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Gammon Go (GG) and Gammon Save (GS) Considerations
Posted By: Rick Janowski In Response To: Gammon Go (GG) and Gammon Save (GS) Considerations (Tom Keith)
Date: Thursday, 16 May 2013, at 2:01 p.m.
Hi Tom and David,
Interesting and tough questions. One can develop an understanding of the relative importance of GG+ to GG (or GS and GS+) by considering the results of critical rollouts and evaluations, as in the following examples:
(1) Compare the scale of equity errors (either in terms of normalised equity or match equity)
(2) Where the GG and GG+ plays are different (or GS and GS+) then the GG+ play (or GS+) is normally a better representative of the extremes of the pre-Crawford scores. Conversely, the GG (or GS) play is often a better representative of Crawford and post-Crawford scores, though I think in such cases relative errors between GG and GG+ plays are usually small/negligible (similarly comparing GS with GS+).
(3) There are examples where the GG play is the same as the GS play but the GS+ play or GG+ play is different (example opening 21). The converse can also occur of course.
With regard to your questions on proportions of undoubled gammon win/losses and gammon prices, I am not sure whether knowledge of these areas is essential to getting a handle on the problem, though it could certainly help. These are tough questions. I am not very familiar with Gnu, but I think statistics on undoubled gammons might be available from rollout results. Gammon prices could be calculated for theoretical live cubes by considering the marginal utility of say 1% additional single wins to 1% gammon wins. I estimated that the live gammon prices are about 0.86 and 0.00 for the GG+ and GS+ sides respectively. The dead cube gammon values are not so straight forward because the case of both sides never using the cube is not a realistic lower-bound for these two scores. This is because the trailer does much better doubling immediately than never doubling. It would appear that more realistic dead cube gammon prices are those with the match leader owning a 2-cube, ie. 1.00 and 0.00 for the GG+ and GS+ sides respectively. The effective gammon price for the match trailer appears to be somewhere between 0.86 and 1.00, say about 0.93, according to my estimates. The match leader's gammon value seems to be virtually nil, because the match leader can kill gammons at any time. Douglas Zare has much better knowledge of this area than I do.
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