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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 2-ply 1296 game rollout.

Using the Depreli Rollouts (3-ply/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 2-ply] yet). I also got some data for 3-ply Red RO (108, 1296) and the data from GnuBg 2-ply 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 RO

I would be interesting to see people suggestions in what PR_inf and VR functions looks like (or of course any other formula idea).
For instance

PR_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.

Messages In This Thread

• Rollout strength - Your thoughts on a mathematical model
  eXtreme Gammon -- Friday, 10 February 2012, at 1:41 p.m.
  • Rollout strength - Your thoughts on a mathematical model
    Bob Koca -- Friday, 10 February 2012, at 2:28 p.m.
    • Rollout strength - Your thoughts on a mathematical model
      eXtreme Gammon -- Friday, 10 February 2012, at 2:55 p.m.
  • Rollout strength - A mathematical model
    eXtreme Gammon -- Friday, 17 February 2012, at 3:33 p.m.
    • Rollout strength - A mathematical model
      Maik Stiebler -- Saturday, 18 February 2012, at 10:03 a.m.
      • Rollout strength - A mathematical model
        eXtreme Gammon -- Saturday, 18 February 2012, at 4:53 p.m.
        • Rollout strength - A mathematical model
          Maik Stiebler -- Sunday, 19 February 2012, at 10:10 a.m.