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Half as wild

Posted By: Timothy Chow
Date: Thursday, 22 April 2010, at 5:01 p.m.

In Response To: Half as wild (Daniel Murphy)

Daniel Murphy wrote:

If, for instance, we want to combine the relative equities of the XG 4-ply and Gnubg 2-ply rollouts, even though their absolute results are out of each other's 95% confidence intervals, is there a rationale for doing that, other than the old standby

I don't believe so. In fact I would be in favor of averaging absolute equities.

And another question: a rollout of two plays reports standard deviations or 95% confidence intervals for the absolute equity of each play. But what's the confidence interval of the relative equity?

If A and B are independent random variables then the variance of A – B is the sum of the variances of A and B. In terms of standard deviations, if s is the standard deviation of A and t is the standard deviation of B, then the standard deviation of A – B is the square root of s² + t². In particular if s = t then the standard deviation of A – B is going to be larger than s by a factor of sqrt(2).

The assumption that A and B are independent is a subtle one. In this context it means, roughly speaking, that the positions that arise after play A are "unrelated" to the positions that arise after play B. It's probably a reasonable assumption though I'm unaware of anyone who has studied it thoroughly.

Messages In This Thread

• 4 ply RO of 21$-54
  neilkaz -- Monday, 19 April 2010, at 5:18 p.m.
  • 4 ply RO of 21$-54
    Nack Ballard -- Monday, 19 April 2010, at 6:18 p.m.
  • 4 ply RO of 21$-54
    Chase -- Monday, 19 April 2010, at 6:21 p.m.
    • 4 ply RO of 21$-54
      neilkaz -- Monday, 19 April 2010, at 6:48 p.m.
  • 4 ply RO of 21$-54
    Nack Ballard -- Monday, 19 April 2010, at 6:25 p.m.
    • 4 ply RO of 21$-54
      eXtreme Gammon -- Monday, 19 April 2010, at 6:32 p.m.
      • 4 ply RO of 21$-54
        Nack Ballard -- Tuesday, 20 April 2010, at 7:19 p.m.
  • ... and XG 3-ply RO of 21$-54
    Chase -- Monday, 19 April 2010, at 7:39 p.m.
    • ... and XG 3-ply RO of 21$-54
      Neil Robins -- Monday, 19 April 2010, at 8:38 p.m.
    • Currently [S R5]16k *NM*
      neilkaz -- Tuesday, 20 April 2010, at 7:41 p.m.
    • ... and XG 3-ply RO of 21$-54
      Nack Ballard -- Tuesday, 20 April 2010, at 7:54 p.m.
      • ... and XG 3-ply RO of 21$-54
        Chase -- Tuesday, 20 April 2010, at 8:39 p.m.
        • ... and XG 3-ply RO of 21$-54
          Chase -- Tuesday, 20 April 2010, at 8:46 p.m.
          • 41$-63, 21$-63, 51$-63 and 62$-63
            Nack Ballard -- Wednesday, 21 April 2010, at 4:35 a.m.
            • 41$-63, 21$-63, 51$-63 and 62$-63
              Chase -- Wednesday, 21 April 2010, at 10:43 a.m.
              • 41$-63, 21$-63, 51$-63 and 62$-63
                Matt Cohn-Geier -- Wednesday, 21 April 2010, at 10:51 a.m.
                • 41$-63, 21$-63, 51$-63 and 62$-63
                  Chase -- Wednesday, 21 April 2010, at 11:03 a.m.
                • 41$-63, 21$-63, 51$-63 and 62$-63
                  Nack Ballard -- Wednesday, 21 April 2010, at 2:11 p.m.
                  • 41$-63, 21$-63, 51$-63 and 62$-63
                    Chase -- Wednesday, 21 April 2010, at 4:53 p.m.
                    • 41$-63, 21$-63, 51$-63 and 62$-63
                      Nack Ballard -- Wednesday, 21 April 2010, at 5:44 p.m.
              • Nacbrac information
                Nack Ballard -- Wednesday, 21 April 2010, at 2:43 p.m.
                • Nacbrac information
                  Chase -- Wednesday, 21 April 2010, at 5:04 p.m.
                  • Nacbrac information
                    Nack Ballard -- Wednesday, 21 April 2010, at 5:25 p.m.
        • ... and XG 3-ply RO of 21$-54
          Nack Ballard -- Wednesday, 21 April 2010, at 3:39 a.m.
      • ... and XG 3-ply RO of 21$-54 w/Jacoby
        neilkaz -- Wednesday, 21 April 2010, at 3:07 a.m.
        • Will extend this 3 ply to 100k
          neilkaz -- Wednesday, 21 April 2010, at 12:38 p.m.
    • XG 3-ply RO of 21$-54 - w/ Jacoby
      Chase -- Wednesday, 21 April 2010, at 11:16 a.m.
  • 4 ply RO of 21$-54
    Nack Ballard -- Tuesday, 20 April 2010, at 8:19 p.m.
    • 4 ply RO of 21$-54
      neilkaz -- Tuesday, 20 April 2010, at 10:11 p.m.
  • 3 ply RO of 21$-54..over 100k
    neilkaz -- Wednesday, 21 April 2010, at 10:11 p.m.
    • Wild rollout results (bug?)
      Nack Ballard -- Thursday, 22 April 2010, at 1:05 a.m.
      • Wild rollout results (bug?)
        neilkaz -- Thursday, 22 April 2010, at 1:53 a.m.
        • Re-run of RO w/ random seed and Jacoby in progress
          Chase -- Thursday, 22 April 2010, at 2:08 a.m.
          • Re-run of RO w/ random seed and Jacoby in progress
            Nack Ballard -- Thursday, 22 April 2010, at 2:27 a.m.
            • Re-run of RO w/ random seed and Jacoby in progress
              Chase -- Thursday, 22 April 2010, at 2:42 p.m.
          • Completed RO w/ Jacoby and random seed
            Chase -- Thursday, 22 April 2010, at 3:05 p.m.
        • My 10k with seed 2
          neilkaz -- Thursday, 22 April 2010, at 3:09 a.m.
      • Wild rollout results (bug?)
        Chase -- Thursday, 22 April 2010, at 2:02 a.m.
      • Half as wild
        Daniel Murphy -- Thursday, 22 April 2010, at 2:37 a.m.
        • Half as wild
          Neil Robins -- Thursday, 22 April 2010, at 11:34 a.m.
        • Half as wild
          Timothy Chow -- Thursday, 22 April 2010, at 5:01 p.m.
      • 21$-54 rollout data (equities, links)
        Nack Ballard -- Thursday, 22 April 2010, at 7:50 p.m.
        • 21$-54 rollout data (equities, links)
          Daniel Murphy -- Thursday, 22 April 2010, at 8:34 p.m.
          • 21$-54 rollout data (equities, links)
            Nack Ballard -- Friday, 23 April 2010, at 9:03 a.m.
  • 4 ply RO of 21$-54 19k and finished
    neilkaz -- Thursday, 22 April 2010, at 12:08 a.m.
  • Snowie RO of 21$-54
    Nack Ballard -- Thursday, 22 April 2010, at 7:16 p.m.
    • Snowie RO of 21$-54
      Daniel Murphy -- Thursday, 22 April 2010, at 7:37 p.m.