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15552-game rollout of 41Z-65R-43

Posted By: Timothy Chow
Date: Monday, 28 December 2009, at 7:33 p.m.

In Response To: 15552-game rollout of 41Z-65R-43 (Chuck Bower)

I mentioned one example (buried deep in another thread, I admit) to Bob Koca, regarding transpositions. Suppose one rolled-out game starts with the dice 41-65-43 and reaches position P1, and another rolled-out game starts with the dice 43-65-41 and reaches position P2. When calculating the equity of the original position, you'll find yourself doing the computation equity(P1) + equity(P2) at some point. The standard assumption is that equity(P1) and equity(P2) are independent random variables, so that when you add them, their variances add: Var(equity(P1)) + Var(equity(P2)). However, perhaps P1 = P2 (i.e., the variations transpose). Then Var(equity(P1) + equity(P2)) = Var(2*equity(P1)) = 4*Var(equity(P1)), so your estimate of 2*Var(equity(P1)) is an underestimate.

Messages In This Thread

• 15552-game rollout of 41Z-65R-43
  Timothy Chow -- Sunday, 27 December 2009, at 12:23 a.m.
  • 15552-game rollout of 41Z-65R-43
    Leonardo Jerkovic -- Sunday, 27 December 2009, at 12:34 a.m.
  • 15552-game rollout of 41Z-65R-43
    Stick -- Sunday, 27 December 2009, at 12:41 a.m.
    • 15552-game rollout of 41Z-65R-43
      neilkaz -- Sunday, 27 December 2009, at 1:03 a.m.
    • 15552-game rollout of 41Z-65R-43
      Timothy Chow -- Sunday, 27 December 2009, at 2:08 a.m.
  • 15552-game rollout of 41Z-65R-43
    Nack Ballard -- Sunday, 27 December 2009, at 1:38 a.m.
    • 15552-game rollout of 41Z-65R-43
      Timothy Chow -- Sunday, 27 December 2009, at 2:02 a.m.
      • there are lies,
        garyo -- Sunday, 27 December 2009, at 4:00 a.m.
        • rollouts make an assumption
          garyo -- Monday, 28 December 2009, at 3:09 a.m.
      • 15552-game rollout of 41Z-65R-43
        Chuck Bower -- Sunday, 27 December 2009, at 2:52 p.m.
        • 15552-game rollout of 41Z-65R-43
          Timothy Chow -- Sunday, 27 December 2009, at 6:47 p.m.
          • 15552-game rollout of 41Z-65R-43
            Rich Munitz -- Sunday, 27 December 2009, at 7:12 p.m.
          • 15552-game rollout of 41Z-65R-43
            Chuck Bower -- Sunday, 27 December 2009, at 7:25 p.m.
          • 15552-game rollout of 41Z-65R-43
            Chuck Bower -- Monday, 28 December 2009, at 2:14 p.m.
            • 15552-game rollout of 41Z-65R-43
              Timothy Chow -- Monday, 28 December 2009, at 7:33 p.m.
              • 15552-game rollout of 41Z-65R-43
                Maik Stiebler -- Tuesday, 29 December 2009, at 8:45 a.m.
          • 15552-game rollout of 41Z-65R-43
            Daniel Murphy -- Wednesday, 16 June 2010, at 1:57 a.m.
        • 15552-game rollout of 41Z-65R-43
          Tom Keith -- Sunday, 27 December 2009, at 6:57 p.m.
    • 15552-game rollout of 41Z-65R-43
      Daniel Murphy -- Tuesday, 29 December 2009, at 12:58 a.m.
    • 41S-65R-43
      Matt Cohn-Geier -- Wednesday, 16 June 2010, at 1:06 a.m.
      • 41S-65R-43
        Nack Ballard -- Wednesday, 16 June 2010, at 1:53 a.m.
        • 41S-65R-43
          Stick -- Wednesday, 16 June 2010, at 3:30 a.m.