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Any reason to roll out multiple-of-36 games?

Posted By: Bob Koca
Date: Monday, 28 September 2009, at 7:27 p.m.

In Response To: Any reason to roll out multiple-of-36 games? (Rich Munitz)

I figure that the double counting technique is actually worse.

Protocol A uses each of the 36 rolls. It is reasonable to figure that the variances in the rollout results are close to being independent and equal. So suppose we have X1, X2, ...X36 as indep random variables with a common variance V. We have Var[(X1+X2+X3+...+X36)/36] = (1/36)V. The std dev is 1/6th the sdev of a single observation.

Protocal B uses only 21 rolls and counts the non-doubles twice. If X1, X2, ... X21 are ind random variables with a common variance V then Var[ (X1 + X2 + ...X6 + 2(X7 + X8 + ...X21))/36] = (6 + 4*15)V/36^2 =approx. 1.83(1/36)V. The std dev is approx. 1.35(1/6th) the sdev of a single observation. So 21/36 of the number of rollouts but the std dev is 1.35 times greater. Is it worth the trade?

No. Multiplying the number of rollouts by M divides the std. dev by SQRT(M). SQRT(36/21) = 1.309 which is lower than the 1.35 factor from before. Another way to look at is to compare 21 sets of protocol A with 36 sets of protocol B.

Messages In This Thread

• Any reason to roll out multiple-of-36 games?
  Timothy Chow -- Monday, 28 September 2009, at 5:01 p.m.
  • Any reason to roll out multiple-of-36 games?
    Gregg Cattanach -- Monday, 28 September 2009, at 5:27 p.m.
    • Any reason to roll out multiple-of-36 games?
      Michael Petch -- Monday, 28 September 2009, at 5:38 p.m.
  • Any reason to roll out multiple-of-36 games?
    Frank Berger -- Monday, 28 September 2009, at 5:58 p.m.
    • Any reason to roll out multiple-of-36 games?
      Rich Munitz -- Monday, 28 September 2009, at 6:47 p.m.
      • Any reason to roll out multiple-of-36 games?
        Bob Koca -- Monday, 28 September 2009, at 7:27 p.m.
        • Any reason to roll out multiple-of-36 games?
          Maik Stiebler -- Monday, 28 September 2009, at 9:32 p.m.
        • Any reason to roll out multiple-of-36 games?
          Timothy Chow -- Wednesday, 30 September 2009, at 1:55 a.m.
          • Any reason to roll out multiple-of-36 games?
            Bob Koca -- Wednesday, 30 September 2009, at 2:44 a.m.
            • Any reason to roll out multiple-of-36 games?
              Maik Stiebler -- Wednesday, 30 September 2009, at 11:17 a.m.
          • Any reason to roll out multiple-of-36 games?
            Maik Stiebler -- Wednesday, 30 September 2009, at 11:25 a.m.
  • Any reason to roll out multiple-of-36 games?
    Jason Lee -- Monday, 28 September 2009, at 7:29 p.m.
    • Any reason to roll out multiple-of-36 games?
      Maik Stiebler -- Monday, 28 September 2009, at 9:13 p.m.
    • Any reason to roll out multiple-of-36 games?
      Ian Shaw -- Monday, 28 September 2009, at 9:33 p.m.