The European Physical Journal B

, Volume 80, Issue 4, pp 555–563 | Cite as

The aggregate complexity of decisions in the game of Go

  • M. S. HarréEmail author
  • T. Bossomaier
  • A. Gillett
  • A. Snyder


Artificial intelligence (AI) research is fast approaching, or perhaps has already reached, a bottleneck whereby further advancement towards practical human-like reasoning in complex tasks needs further quantified input from large studies of human decision-making. Previous studies in psychology, for example, often rely on relatively small cohorts and very specific tasks. These studies have strongly influenced some of the core notions in AI research such as the reinforcement learning and the exploration versus exploitation paradigms. With the goal of contributing to this direction in AI developments we present our findings on the evolution towards world-class decision-making across large cohorts of subjects in the formidable game of Go. Some of these findings directly support previous work on how experts develop their skills but we also report on several previously unknown aspects of the development of expertise that suggests new avenues for AI research to explore. In particular, at the level of play that has so far eluded current AI systems for Go, we are able to quantify the lack of ‘predictability’ of experts and how this changes with their level of skill.


Entropy Mutual Information Kolmogorov Complexity Game Tree Cognitive Brain Research 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    D. Stern, T. Graepel, D. MacKay, Advances in neural information processing 16, 33 (2004) Google Scholar
  2. 2.
    S. Sanner, T. Graepel, R. Herbrich, T. Minka, Learning CRFs with Hierarchical Features: An Application to Go, in International Conference on Machine Learning (ICML) Workshop (2007) Google Scholar
  3. 3.
    J. Lafferty, A. McCallum, F. Pereira, Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data, in Machine Learning – International Workshop then Conference (2001), pp. 282–289 Google Scholar
  4. 4.
    T. Cazenave, Advances in Computer Games 9, 275 (2001) Google Scholar
  5. 5.
    D. Stern, R. Herbrich, T. Graepel, Bayesian pattern ranking for move prediction in the game of Go, in Proc. 23rd int. conf. on machine learning (2006), Vol. 148, pp. 873–880 Google Scholar
  6. 6.
    T. Graepel, M. Goutrie, M. Krüger, R. Herbrich, Learning on graphs in the game of Go, Artificial Neural Networks – ICANN (2001), pp. 347–352 Google Scholar
  7. 7.
    E. Berlekamp, D. Wolfe, Mathematical Go: Chilling Gets the Last Point, edited by A.K. Peters (1997) Google Scholar
  8. 8.
    N. Charness, Psychol. Res. 54, 4 (1992) CrossRefGoogle Scholar
  9. 9.
    F. Gobet, A. de Voogt, J. Retschitzki, Moves in mind: The psychology of board games (Psychology Pr, 2004) Google Scholar
  10. 10.
    H.A. Simon, W.G. Chase, Am. Sci. 61, 393 (1973) ADSGoogle Scholar
  11. 11.
    D. Holding, The psychology of chess skill (L. Erlbaum Assoc., Hillsdale, NJ, 1985) Google Scholar
  12. 12.
    D. Holding, Psychol. Res. 54, 10 (1992) CrossRefGoogle Scholar
  13. 13.
    H. Simon, K. Gilmartin, Cogn. Psychol. 5, 29 (1973) CrossRefGoogle Scholar
  14. 14.
    F. Gobet, H. Simon, Recall of rapidly presented random chess positions is a function of skill (1996) Google Scholar
  15. 15.
    W.G. Chase, H.A. Simon, Cogn. Psychol. 4, 55 (1973) CrossRefGoogle Scholar
  16. 16.
    N. Charness, Journal of Experimental Psychology: Human Perception and Performance 7, 467 (1981) CrossRefGoogle Scholar
  17. 17.
    A. Cleveland, The American Journal of Psychology 18, 269 (1907) CrossRefGoogle Scholar
  18. 18.
    E. Reingold, N. Charness, M. Pomplun, D. Stampe, Psychol. Sci. 12, 48 (2001) CrossRefGoogle Scholar
  19. 19.
    A. Waters, F. Gobet, G. Leyden, British Journal of Psychology 93, 557 (2002) CrossRefGoogle Scholar
  20. 20.
    M. Atherton, J. Zhuang, W. Bart, X. Hu, S. He, Cognitive Brain Research 16, 26 (2003) CrossRefGoogle Scholar
  21. 21.
    X. Chen, D. Zhang, X. Zhang, Z. Li, X. Meng, S. He, X. Hu, Cognitive Brain Research 16, 32 (2003) CrossRefGoogle Scholar
  22. 22.
    J. Reitman, Cogn. Psychol. 8, 336 (1976) CrossRefGoogle Scholar
  23. 23.
    F. Gobet, P. Lane, S. Croker, P. Cheng, G. Jones, I. Oliver, J. Pine, Trends in Cognitive Sciences 5, 236 (2001) CrossRefGoogle Scholar
  24. 24.
    A. Zobrist, A model of visual organization for the game of Go, in Proceedings of the May 14-16, 1969, spring joint computer conference (ACM, 1969), pp. 103–112 Google Scholar
  25. 25.
    S. Epstein, J. Gelfand, E. Lock, Constraints 3, 239 (1998) CrossRefMathSciNetzbMATHGoogle Scholar
  26. 26.
    B. Bouzy, Spatial Reasoning in the game of Go, in Workshop on Representations and Processes in Vision and Natural Language, ECAI (Citeseer, 1996), pp. 78–80 Google Scholar
  27. 27.
    X. Ping, K. Keqing, Psychological Research, 03 (2009) Google Scholar
  28. 28.
    H. Masunaga, J. Horn, Learning and individual differences 12, 5 (2000) CrossRefGoogle Scholar
  29. 29.
    X. Cai, D. Wunsch, Computer Go: A grand challenge to AI, in Challenges for Computational Iintelligence (Springer Berlin, 2007), pp. 443–465 Google Scholar
  30. 30.
    M.S. Campbell, A.J. Hoane, F. Hsu, Search control methods in Deep Blue, AAAI Spring Symposium on Search Techniques for Problem Solving under Uncertainty and Incomplete Information, pp. 19–23 (1999) Google Scholar
  31. 31.
    J. Burmeister, J. Wiles, The challenge of Go as a domain for AI research: A comparison between Go and chess, in Proceedings of the Third Australian and New Zealand Conference on Intelligent Information Systems (1995) Google Scholar
  32. 32.
    S. Gelly, D. Silver, Achieving master level play in \(9\times 9\) computer go, in Proceedings of AAAI (2008), pp. 1537–1540 Google Scholar
  33. 33.
    C. Lee, M. Wang, G. Chaslot, J. Hoock, A. Rimmel, O. Teytaud, S. Tsai, S. Hsu, T. Hong, Computational Intelligence and AI in Games, IEEE Transactions on 1, 73 (2009) Google Scholar
  34. 34.
    T. Cazenave, B. Helmstetter, Combining Tactical Search and Monte-Carlo in the Game of Go, in Proceedings of the IEEE Symposium on Computational Intelligence in Games (2005), pp. 171–175 Google Scholar
  35. 35.
    S. Gelly, Y. Wang, R. Munos, O. Teytaud, Modification of UCT with Patterns in Monte-Carlo Go (2006) Google Scholar
  36. 36.
    F. Gobet, H. Simon, Psychol. Res. 61, 204 (1998) CrossRefGoogle Scholar
  37. 37.
    C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948) MathSciNetzbMATHGoogle Scholar
  38. 38.
    T. Cover, J. Thomas, Elements of Information Theory, 2nd edn. (Wiley, 2006) Google Scholar
  39. 39.
    P. Grünwald, The Minimum Description Length Principle (The MIT Press, 2007) Google Scholar
  40. 40.
    S. Leung-Yan-Cheong, T. Cover, IEEE Trans. Inf. Theory 24, 331 (2002) CrossRefMathSciNetGoogle Scholar
  41. 41.
    J. Crutchfield, K. Young, Phys. Rev. Lett. 63, 105 (1989) CrossRefADSMathSciNetGoogle Scholar
  42. 42.
    G. Boffetta, M. Cencini, M. Falcioni, A. Vulpiani, Phys. Rep. 356, 367 (2002) CrossRefADSMathSciNetzbMATHGoogle Scholar
  43. 43.
    D. Mackay, Information theory, inference, and learning algorithms (Cambridge University Press, New York, 2003) Google Scholar
  44. 44.
    M. Roulston, Physica D: Nonlinear Phenomena 125, 285 (1999) CrossRefADSzbMATHGoogle Scholar
  45. 45.
    Y. Wang, S. Gelly, Modifications of UCT and sequence-like simulations for Monte-Carlo Go, in Proceedings of the IEEE Symposium on Computational Intelligence and Games (2007), pp. 171–182 Google Scholar
  46. 46.
    R. Sutton, A. Barto, Reinforcement Learning: An Introduction (The MIT Press, 1998) Google Scholar
  47. 47.
    M. Frank, A. Moustafa, H. Haughey, T. Curran, K. Hutchison, Proceedings of the National Academy of Sciences 104, 16311 (2007) CrossRefADSGoogle Scholar
  48. 48.
    M. Cohen, C. Ranganath, J. Neurosci. 27, 371 (2007) CrossRefGoogle Scholar
  49. 49.
    S. Ishii, W. Yoshida, J. Yoshimoto, Neural Networks 15, 665 (2002) CrossRefGoogle Scholar
  50. 50.
    N. Schweighofer, K. Doya, Neural Networks 16, 5 (2003) CrossRefGoogle Scholar
  51. 51.
    F. Gobet, H. Simon, Mem. Cogn. 24, 493 (1996) CrossRefGoogle Scholar
  52. 52.
    M. Van De Wiel, H. Boshuizen, H. Schmidt, Eur. J. Cogn. Psychol. 12, 323 (2000) CrossRefGoogle Scholar
  53. 53.
    H. Boshuizen, R. Bromme, H. Gruber, Professional learning: Gaps and transitions on the way from novice to expert (Kluwer Academic Publishers, 2004) Google Scholar
  54. 54.
    I. Davies, P. Green, M. Rosemann, M. Indulska, S. Gallo, Data and Knowledge Engineering 58, 358 (2006), CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • M. S. Harré
    • 1
    Email author
  • T. Bossomaier
    • 2
  • A. Gillett
    • 1
  • A. Snyder
    • 1
  1. 1.The Centre for the Mind, The University of SydneySydneyAustralia
  2. 2.Centre for Research in Complex Systems, Charles Sturt UniversityBathurstAustralia

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