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Subject: The probability to find better move is simply irrelevant for diminishing

Author: Uri Blass

Date: 04:08:35 02/09/02


returns.

Imagine the following simple game:
Every side need to say in it's turn if it resigns or not resign.
The game is finished only when one side resigns.

If both sides never resign the game is never finished.


Imagine the following 3 programs for that simple game:


Program A resigns with probability of 10% in every move
Program B resigns with probability of 1% in every move
Program C never resigns.

program C finds better move than program B only in 1% of the cases but in games
C always wins against B(B will do a mistake of resigning after enough moves).

Program B finds better move than program A in 9% of the cases but program A has
positive chance to beat program B.

I think that this is a convincing argument to prove that reducing the
probability to find a better move in the next ply has nothing to do with
diminishing resturns.

In practical games programs never do a mistake when they say resign but part of
the stupid moves are practically the same as say resign.
It is more complicated because losing moves from theoretical game do not finish
the game when the opponent can blunder and there are also draws but the idea is
similiar.

Uri



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