I hope this isn't original but to humor Gerard who seems to

want to discuss models.

Preliminary about Computer EvaluationTo start with let G = { L | R } be a game where black, or left, can move to game L and white, or right, can move to game R.

Programs like KataGo can compute or rather estimate left's

negamax value and right's negamax value for a game. This estimate can be related to the mean and temperature of G as shown

lnv(G) ~= mean(G) + temperature(G) , left's negamax value

rnv(G) ~= mean(G) - temperature(G) , right's negamax value

and importantly

mean(G) = (mean(G) + temperature(G) + mean(G) - temperature(G)) / 2 ~= (lnv(G) + rnv(G)) / 2

I'll most of the time use equality signs instead of some other sign that may be more correct, just for convenience.

Later proof reading: I might have to check the previous part again later

Simple ModelNow let's look at the simple for total effect of a local position

*e* =

*t* +

*s* +

*x*The meaning of the variables are as follows, but briefly:

*e* : for total effect

*t* or

*k**

*t* : for a penalty or a tax for extra moves in the local position. Sometimes I'll write

*k**

*t* instead of

*t* and let

*k*=-7 (or other value) and

*t* be the difference between black and white moves in the local position.

*s* : for the difference in territory

*x* : for outside influence and other effects

To give total effect for a local position P in game G a meaning I’ll refer to a null game N. The null game is a proxy for G – P, or game G without P, which we may be able to realize in some simple cases and be unable to in more intricate cases. One way to realize G – P would be to remove the position P from G or replace it with something neutral.

Let’s assume that we can find a suitable null game and define the total effect as follows

*e* = mean(G) - mean(N)

This definition suffices to solve for the outside effect

*x* in some situations as follows.

Let

*e*^L =

*k* * (

*t* + 1) +

*s*^L +

*x**e*^R =

*k* * (

*t* - 1) +

*s*^R +

*x*be models for the left and right subgames of the local position P. P is embedded in the game G but I'll sometimes treat it as if it were a game, without trying to get into when that is justified and when not.

Using little bit of algebra we can write

mean(G) - mean(N) =

*e* = (

*e*^L +

*e*^R) / 2 = ((

*k* * (

*t* + 1) +

*s*^L +

*x*) + (

*k* * (

*t* - 1) +

*s*^R +

*x*)) / 2 = (

*s*^L +

*s*^R) / 2 +

*x*Note: The last equality is only justified when there are equal number of moves by both players and therefore t = 0.

Which gives us a formula for the outside effect

*x**x* = mean(G) - mean(N) - (

*s*^L +

*s*^R) / 2

In the next post I'll apply this model to a position suggested by Gerard.