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72-game rollouts in XG

Posted By: eXtreme Gammon
Date: Sunday, 1 May 2011, at 10:59 p.m.

In Response To: 72-game rollouts in XG (Timothy Chow)

Astute observation.

This is due to the fact that when reaching 72 games and on the way forward, the confidence interval is calculated based on the Variance of all 36 possible rolls, which are then recombined into one number. Most of the time the composite number is very close to the straight number (but always lesser). But in the case where the very next roll lead to positions that are quite clear one way or the other, this system will be valuable and report a smaller and "truer" CI.

A trivial example: if 19 dice leads to a sure win (+1.000), and 17 to a sure lost (-1.000), after 72 roll, the straight standard deviation is 0.9985 with a 95% confidence interval of 0.230

If you look at each set of 2 results for each dice, you see that the std dev is 0 and so is the combine one and report correctly eq=0.05556 +/- 0.0000

VR will lessen the advantage of that system, but it still helps.

Messages In This Thread

• 72-game rollouts in XG
  Timothy Chow -- Sunday, 1 May 2011, at 8:29 p.m.
  • 72-game rollouts in XG
    neilkaz -- Sunday, 1 May 2011, at 9:26 p.m.
    • 72-game rollouts in XG
      Timothy Chow -- Monday, 2 May 2011, at 4:02 p.m.
  • 72-game rollouts in XG
    eXtreme Gammon -- Sunday, 1 May 2011, at 10:59 p.m.
    • 72-game rollouts in XG
      Bob Koca -- Monday, 2 May 2011, at 1:58 a.m.
      • 72-game rollouts in XG
        eXtreme Gammon -- Monday, 2 May 2011, at 2:07 a.m.
    • 72-game rollouts in XG
      Bob Koca -- Monday, 2 May 2011, at 2:00 a.m.
      • 72-game rollouts in XG
        eXtreme Gammon -- Monday, 2 May 2011, at 2:09 a.m.
        • 72-game rollouts in XG
          Neil Robins -- Monday, 2 May 2011, at 11:56 a.m.
        • 72-game rollouts in XG
          Timothy Chow -- Monday, 2 May 2011, at 10:03 p.m.
          • 72-game rollouts in XG
            eXtreme Gammon -- Tuesday, 3 May 2011, at 1:39 a.m.
            • 72-game rollouts in XG
              Neil Robins -- Tuesday, 3 May 2011, at 11:42 a.m.
              • 72-game rollouts in XG
                eXtreme Gammon -- Tuesday, 3 May 2011, at 2:09 p.m.
            • 72-game rollouts in XG
              Timothy Chow -- Tuesday, 3 May 2011, at 3:27 p.m.
            • 72-game rollouts in XG
              Timothy Chow -- Monday, 23 May 2011, at 2:41 p.m.
              • 72-game rollouts in XG
                eXtreme Gammon -- Monday, 23 May 2011, at 3:53 p.m.