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XGR+ hates my play in the right diagram.
I'm guessing that you played X (or x). I hope XGR+'s reaction wasn't personal. :)
For money, according to the rollouts on this site, in the left diagram S(24/20 13/8) is 2.5 millipoints ahead of X(24/20 6/1*).
There is a lot of variance in a 7800-trial rollout. Two GnuBG rollouts were done for 63R-54, both about that length. The first (the one on this site) yielded [S X2.5], and the second one [S X10.3]. This averages to [S X6.4], rounded to [S X6] in the bot summary below. (The "/15" means GnuBG 15000+ trials.)
Also GnuBG's rollout results tend to have a bias towards X (hit-and-split) when hitting on a deep point, at least compared to other bots. With 63R-54, for example (for Snowie, GnuBG, XG):
[S X16] ~31
[S X6] /15
[S X12] <62
So, for an "agg" (bot aggregate), one might assign about [S X12] to the left-hand position, which, depending upon one's standard, may be somewhat different than [S X2.5].
What should this tell me about 23/21 13/8 vs. 23/21 6/1* (S vs. X, too, I guess, or is it s vs. x?) in the right diagram?
The side-by-side diagrams are repeated below, so that you can scroll either up or down to view them.
Let us first clarify the Nactation. When there is only one number with which the back checkers can split, you can use S (Split) or Z (reverse split), doesn't matter. For example, opening 52S (i.e., 52 played 24/22 13/8) can also be nactated 52Z. I prefer "S" in that situation (especially for beginners) only because it more instantly suggests the word "Split." Likewise, 63R-54 played 24/20 13/8 can be nactated either S or Z. [I'll be using Z in the analysis below because it is common to the two positions in question.]
For 51S-62R-52 (right-hand diagram), there is more than one way a back checker can "split" (which really just means "move," in the broader sense; Bob Koca suggests the S-word "scoot" for these splitting options).
It is possible to move a back checker either 5 or 2. As 23/18 splits with the larger number, by definition the 23/18 13/11 move is allocated S. As 24/22 and 23/21 split with the smaller number, they are both allocated to the Z family. Between those two, 23/21 moves closer to home (is closer to one's own 6pt) and is therefore Z. And 24/22 is z. (And 13/8 is of course the other half of the Z/z move.)
In short, S = 23/18 13/11, Z = 23/21 13/8, z = 24/22 13/8. Other candidates are: X (hit-and-split) = 23/21 6/1*, x (alt hit-and-split) = 24/22 6/1*, U (Up) = 24/22 23/18, and R = 23/16.
Now, permit me to rephrase your question: "What should the 63R-54 [Z X12] value tell us about 51S-62R-52 (right-hand diagram)?"
Here are some factors to consider:
1) Blue has already brought a checker down to the 8pt on the previous turn: his 13pt/8pt distribution is 4:4 instead of 5:3. I estimate that affects the Z/X margin by .03 to .04. In isolation, that factor suggests X crosses over and becomes better than Z (and by .02 or more). However...
2) X duplicates White's aces (Bar/24* or 6/5*) in the left-hand position. X does not duplicate aces in the right-hand position. This is the monster factor, bigger than #1. That is why I'm confident, even without having a rollout for the latter, that Z beats X by a significantly larger margin in 51S-62R-52 (or 51S-63R-52, not diagrammed) than in 63R-54.
I'll put it another way. If you alter the left-hand position by moving a Blue 13pt spare to the 8pt prior to playing the 54, X (instead of being .012 worse) must be clearly better than Z, with both the ace duplication and the distribution being X-aligned. Or if you alter the right-hand position by moving a Blue 8pt spare back to the 13pt, then the position is Z-aligned, and X (instead of being "only" a mistake of perhaps -.04 or so) is a blunder.
3) Whether Blue plays 13/8 or 6/1* with the 5, he has two ways to play the deuce in the back. Typically, 23/21 is better because it strives for a better anchor, controls more of the outfield, and puts only one back checker instead of two in direct range of Opp's 8pt spare. Specific numbers or duplications sometimes countermand, but I don't see that being the case here.
4) In the right-hand position, Blue has other conceivable options (besides hitting) that keep four checkers on the midpoint. Instead of it being a contest between merely X and Z, not only is there x and z, but Blue can consider U or even R, which are not legal in the left-hand position. He might also consider S for ace duplication IF White's blot is on her 15pt as in the undiagrammed 51S-63R-52. I might consider R, though not U or S, vs the 16pt blot. In truth, though, the 24/21 part of the move is highly efficient against Opp's 16pt blot; there is no cogent motive to deviate.
Does the score 3a:3a make a difference?
I'd guess that X/x might weaken a few millipoints compared to other candidates when going from money to 𣛩 (and that would have no effect on best play decision for 51S-62R-52, assuming that Z is already a standout). For the most part, I find that treating 𣛩 like money has served me well until there's a pending cube turn. (A score of 𣛨 or 𣇽 is a different story.)
Nack
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