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BGonline.org Forums
Jump model for cube decisions
Posted By: Rick Janowski In Response To: Jump model for cube decisions (Mark Higgins)
Date: Wednesday, 25 April 2012, at 5:53 p.m.
I have been in close correspondence with Mark since the initial drafts of his paper, who I think has done splendid work in expanding theoretical knowledge into this area of backgammon theory. Key features of his work include:
* Thorough understanding and practical knowledge of previous work by Keeler, Zadeh. Kleinman and myself.
* Independent verification of the live cube model extended to gammons and backgammons originally developed in my paper, “Take-points in money games”.
* Development of alternative "discontinuous" theoretical methods of analysis introducing the original concept of "jump volatility".
* Proof and elaboration of a rigorous solution employing both "local" and remote" jump volatilities.
* The development of a simplified and practical approach where a single composite jump volatility is considered (including the introduction of optimised non-linear and linear approximations).
* Comparison of the single composite jump volatility approach with the basic approach from my paper - demonstrating close correlation between both non-linear and linear approximations and the basic method from my paper (utilising an optimal average value of 0.7 established from bot simulation/rollouts).
* The close correlation between the simplified jump volatility approach and the algebraic/interpolative cube-efficiency approach tends to provide complimentary confidence that both approaches are practically valid.
* The equity plots resulting from the rigorous single composite jump volatility approach (and its non-linear approximation) show remarkable similarity from actual equity plots I derived from the Sconyers Bearoff Database (particularly in the zone covering optimal double and cash points) a few years ago. In my opinion this strong evidence that the jump volatility model is consistent with the nitty gritty mechanics of the cube in the vicinity of too optimal doubling points.
I would like to say that I was very pleased to be associated with this work in providing a checking/advisory role. Moreover, I fully support the validity of this work which I believe has made a significant contribution to the science and understanding of the doubling cube in backgammon. I look forward to further work calibrating/optimising the more rigorous approach utilising both local and remote jump probabilities.
Excellent work, Mark!
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