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standard error reported by gnu

Posted By: Timothy Chow
Date: Friday, 9 December 2016, at 4:53 a.m.

In Response To: standard error reported by gnu (rambiz)

Suppose you're interested in the equities of two candidate plays. Let X1 denote the result of playing out the game after making move 1, and let X2 denote the result of playing out the game after making move 2. You are interested in estimating the mean values E[X1] and E[X2].

The first thing to note is that X1 and X2 are independent. One way to see this is to imagine that you have two boards in front of you with the same position. On one board you play the first move and on the other board you play the second move. Then you continue playing the games to completion, using separate dice. What would it mean for X1 and X2 to not be independent? It would mean that knowing the value of X1 would provide some information about the value of X2. But clearly, knowing the outcome of the first game provides you with no information at all about the outcome of the second game. So X1 and X2 are independent.

The only plausible way I can see for some kind of dependence to arise is if the rollouts use the same set of dice for both moves. I'm not sure if the bots do this. If so, then in principle the random variables X1 and X2 are correlated. But the correlation should be very small. For example, knowing that I won a gammon in the first game gives some information about the sequence of dice rolls (they must have been lucky for me) and therefore gives a tiny bit of information about the result of the second game. But in most cases it really is tiny because a sequence of dice rolls that is lucky for move 1 isn't necessarily going to be lucky (or unlucky) for move 2.

Messages In This Thread

• standard error reported by gnu
  rambiz -- Thursday, 3 February 2011, at 10:11 p.m.
  • standard error reported by gnu
    Tom Keith -- Friday, 4 February 2011, at 3:30 a.m.
    • standard error reported by gnu
      rambiz -- Friday, 4 February 2011, at 9:32 p.m.