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BGonline.org Forums
Calculating confidence values
Posted By: Bob Koca In Response To: Calculating confidence values (Timothy Chow)
Date: Sunday, 30 August 2009, at 2:08 a.m.
"Let's say we're examining two ways to play a roll, Play A and Play B. We generate a random series of dice rolls and play them out both ways. If for example Play A wins while Play B loses, then we estimate the equity difference A – B to be 1 – (–1) = 2. We repeat with another set of dice rolls, etc., accumulating samples of the equity difference."
There are two ways you could do it. You could keep a list of the equity differences and work directly with that (matched pairs test), or you could separately find the means and s.d. for each play individually and then compare (2 sample t-test). I think gnu does it the second way. I think the first is better though since the use of parallel dice can make the two streams dependent. I am guessing the first way is used since an estimate for each play individually is given as well as for the difference.
" For example, if Play A resulted in a win, then for each i, we multiply the value of A[i] by i/1000 (because this is the probability of getting a win if the MWC really were i/1000). "
I would like to introduce v ariance reduction back into the picture. Suppose the variance reduced result is 60% win chance for a play. How would you update?
Along those lines consider a position in which the variance reduction is very effective, for example a race which soon goes to a DMP database. Suppose the actual win% is 60%. Doing it the conventional way there will be results all close to .60 The sample deviation will be very small and we quickly have a lot of confidence that the true win % is very close to 60%. How long would it take for the Bayesian updating to give that result? I think that most of the advantage of VR vanishes.
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