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XG cube analysis -- Methodology question

Posted By: Rick Janowski
Date: Tuesday, 4 December 2012, at 7:30 p.m.

In Response To: XG cube analysis -- Methodology question (Chuck Bower)

Danny Kleinman had developed an approach in the 1980s where he used gammon-adjusted win probabilities to assess cube actions. Essentially, the approach was for any position (with gammons, backgammons, etc) to calculate its cubeless equity and then calculate the equivalent cubeless gammonless probability (ie, probability in a running game that would yield the same cubeless equity as the position under consideration). This methodology is contained in Danny's books.

Intuitively, this seemed (and probably still seems) reasonable but it contradicted the generic take-point equation I had developed and and subsequently verified. Danny was very active in checking through this work at the time for which I was very grateful. This issue came up in correspondence which you can see in Appendix 6 of my paper in the Section "A Simpler Dead Cube Model".

I think Kit Woolsey may also have employed a similar methodology to Danny's in the 80s and early 90s.

Incidentally, the generic form of the take equity equation is:

E take = 0.5 + 0.5*x*(L-0.5)/(W+L+0.5*x)

where W and L are average values for all games won and all games lost respectively, and x is the cube efficiency (a value between 0 and 1, typically 2/3).

For races or other gammonless games where W = L = 1, this simplifies to:

E take = 0.5 +0.5*x/(4+x)

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