Go thermography is more complex than thermography for classical combinatorial games because of loopy games called kos. In most situations, go rules forbid the loopiness of a ko by banning the play that repeats a position. Because of the ko ban one player may be able to force her opponent to play elsewhere while she makes more than one play in the ko, and that fact gives new slopes to the lines of ko thermographs. Each line of a thermograph is associated with at least one line of orthodox play [Berlekamp 2000, 2001]. Multiple kos require a new definition of thermograph, one based on orthodox play in an enriched environment, rather than on taxes or on composing thermographs from the thermographs of the followers [Spight 1998]. Orthodox play is optimal in such an environment.

Reading a Thermograph

Many go terms have associations with thermographs. They are not defined in terms of thermographs, but I will be using them in talking about the game, and it will be helpful to be able to visualize the thermographs when I do. The inverse of the slope of a thermographic line indicates the net number of local plays. If one player makes 2 local plays while her opponent makes only plays in the environment, the slope will be plus or minus 1/2. The color of a line indicates which player can afford to play locally at a certain temperature. The player does not necessarily wish to play at that temperature, but she can do so without loss.

In the simple thermograph in Figure 1, the black mast at the top extends upward to infinity. It indicates a region of temperature in which neither player can afford to play locally without taking a loss. The mast starts at temperature, t = 2, which we call the temperature of this game, at the top of the hill. It also indicates the local count (or mast value), which is —5. Just below the top of the hill, the blue line of the Left wall indicates that Black (or Left) will not be unhappy to make a local play in this region of temperature. And it shows what the local score at each temperature would be when Black plays first. Similarly, the red line of the Right wall indicates an initial play by White (or Right).