Thermography

The thermograph of a game is a graphical representation of the value of playing in it at different temperatures. The axes of the thermograph are the temperature (vertical) and the count (horizontal). At each temperature, the left wall of the thermograph shows what Left (Black) gets by playing first, and the right wall shows what Right (White) gets by playing first. At high enough temperatures the thermograph is topped by a vertical mast, which coincides with the left and right walls, and represents the count of the game. The temperature at the base of this vertical mast is the temperature of the game. In go it corresponds to miai value.

An example for a thermograph is shown in Cooling.

In ONAG thermographs are defined in terms of a tax on plays, but they may also be defined in terms of minimax play at different temperatures. Doing so allows the computation of the thermograph for a game with multiple kos or superkos. I did that in my paper, "Extended Thermography for Multiple Kos in Go" in Computers and Games 1998, pp. 232-251, Springer Verlag. An extension of the paper appears in Theoretical Computer Science 252(1-2): 23-43 (2001), a journal published by Elsevier.

See also Calculating a thermograph.

Bibliography

• Martin Müller, Elwyn Berlekamp, Bill Spight: Generalized Thermography: Algorithms, Implementation, and Application to Go Endgames. University of California, Berkeley, 1996, tr-96-030.ps.gz tr-96-030.pdf tr-96-030b.ps.gz tr-96-030b.pdf

Bill Spight: Not such a good introduction, as it is a little advanced. There are also several errors. It was a little advanced for us at the time. ;-) (Just kidding, Martin. The errors are mostly in diagrams and typos.) I recommend

• Winning Ways, by Berlekamp, Conway, and Guy

recently republished, or my write-up of the first environmental go game in

• Spight: "Go thermography: The 4/21/98 Jiang-Rui endgame" in More Games of No Chance, Richard Nowakowski (ed.), Cambridge University Press, 2002

There is a streaming video of my talk on that game.