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The Opening Bell Curve

Posted By: Daniel Murphy
Date: Monday, 4 June 2007, at 3:36 p.m.

http://www.fibs.com/golarchive/members/board/config.cgi?read=141188

Has anyone already done any work with the value of winning/losing the opening roll in a money game session or at any particular match score?

The 30 possible opening roll equities (cubeless equities, Tom Keith's bkgm.com gnubg 0-ply cubeless rollouts) are:

-0.1670
-0.1234
-0.1035
-0.0638
-0.0545
-0.0155
-0.0125
-0.0102
-0.0088
-0.0072
-0.0066
-0.0056
-0.0053
-0.0032
-0.0024
0.0024
0.0032
0.0053
0.0056
0.0066
0.0072
0.0088
0.0102
0.0125
0.0155
0.0545
0.0638
0.1035
0.1234
0.1670
Average equity attained from the opening roll = 0.0000
Average equity attained from winning the opening roll = 0.0393
Median equity attained from winning the opening roll = 0.0102

In the gammonlife.com forum there is a post from a Jakob Garal, Dr.Eng. His own site is www.fairbg.com and he thinks that the vagaries of winning the opening roll are so unfair that we need an entirely new system -- his system -- for scoring match play.

His suggestions are going nowhere, certainly, but in the category "if it ain't broke, don't fix it" I'm wondering if anyone's given any thought to the probability of fairness of the distribution of the opening roll.

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