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$$ 16cube reship
Posted By: Timothy Chow
Date: Friday, 21 May 2010, at 3:21 a.m.
In Response To: $$ 16cube reship (bob koca)
First of all, the context of the current conversation is not what is useful for practical understanding of the game, but what makes most sense as a precise definition for an attempt to push the mathematical limits in a construction task. In a practical context it's O.K. to blur various concepts and use language inconsistently if it is useful to do so. Not when trying to push mathematical boundaries.
Secondly, your particular example doesn't even prove what you want it to prove. It doesn't prove that the appropriate definition of "probability of winning" of a money game is the cubeless probability of winning; it merely proves that the concept of the cubeless probability of winning from a particular position can be a useful tool for understanding a money game.
I still say that it is bizarre, in the context of trying to construct a mathematically extreme example, to ask for a moneygame take for which minimizes the probability of winning if the subsequent checker play were cubeless. Why the cubeless probability of winning instead of the DMP probability of winning, for example?
If A and B play a backgammon game, and it ends, and I ask, "Who won?" then the answer will be either "A" or "B." Nobody says, "A won 79%." The game ended; somebody won. That's what the word "winning" normally means. The probability of winning should surely be defined as, um, the probability of winning (assuming correct play). I can't see why it should be defined any other way.

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