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same dice or not?!

Posted By: Timothy Chow
Date: Saturday, 10 December 2016, at 6:44 p.m.

In Response To: same dice or not?! (rambiz)

rambiz wrote:

The variance of the difference of two random variables is definitely the sum of variances minus two times the covariance.

Yes, but if the variables are independent, then the covariance is zero.

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!?

I don't know what you mean by "must." This is a free country. You can do whatever you want.

Whether you use different dice or the same dice, your estimate of the equities will be unbiased. That's what most people care about.

Using different dice will eliminate your concerns about the covariance. But I don't see that as anything to be too worried about in any case.

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