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BGonline.org Forums
Varianace Reduction for Dummies
Posted By: Stein Kulseth In Response To: Varianace Reduction for Dummies (rambiz)
Date: Thursday, 11 August 2016, at 7:23 p.m.
David Montgomery explains it well here.
An example, say you want to roll out the last roll where Blue has 1 on 2 and 1 on 5 - vs White's 2 on 1. We know that Blue has 19 rolls to get off, so his true equity is (19-17)/36 = 2/36.
Say we do a 36 game rollout w/o VR, and Blue gets somewhat lucky and the result comes out 22 - 14 in Blues favour. The estimated equity is (22-14)/36 = 8/36
Now enter VR, we have a crude racing estimator that says that the 9 big numbers (4,5,6 combos) are good - assign a luck factor of .45 to these, whereas the 27 others are bad - assign a luck factor of -.15 to these. Obviously here some of the bad rolls do get off, so the estimator is far from perfect, but it is not tailor made to this position.
Now, lets say the Blues 22 wins come from 11 big numbers, and 11 numbers where one of the dice has a 2 or a 3 in it. Then the VR equity estimate becomes: (11 * (1-.45) + 11 * (1 + .15) + 14 * (-1 + .15) ) / 36 = 6.8 / 36
Even with this crude estimator the VR estimate came out a tad better than the raw result.
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