Celebratio Mathematica — Berlekamp

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E. R. Berlekamp, M. Müller, and B. Spight: Generalized thermography: Algorithms, implementation, and application to Go endgames. Technical report TR-96-030, International Computer Science Institute (Berkeley, CA), October 1996. techreport

Thermography [Berlekamp et al. 1982] is a powerful method for analyzing combinatorial games. It has been extended to games that contain loops in their game graph by Berlekamp [1996]. We survey the main ideas of this method and discuss how it applies to Go endgames. After a brief review of the methodology, we develop an algorithm for generalized thermography and describe its implementation.

To illustrate the power and scope of the resulting program, we give an extensive catalog of examples of ko positions and their thermographs.

We introduce a new method related to thermography for analyzing ko in the context of a specific ko threat situation. We comment on some well-known Go techniques, terminology, and “exotic” Go positions from a thermography point of view. Our analysis shows that a framework based on generalized thermography can be useful for the opening and midgame as well. We suggest that such a framework will serve as the basis for future strong Go programs.

Martin Müller	Related
William L. Spight	Related

T. Nakamura and E. Berlekamp: “Analysis of composite corridors,” pp. 213–229 in Computers and games: Third international conference (Edmonton, AB, 25–27 July 2002). Edited by J. Schaeffer, M. Müller, and Y. Björnsson. Lecture Notes in Computer Science 2883. Springer (Berlin), 2003. incollection

This work began as an attempt to find and catalog the mean values and temperatures of a well-defined set of relatively simple common Go positions, extending a similar but smaller catalog in Table E.10, Appendix E of the book Mathematical Go [Berlekamp and Wolf 1994].

The major surprises of our present work include the following

A position of chilled value *2 (previously unknown in Mathematical Go), shown at the end of Sect. 3.1.
A surprisingly “warm” position, whose temperature is routinely underestimated even by very strong Go players, shown in Sect. 4.
More insights into decompositions.

It is hoped that these results may someday provide the basis for further new insights and generalizations.

Jonathan Schaeffer	Related
Yngvi Björnsson	Related
Martin Müller	Related