What is the value of a move in a yose ko?

[Gérard TAILLE]

Please do understand that the definition of rich environment relies on contextual assumptions for considering every D. It is denser than you can and want to imagine. Arbitrarily, infinitely dense. When playing a rich ensemble in order of decreasing values, the remaining stack of smaller move values in the rest of the rich environment remains arbitrarily dense until the very end. You have taken the last local endgame move and the rest of the rich environment proceeds, e.g., by taking 1/128, then 1/128 - eps, where 1 >> eps > 0, then 1/128 - 2*eps etc. to, after arbitrarily many moves, eventually eps, then 0.

OK Robert. Now, coming back to this thread (What is the value of a move in a yose ko)

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Click Here To Show Diagram Code

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Do you agree that the value of a move in this position is (a-b)/5 = 18/5 = 3.6 ?
If not what is your evaluation?

[RobertJasiek]

(Assuming outer stones are unconditionally alive.)

If evaluated closely to CGT-like theory, approach kos have different move values for different (types of) environments. Black | White Komaster, Black | White komonster, neutral threat environment etc.

If evaluated naively / pragmatically, one uses the tally to derive some move value. Here, this tally is 4.

One can also circumvent using local move values by fighting the ko globally and deciding, e.g., by [Tactical] Reading and [decision-making due to] Counting [of quiet followers].

I have not followed your discussion with kasir in detail so I missed where your divisor 5 comes from. I am sure there can be some justification for it. As can there be for the divisor 2 (when White is komonster).

[Gérard TAILLE]

(Assuming outer stones are unconditionally alive.)

If evaluated closely to CGT-like theory, approach kos have different move values for different (types of) environments. Black | White Komaster, Black | White komonster, neutral threat environment etc.

If evaluated naively / pragmatically, one uses the tally to derive some move value. Here, this tally is 4.

One can also circumvent using local move values by fighting the ko globally and deciding, e.g., by [Tactical] Reading and [decision-making due to] Counting [of quiet followers].

I have not followed your discussion with kasir in detail so I missed where your divisor 5 comes from. I am sure there can be some justification for it. As can there be for the divisor 2 (when White is komonster).

Yes of OC the value of this approach ko depends on the environment. The context is the following : assuming a ko fight takes place kvasir suggested that the player who will win the ko must pay in compensation a kind of tax due the ko threats used. With this in mind I did not assume Black | White Komaster, Black | White komonster, or a neutral threat environment without any ko threat. Instead I assumed each player may use a set of ideal ko threats from the biggest one to the smaller ones. In addition I assume the set of black ko threats and the set of white ko threats are quite identical (no advantage for black or white in the ko threats environment).
With this assumption it is clear that the value of the ko is smaller than usual because the player winning the ko would give compensation to the other player.

[RobertJasiek]

Ok, ko threat analysis is another valid kind of evaluation but there is little theory so far (other than my local ko threat per-move move value comparison). Mostly, theory needs to be built from ground up. Good luck you two and whoever with that!