We introduce a novel approach to measuring how
humans learn based on techniques from information theory and
apply it to the oriental game of Go. We show that the total amount
of information observable in human strategies, called the strategic
information, remains constant for populations of players of differing
skill levels for well studied patterns of play. This is despite the very
large amount of knowledge required to progress from the recreational
players at one end of our spectrum to the very best and most
experienced players in the world at the other and is in contrast to
the idea that having more knowledge might imply more 'certainty'
in what move to play next. We show this is true for very local
up to medium sized board patterns, across a variety of different
moves using 80,000 game records. Consequences for theoretical and
practical AI are outlined.
[1] Xindi Cai and Donald Wunsch, "Computer Go: A grand challenge
to AI," in Challenges for Computational Iintelligence, pp. 443-465.
Springer Berlin, 2007.
[2] Fernand Gobet, Jean Retschitzki, and Alex de Voogt, Moves in Mind:
The Psychology of Board Games, Psychology Press, 2004.
[3] Xiangchuan Chen, Daren Zhang, Xiaochu Zhang, Zhihao Li, Xiaomei
Meng, Sheng He, and Xiaoping Hu, "A functional MRI study of highlevel
cognition II. The game of Go," Cognitive Brain Research, vol. 16,
no. 1, pp. 32 - 37, 2003.
[4] Yasuomi Ouchi, Toshihiko Kanno, Etsuji Yoshikawa, Masami Futatsubashi,
Hiroyuki Okada, Tatsuo Torizuka, and Mitsuo Kaneko, "Neural
substrates in judgment process while playing Go: A comparison of
amateurs with professionals," Cognitive Brain Research, vol. 23, no.
2-3, pp. 164 - 170, 2005.
[5] J. Burmeister and 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.
[6] Y. Wang and S. Gelly, "Modifications of UCT and sequence-like
simulations for monte-carlo Go," in IEEE Symposium on Computational
Intelligence and Games, 2007., 2007, pp. 175-182.
[7] L. Chang-Shing, W. Mei-Hui, G. Chaslot, J.-B. Hoock, A. Rimmel,
O. Teytaud, Shang-Rong T., Shun-Chin H., and H. Tzung-Pei, "The
computational intelligence of MoGo revealed in Taiwan-s computer Go
tournaments," in IEEE Transactions on Computational Intelligence and
AI in Games., 2009, vol. 1, pp. 73-79.
[8] Fernand Gobet, Peter C.R. Lane, Steve Croker, Peter C-H. Cheng, Gary
Jones, Iain Oliver, and Julian M. Pine, "Chunking mechanisms in human
learning," TRENDS in Cognitive Sciences, vol. 5, no. 6, pp. 236 - 243,
2001.
[9] C. Shannon, "Programming a computer for playing Chess," Philosophical
Magazine, vol. 41, no. 314, 1951.
[10] J. Robson, "The complexity of Go," in Proceedings of IFIP Congress,
1983, pp. 413-417.
[11] T. Cover and J. Thomas, Elements of Information Theory, 2nd edition,
Wiley, 2006.
[12] Peter D. Gr¨unwald and A. Philip Dawid, "Game theory, maximum
entropy, minimum discrepancy and robust bayesian decision theory,"
The Annals of Statistics, vol. 32, no. 4, pp. 1367-1433, 2004.
[13] S. Kullback and R. A. Leibler, "On information and sufficiency," The
Annals of Mathematical Statistics, vol. 22, no. 1, pp. 79-86, 1951.
[14] J. Lin, "Divergence measures based on the shannon entropy," Information
Theory, IEEE Transactions on, vol. 37, no. 1, pp. 145-151, August
2002.
[15] E. Berlekamp and D. Wolfe, Mathematical Go: Chilling gets the last
point, AK Peters, 1994.
[16] J. S. Reitman, "Skilled perception in Go: Deducing memory structures
from inter-response time," Cognitive Psychology, vol. 8, pp. 336-356,
1976.
[17] Mark S. Roulston, "Estimating the errors on measured entropy and
mutual information," Physica D: Nonlinear Phenomena, vol. 125, no.
3-4, pp. 285 - 294, 1999.
[18] D. Messick and A. Rapaport, "Expected value and response uncertainty
in multiple-choice decision behavior," Journal of Experimental Psychology,
vol. 70, no. 2, pp. 224 - 230, 1965.
[19] A. Borst and F. Theunissen, "Information theory and neural coding,"
Nature Neuroscience, vol. 2, no. 11, pp. 947 - 957, 1999.
[20] G. Halford, N. Cowan, and G. Andrews, "Separating cognitive capacity
from knowledge: a new hypothesis," TRENDS in Cognitive Science, vol.
11, no. 6, pp. 236 - 242, 2008.
[21] G. Orb'an, J. Fiser, R. Aslin, and M. Lengyel, "Bayesian learning of
visual chunks by human observers," PNAS, vol. 105, no. 7, pp. 2745 -
2750, 2008.
[1] Xindi Cai and Donald Wunsch, "Computer Go: A grand challenge
to AI," in Challenges for Computational Iintelligence, pp. 443-465.
Springer Berlin, 2007.
[2] Fernand Gobet, Jean Retschitzki, and Alex de Voogt, Moves in Mind:
The Psychology of Board Games, Psychology Press, 2004.
[3] Xiangchuan Chen, Daren Zhang, Xiaochu Zhang, Zhihao Li, Xiaomei
Meng, Sheng He, and Xiaoping Hu, "A functional MRI study of highlevel
cognition II. The game of Go," Cognitive Brain Research, vol. 16,
no. 1, pp. 32 - 37, 2003.
[4] Yasuomi Ouchi, Toshihiko Kanno, Etsuji Yoshikawa, Masami Futatsubashi,
Hiroyuki Okada, Tatsuo Torizuka, and Mitsuo Kaneko, "Neural
substrates in judgment process while playing Go: A comparison of
amateurs with professionals," Cognitive Brain Research, vol. 23, no.
2-3, pp. 164 - 170, 2005.
[5] J. Burmeister and 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.
[6] Y. Wang and S. Gelly, "Modifications of UCT and sequence-like
simulations for monte-carlo Go," in IEEE Symposium on Computational
Intelligence and Games, 2007., 2007, pp. 175-182.
[7] L. Chang-Shing, W. Mei-Hui, G. Chaslot, J.-B. Hoock, A. Rimmel,
O. Teytaud, Shang-Rong T., Shun-Chin H., and H. Tzung-Pei, "The
computational intelligence of MoGo revealed in Taiwan-s computer Go
tournaments," in IEEE Transactions on Computational Intelligence and
AI in Games., 2009, vol. 1, pp. 73-79.
[8] Fernand Gobet, Peter C.R. Lane, Steve Croker, Peter C-H. Cheng, Gary
Jones, Iain Oliver, and Julian M. Pine, "Chunking mechanisms in human
learning," TRENDS in Cognitive Sciences, vol. 5, no. 6, pp. 236 - 243,
2001.
[9] C. Shannon, "Programming a computer for playing Chess," Philosophical
Magazine, vol. 41, no. 314, 1951.
[10] J. Robson, "The complexity of Go," in Proceedings of IFIP Congress,
1983, pp. 413-417.
[11] T. Cover and J. Thomas, Elements of Information Theory, 2nd edition,
Wiley, 2006.
[12] Peter D. Gr¨unwald and A. Philip Dawid, "Game theory, maximum
entropy, minimum discrepancy and robust bayesian decision theory,"
The Annals of Statistics, vol. 32, no. 4, pp. 1367-1433, 2004.
[13] S. Kullback and R. A. Leibler, "On information and sufficiency," The
Annals of Mathematical Statistics, vol. 22, no. 1, pp. 79-86, 1951.
[14] J. Lin, "Divergence measures based on the shannon entropy," Information
Theory, IEEE Transactions on, vol. 37, no. 1, pp. 145-151, August
2002.
[15] E. Berlekamp and D. Wolfe, Mathematical Go: Chilling gets the last
point, AK Peters, 1994.
[16] J. S. Reitman, "Skilled perception in Go: Deducing memory structures
from inter-response time," Cognitive Psychology, vol. 8, pp. 336-356,
1976.
[17] Mark S. Roulston, "Estimating the errors on measured entropy and
mutual information," Physica D: Nonlinear Phenomena, vol. 125, no.
3-4, pp. 285 - 294, 1999.
[18] D. Messick and A. Rapaport, "Expected value and response uncertainty
in multiple-choice decision behavior," Journal of Experimental Psychology,
vol. 70, no. 2, pp. 224 - 230, 1965.
[19] A. Borst and F. Theunissen, "Information theory and neural coding,"
Nature Neuroscience, vol. 2, no. 11, pp. 947 - 957, 1999.
[20] G. Halford, N. Cowan, and G. Andrews, "Separating cognitive capacity
from knowledge: a new hypothesis," TRENDS in Cognitive Science, vol.
11, no. 6, pp. 236 - 242, 2008.
[21] G. Orb'an, J. Fiser, R. Aslin, and M. Lengyel, "Bayesian learning of
visual chunks by human observers," PNAS, vol. 105, no. 7, pp. 2745 -
2750, 2008.
@article{"International Journal of Information, Control and Computer Sciences:60432", author = "Michael Harre and Terry Bossomaier and Ranqing Chu and Allan Snyder", title = "Strategic Information in the Game of Go", abstract = "We introduce a novel approach to measuring how
humans learn based on techniques from information theory and
apply it to the oriental game of Go. We show that the total amount
of information observable in human strategies, called the strategic
information, remains constant for populations of players of differing
skill levels for well studied patterns of play. This is despite the very
large amount of knowledge required to progress from the recreational
players at one end of our spectrum to the very best and most
experienced players in the world at the other and is in contrast to
the idea that having more knowledge might imply more 'certainty'
in what move to play next. We show this is true for very local
up to medium sized board patterns, across a variety of different
moves using 80,000 game records. Consequences for theoretical and
practical AI are outlined.", keywords = "Board Games, Cognitive Capacity, Decision Theory,Information Theory.", volume = "4", number = "5", pages = "980-6", }
