What is the theoretical value of the first move of a game?

[Bill Spight]

Good news Bill, I think we are completly in line!

I understand now that your hypothesis was different. You do not analyse a ko with the value of the ko just a little hooter than the temperature but also in the case where the value of the ko move (15) is far highter than the temperature (7 in your analysis).

Yes. Thermography is not just a tool to discover the average value of a position or combination of positions, and how much a play gains, but also to discover different strategies at different ambient temperatures.

Taking my calculation with your hypothesis it remains
b1 < b2 => -2x + 2y - t/2 < x - 3t/2 => 2y < 3x - t

but now I cannot put x = t.
I that case:
b1 < b2 => t < 3x - 2y
if x = 15 and y = 19 then b1 < b2 => t < 7 which is exactly your result.

When you look at the formula
t < 3x - 2y
you see that you have to compare the temperature to the global value of the ko (3x) minus the global value of the ko threat (2y) and that does not hurt my common sense though it seems not a known rule.

I discovered that rule and others in the early 1970s, but as a mere amateur shodan I had no thought of publishing anything. This and other rules are derived in the 1996 Mueller, Berlekamp, Spight paper: http://citeseerx.ist.psu.edu/viewdoc/su ... .1.34.6699

[Gérard TAILLE]

Let me test if you agree with my calculation in order to know when starting a ko in an ideal environment.

Let's suppose that the environment is made of pure gote areas with values equal to g1, g2, g3, g4, ...
Because I suppose an ideal environmment I expect
g1 - g2 + g3 - g4 ... = g1 / 2
g2 - g3 + g4 - g5 ... = g2 / 2
etc.

if x is the value of a ko move then
1) In absence of ko threat you start the ko when 3x >= 2g1 + g2
2) If your opponent has one ko threat you start the ko a little earlier when 3x >= 2g1 + g4
3) If your opponent has two ko threats you start the ko still a little earlier when 3x >= 2g1 + g6
4) If your opponent has a lot of ko threats you can even start the ko as soon as 3x >= 2g1

Note : if you are not in the endgame phase and if the value of the ko is equal to the temperature then, you may consider g1 = g2 = g3 = g4 ...,
the number of ko threat is irrelevant and there are no stress at all for this ko. It's equivalent to play in the ko or to play in the environment. In this case keep all your threats for another occasion and play where you want, in the ko or the environment.

[Bill Spight]

Let me test if you agree with my calculation in order to know when starting a ko in an ideal environment.

Let's suppose that the environment is made of pure gote areas with values equal to g1, g2, g3, g4, ...
Because I suppose an ideal environmment I expect
g1 - g2 + g3 - g4 ... = g1 / 2
g2 - g3 + g4 - g5 ... = g2 / 2
etc.

if x is the value of a ko move then
1) In absence of ko threat you start the ko when 3x >= 2g1 + g2
2) If your opponent has one ko threat you start the ko a little earlier when 3x >= 2g1 + g4
3) If your opponent has two ko threats you start the ko still a little earlier when 3x >= 2g1 + g6
4) If your opponent has a lot of ko threats you can even start the ko as soon as 3x >= 2g1

Bravo!

This was basically my first result, many moons ago. Note that each ko threat must be so large that it must be answered.

Technically, this result does not fit the model of thermography, because each gote and each threat that you take into account actually adds to the game with the ko. They are not considered part of the environment. (Edit: In thermography the right side is always 2g1 + t.) However, this result can be made more abstract to produce what Professor Berlekamp dubbed pseudo-thermography. A different form of pseudo-thermography was developed by Kim Yonghoan.