Ambient Temperature

The ambient temperature is the temperature of the rest of the board outside the play or plays in focus, for instance, a ko fight. It is an abstraction, roughly equal to the miai value of the largest play not in focus.

The ambient temperature may affect the local play. In the case of Ko Threat - Rule of Thumb, it figures in the estimate of the ko exchange.

More precisely, ambient temperature is the highest miai value on the board, but constrained to never rise. The ambient temperature starts at the highest miai value on the board at the beginning of the game. After each move, if the highest miai value is lower than the ambient temperature, then the ambient temperature falls to that miai value. Otherwise the ambient temperature stays the same.

Intuitively, it makes sense for the ambient temperature to never rise: In Go, experience shows that there are generally diminishing returns, and ambient temperature measures "how slim the pickings are now" after all the lower-hanging fruit have been snapped up. It was profitable for the players to play all those high-value endgames earlier in the game, so they are all gone now. The days of abundant high-value endgame moves will never come back. Even if a region temporarily heats up, it won't change this big picture.

Another way to keep track of ambient temperature is to consider Environmental Go, where you have a sorted stack of coupons with positive point values on them, high values on top. The point values are dense in the sense that there are no large gaps between consecutive coupons. Instead of playing a move, either player may instead take the top coupon. A coupon with the number x on it is equivalent to a switch {x | -x}, which has the miai value of x. This simulates a rich environment, where gote moves of all sizes are available to the players, and there are no large tedomari to spoil an orthodox strategy.

In a position where a perfect player would rather take a coupon than play on the board, keep discarding the top coupon (this simulates "low-hanging fruit being snapped up") until the perfect player prefers to play on the board. Otherwise do not touch the coupon stack. In any position, after the discarding procedure is done, the miai value of the top coupon is the ambient temperature (up to the rounding error caused by the coupon values not being dense enough to measure the ambient temperature precisely). The coupon stack is the environment, and its temperature is the ambient temperature. In this procedure, the coupon stack is not actually used by the players, it simply exists as a fictitious device used to measure ambient temperature. It enforces monotonicity, ensuring that the ambient temperature never rises, just as already picked fruit are never returned to the trees.