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BGonline.org Forums
Gammon Go (GG) and Gammon Save (GS) Considerations
Posted By: Rick Janowski
Date: Wednesday, 15 May 2013, at 4:57 p.m.
It is fairly common knowledge that the Crawford scores 1 away 2 away (GS) and 2 away 1 away (GG) represent extreme cases of gammon price. Generally, they are very useful in determining the range of feasible conservative or aggressive plays which may be appropriate at a particular match score. However there are two other extreme scores which tend to be more critical than the GG and GS cases. These are 4 away 2 away (as a more extreme version of GG) and 2 away 4 away (as a more extreme version of GS). For convenience, let's call these two scores GG+ and GS+ respectively.
The reason these scores are more extreme than the conventional Crawford score based GG and GS, appears to be because of the additional and significant cube-leverage the match trailer has at these scores (combined with the generally quite negligible leverage of the match leader). Note that for certain typically slot versus split plays, the scores 2 away 6 away and/or 2 away 8 away might be slightly more extreme than GS+ but the effect is negligible. There are a few general effects that may be postulated from considerations of GG+ and GS+:
(1) Where the GG+ and GS+ plays are equal, it would appear that this play should be correct at all scores, or if not there will be negligible error.
(2) Where the GG+ and GS+ plays are not equal, then usually (but always) all other plays at various match scores will be either of these two plays. An exception to this general tendency is the opening 64 where a mixed strategy play (64S) takes a large section of the middle ground. Where the optimal plays at DMP or money/Unlimited Games(ULG) are different from either the GG+ and GS+ plays, then there will be at least three candidate plays to consider (or maybe four plays in very rare cases).
(3) In the case where the DMP and ULG plays are the same as either the GG+ or GS+ plays, it is possible to assess the optimal play at a particular score from calculation of a play aggression index, which I would define as follows:
Play aggression index (PAI) is the ratio of the GG+ error to the GS+ error, where the GG+ error is the equity error of making the GS+ play at the GG+ score, and the GS+ error is the equity error of making the GG+ play at the GS- score.
From consideration of XG++ evaluations, which serve as a fairly good model of equities I have ascertained that at a PAI value greater than 1.2 the GG+ play is generally optimal at ULG and almost all symmetrical match scores. I have also derived two algorithms which predict the correct play at various match scores by relating PAI to the ratio of points required by the opponent to the points required by the player on roll with excellent correlation. However, these formulae should ideally be checked/calibrated using XG2 rollout results rather than XG++ evaluations.
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