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Counterexample by Lamford?

Posted By: Timothy Chow
Date: Friday, 26 September 2014, at 3:42 p.m.

In Response To: Counterexample by Lamford? (Bob Koca)

Bob Koca wrote:

The non cube in step 4 is then indeed an error. He seems to think that if player A knew he would get that 5-5 dance sequence that A should not double. It is not hard to see why that is faulty: Suppose that the opponent B will cube if he himself has a market losing sequence (note this is possibly suboptimal). B will always win 2 points when he wins a played out game but when he loses a played out game will sometimes lose two but sometime LOSE ONLY ONE. He might get cashed out but at that point if the drop is correct A regrets not having doubled before that initial market loss.

Contrast this to the situation if A just doubled initially. The game is always worth 2. Clearly a better situation for A.

While trying to explain this argument to AP by email, I found what might be a small logical loophole. Here was my paraphrase. Let us make the explicit assumption (that I think you were making implicitly) that B employs DMP checkerplay. Then the four possible ways that Lamford's recommended procedure could end are:

1. At some point, B doubles and A takes.
2. At some point, A doubles and B takes.
3. The cube is never turned and A wins a gammon.
4. At some point, A doubles and B drops.

Then your argument, I believe, is that Case 4 is worse for A than it would have been if he had turned the cube earlier, while the other cases are equivalent.

This argument works if A also employs DMP checkerplay at all times. However, how do we rule out the possibility that A might be able to do better by deviating from DMP checkerplay when the cube is still centered?

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