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New XG rollout statistics: Variance Reduction

Posted By: Timothy Chow
Date: Tuesday, 17 February 2015, at 10:31 p.m.

In Response To: New XG rollout statistics: Variance Reduction (David Rockwell)

I'm not sure exactly what you mean by "converge"; your two rollouts lie within each other's confidence intervals. If you mean that you want the equity to be accurate to the third decimal place, then you need the confidence interval to be on the order of ±0.0005, and it's not often that we roll things out that far, VR or no VR.

In any case, you are right that one needs to be aware of this issue when considering rollout statistics. However, for some purposes, one does not need as many trials as you might think at first. For example, suppose one just wants to estimate the percentage of undoubled gammons, and suppose that this percentage is somewhere around 15%. With 5184 trials, the 95% confidence interval should be about (15 ± 1)% (here I got 1% from 2*sqrt(0.15*0.85/5184)). That is, getting the percentage of undoubled gammons to this degree of accuracy is a much less demanding requirement than getting the equity correct to 3 or even 2 decimal places. Every time the cube gets turned, it has a sizable effect on the non-VR equity calculation.

Messages In This Thread

• New XG rollout statistics: Use case #1
  Timothy Chow -- Tuesday, 17 February 2015, at 9:07 p.m.
  • New XG rollout statistics: Variance Reduction
    David Rockwell -- Tuesday, 17 February 2015, at 10:02 p.m.
    • New XG rollout statistics: Variance Reduction
      Timothy Chow -- Tuesday, 17 February 2015, at 10:31 p.m.