I think 66 is only an average-sized swing number (in terms of preferring one number over the other), perhaps only .004 in favor of $ vs S. The big one is 55, a factor of .500+ / 36 = .014 or so. In isolation, it accounts for more than half the .024 difference in value between $ and S.
Comparing 61P-21$ vs 61P-21S is not so simple, though. The swings on the non-doublet 4 hits range from .005 (roll of 31) to .010 (roll of 54) in favor of S, most being on the upper end of that range. Toss in another .001 for 44 and .002 for 22, and you're up to .056. That is, the swing on 4-hits comes to four times the swing of 55.
My point is that you can't come to any local conclusion about 61P-21$ vs 61P-21S unless you also evaluate the increased strength of Blue's position when his slotted 5pt blot is missed. That adds a slippery level of difficulty.
It is usually more reliable to reference the value of a simpler known position or position pair and compare to that. Here, I would suggest opening 21$ vs 21S.
Don't be fooled by the rollout on this site of opening 21 [$ S19]. David Rockwell's research shows that Gnu's own misreplies should adjust that to [$ S14]. And the other bots' rollouts show significantly lower margins: Snowie [$ S8], XG 3-ply [$ S5] and XG 4-ply [$ S3]. Let's call agg (bot aggregate value) [$ S8] -- i.e., $ beats S by a margin of .008.
By contrast, 61P-21 is agg [$ S24]. The question I would ponder, then, is: Why is Blue more motivated (by about .016) to play $ in reply to 61P (left-hand position below) than on the opening roll (right-hand position)?
Double 5s is certainly a factor. But it's worse whether Opp has already played 61P or not. The swing is only about .008 between the two position pairs. So, on a shallow view that accounts for half of the sought .016 swing.
However, it should be noted that 61P-21S freezes White's stripped 8pt, whereas opening 21S does not do so. If White makes her 5pt or 4pt, she leaves a direct 6 shot. This turns out to be fairly sizable; I think it swings about .005 on the roll of 31, and .003 on 42. Those two together cancel out double 5s.
I haven't looked much deeper than that. It appears that 66, 22 and 44 relatively favor 61P-21$ vs S (compared to 21$ vs S), and that the majority of rolls go the other way but to a lesser extent. Someday, I'll do a more comprehensive analysis.
One factor worth noting is that 21S sets up a great 65@ play for Blue next roll, whereas 61P-21S leaves a garbage 65 next roll. That avoidance of a bad 65 follow-up is the way I chose to remember 61P-21$ long ago (way back when opening 21S rolled out .01 better than 21$, by the way), before it became hard-wired into my brain.
Nack
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