|
BGonline.org Forums
same dice or not?!
Posted By: rambiz In Response To: standard error reported by gnu (Casper Van der Tak)
Date: Friday, 9 December 2016, at 8:24 a.m.
The variance of the difference of two random variables is definitely the sum of variances minus two times the covariance. We all agree and there is absolutely no doubt about it.
However, while comparing two plays, I am not at all sure, if the same sequence of dice must be used or on the contrary we must use independent set of dice, or maybe both same and independent dice will do!?
My guess is that both will do ,but if we use the same set of dice, we are basically doing some sort of variance reduction, meaning that the difference of the outcomes is going to converge faster. The reason behind it is that by using the same set of dice we introduce some positive correlation at least for the inevitable race at the end of the game and so the overall variance of the difference between the two plays is reduced.
Furthermore, I doubt that the play made over the board influences the future dice sequence. If the dice are pseudo-random and basically just read from an electronic memory, the play made over the board has obviously no effect over the dice sequence to come.
Somebody please tell us how it is actually done in Gnu and XG?
|
BGonline.org Forums is maintained by Stick with WebBBS 5.12.