online ISBN: 978-3-319-09165-5

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