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BGonline.org Forums
It is not certain
Posted By: mamabear In Response To: It is not certain (Barry Silliman)
Date: Friday, 13 January 2017, at 10:57 p.m.
Your post has the appearance of a false dichotomy, though that may not have been the intent..."I can't prove it" >>
Every roll is a new cube decision. If they don't double at their first opportunity, that by no means requires them to continue holding off "...in hopes of obtaining that elusive theoretical position that has 1a 2a Crawford equity without having been preceded by any market losing sequences." They can still double at their second opportunity, or their seventh, or their seventeenth. And before the Logic Police kick my door down, I will say they are not restricted to those choices, either.
They have to consider the odds for the current sequence that they will reach a position where their opponent might make a cube error, vs. the chance they will both legitimately lose their market on this sequence and have the opponent recognize this and actually pass. To do this, they have to understand their opponent's game well enough to know the probability of a wrong decision on each possible sequence, including both wrong passes after good sequences where the take is still there, and wrong takes on the market-loss ones, and the amount of equity involved in each case. If they have reason to think their opponent believes himself to be better than them, they may also have to modify all the coefficients to account for adjustments to their cube strategy the opponent might make for that reason.
I could show more work for this, but why bother when the proof is so trivial?
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