My understanding of temperature

xela: I look forward to seeing more here! Just in case you missed it: the examples and discussion at https://lifein19x19.com/viewtopic.php?f=15&t=17069 might be interesting to you; also Bill's comments there on overestimation of sente temperatures. I hope you don't mind me scribbling on your page... feel free to delete this comment once it's served its purpose.

# Definition

The temperature (T) of a board position is the difference between playing a move and passing in that position.

This assumes a perfect scoring mechanism S(P,C) which can calculate the score resulting from a position (P) and with a color (C), Black or White, to play.

In math notation: T(P) = |S(P,B) - S(P,W)|

# Temperature at start and end

• At the start of the game, assuming 7 points is the correct komi for perfect play, the temperature is 14 points. That's the lead one has with reverse komi: if Black passes on the first move, White has the first move AND komi.
• At the end of the game, when the dame are filled, with territory scoring, the temperature is 0. In area scoring, at the last dame the temperature is 2. This is also true for any odd number of dame remaining. If the number of dame remaining is even, the temperature is 0.
White has 7 komi

Black plays first, White has 7 komi, the result is even.

White has 7 komi

Black passes, White plays first, White has 7 komi. Since the game would be even if Black had 7 komi, the difference between playing and passing is 14 points.

# Temperature during the game

Intuitively one might expect the temperature to slowly decrease from 14 to 0, but that is obviously not the case: even at the dame filling stage, it might happen that a chain of 10 stones is in atari. At that point the temperature becomes 20 points, while previously it was 0.

## Late endgame

In the (late) endgame, we can treat local positions as isolated, since their outcome won't affect other positions. In that case, we consider the local temperature to be the temperature as above, assuming that the local position is alone on the board. This allows us to compare temperatures of different local positions. This is elaborated upon in endgame theory? where the (mai) count of a position is the average in the local result between either player moving and the miai value is the difference between that count and one player moving.

The global temperature is still more complicated, as we need to compare two sequences of endgame moves, with either player going first. That's why we estimate the global temperature in the endgame to be half of the biggest local temperature.

## Middle game or early endgame

When local positions influence nearby other positions or distant ones (e.g. ladder breakers, calculating local temperature is even more difficult. We can only rely on substitutes for global temperature like score estimators, in particular KataGo's feature.

# Relationship to value of a move

Since (local) temperature is equivalent to the value of a move but a more obscure term, we may prefer "value of a move".

We can then reserve (ambient) temperature to indicate the value of the biggest move elsewhere. But we can also simply use the latter.

Temperature allows for shorter statements:

```"a move is sente if it results in a local temperature higher than ambient temperature"
vs
" a move is sente if the value of a move in the resulting position is higher than the value of the biggest move elsewhere".
```

DieterVerhofstadt / Temperature last edited by xela on February 16, 2024 - 01:40