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Rollout strength  Your thoughts on a mathematical model
Posted By: eXtreme Gammon
Date: Friday, 10 February 2012, at 1:41 p.m.
Hello everyone,
Considering the large number of mathematicians (professionals and amateurs) here, I figured it is a good place to request insights.
I am a trying to estimate the level of play of RO: for instance how strong is a full 2ply 1296 game rollout.
Using the Depreli Rollouts (3ply/XGRoller, roll until 0.005 95% CI) I got the number for 1 and 2 ply rollout at different length (108, 324, 648, 1296, 2592, 5K, 10K [not for 2ply] yet). I also got some data for 3ply Red RO (108, 1296) and the data from GnuBg 2ply 1296 RO.
I'd like to derive from that data a formula that estimate properly the level of a RO, the idea is that it can be applied to stronger RO settings that are not practical (possible) to test.
Here is my idea:
L: PR of the ply used in the RO N: number of game rolled LL: PR of the ply used for luck in Variance reduction PR(RO) = PR_{inf}(L) + VR(N,LL)
PR_{inf}(L) is a the level that correspond to its level if the RO was infinite. strictly descending and with PR_{inf}(0)=0
VR(N,LL) is strictly descending function with N and LL, converging to 0 when N>infinite that correspond to the noise of the ROI would be interesting to see people suggestions in what PR_{inf} and VR functions looks like (or of course any other formula idea).
For instancePR_{inf} (L)= a.L VR(N,LL) = b.LL/sqrt(N) Where a and b are constants I'll wait a few days to show the formulas I came up (thats not the ones shown above) with and publish the data.

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