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eXtreme Gammon question

Posted By: Timothy Chow
Date: Thursday, 27 August 2009, at 12:11 a.m.

In Response To: eXtreme Gammon question (Matt Cohn-Geier)

What we are trying to determine is whether the difference between the two plays is positive or negative, not the equities of the plays themselves.

That's right. But the point is that the probability distribution is two-dimensional because you have two different plays. The picture is not the familiar one-dimensional bell curve, but a two-dimensional "bell surface," whose "width" will be determined by one of the standard deviations (SD1) and whose "depth" will be determined by the other standard deviation (SD2). A small value for SD1 and a large value for SD2 could lead to the same j.s.d. as as large value for SD1 and a small value for SD2, but the probability masses will be differently distributed, so you'll get different confidence levels in the two cases.

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