This mini article is in reference to Stick's Daily Quiz 5/16
Problem 5
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eXtreme Gammon Version: 2.00.163.beta
These kinds of positions represent a problem in estimating shot equity, as there will often be several rolls before we get any idea as to the number of shots we're likely to get. In any event, the brut-force method of estimating the accumulative probability of several rolls is cumbersome, inefficient and mentally draining; often leading to possible errors in judgement.
Proposal
We can bypass the process of counting shots by estimating the "Problem Space" in terms of pips where, on average we'll figure on hitting a shot 30% of the time. For instance, in problem 5 (5/16), white's probability of getting a shot will most likely materialise between her own 10-pt and blue's 6-pt. Blue has 27 pips to negotiate the mini stack on the 15-pt to the 6-pt or 21.6% of his pip-count. If we were to consider blue's pip-count as the problem space where, in any given "state" white hits a shot, then, white's pip gain would be 21.6*30%, 6.48. In percent, this would convert to 21.6*22.7 = 4.9%.
White's "point of last take" is 146-6.48, indicating a take where she figures to win the game 22.7+4.9, 27.6% of the time.
Majestyk