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How to estimate chances  RO data
Posted By: AP
Date: Wednesday, 28 November 2012, at 4:02 p.m.
In Response To: How to estimate chances  RO data (Daniel Murphy)
Thank you all for the great analysis.
The “another approach” post by Mr. Majestyk was really insightful, and helped me think more clearly about the problem. The post from Daniel corrected and refined some of the calculations, and after chewing on that, here is my summary as of now:
Blue has .08 to hit on next roll.
The number of chances he will get to hit is ~ [(38 spare pips) *(21/36 rolls that don’t blot or pass) ]/(6.48 average pips when white rolls a not hit/not pass)=3.4
The 4th iteration will hardly change anything, so lets assume 3 chances for blue to get a shot.
Daniel’s calculation was: .08*[1+21/36+(21/36)^2+(21/36)^3], but this still does not seem quite right to me. The basis for the calculation that blue has 3 chances to hit was the reservoir of 38 spare white pips…so it seems that on the third iteration, white has no more ‘average’ rolls, and either clears with one of his 7 great rolls or leaves a shot.
Therefore, my calculation (based on the estimation that when white blots blue hits 36% of the time):
.08*[1+21/36+(21/36)^2]+(21/36)^3*(.08+21/36*.36)
=.08*[1+21/36+(21/36)^2+(21/36)^3]+ (21/36)^4*.36
=.21
(compared to Daniel’s analysis you can see I add on one additional term to account for the extra chances blue gets once white’s reservoir of spare pips is gone).
Now for the adjustments:
• White’s gapped 5point has got to hurt him a bit…his 38 spare pips cant be used optimally
• As Daniel pointed out, blue also has limited spare pips, so this hurts blue’s chances. I am not sure exactly how to quantify this myself.
• Both effects should only amount to a few % or so, let’s call it a wash: So, I also come to around 21% hitting chances. Tack on a few extra % of race equity, and we get blue chances of ~24%.
I am still working on a clear way to estimate this type of thing over the board (albeit with less accuracy but good enough). Also thanks to Daniel for showing how to pull the hit chances out of GNU. If it turns out XG does not offer this feature, I may boot up GNU just for this feature alone. Thanks again to everyone.

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