Thank you, Casper, for your astute analysis.
Position 1: My first try was adjusting White 23/22, which, with only a 1-pip change, unduplicates her 5s. This change by itself was enough to bring R (Run, 22/15) within just .007:
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| XGID=---cBBC-BBA-c-----bcBbAb--:0:0:1:52:0:0:0:7:10 | |||||
White's 23pt checker in Mochy #1 is moved to her 22pt | |||||
| 1. | Rollout1 | 22/17 10/8 | eq: +0.904 | |||
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| 2. | Rollout1 | 22/15 | eq: +0.898 (-0.007) | |||
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| 3. | Rollout2 | 22/17 6/4 | eq: +0.853 (-0.052) | |||
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| 4. | Rollout2 | 22/20 10/5 | eq: +0.839 (-0.065) | |||
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| 1 10368 Games rolled with Variance Reduction. Dice Seed: 40310402 Moves: 3-ply, cube decisions: XG Roller 2 1296 Games rolled with Variance Reduction. Dice Seed: 40310402 Moves: 3-ply, cube decisions: XG Roller | ||||||
To knock B (Both, 22/17 10/8) out of first place, it was necessary to move that White back checker to the midpoint (consistent with your second reason), as shown in the main rollout post (Muchy #1), where the 22/20 deuce rises to the top (by .010) though accompanied by a different 5.
Position 2: You isolated the most salient issue: White's 1pt blot.
I first rolled out moving White's 1pt blot to the 6pt. This change wipes out the .074 margin deficit and crosses zero, though only barely (basically, it's a cusp):
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| XGID=--a--aE-DA--dCa--c-e--A--A:0:0:1:54:2:2:0:7:10 | |||||
White's 1pt blot in Mochy #2 is moved to her 6pt | |||||
| 1. | Rollout1 | Bar/20 13/9 | eq: +0.025 | |||
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| 2. | Rollout1 | Bar/20 9/5* | eq: +0.020 (-0.005) | |||
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| 1 10368 Games rolled with Variance Reduction. Dice Seed: 79165659 Moves: 3-ply, cube decisions: XG Roller | ||||||
As you have seen in Muchy #2 (refer to same post as linked earlier), moving White's floating checker another 7 pips (to her 13pt) increases the margin only from .005 to .014.
I also checked moving White's 1pt blot to her 2pt (just a 1-pip change from Mochy #2). This erases the lion's share (.044) of the original .074 margin (rollout not shown). Some second change is needed to tease 13/9 to the top, though the distributional Blue 8/13 is not quite enough (falls .007 short, 5k rollout not shown).
Interestingly, from the original Mochy #2 position, moving two Blue 8pt spares back to the 13pt is not nearly enough to overcome the effect of White's 1pt blot; the gap is only narrowed from .074 to .032 (5k rollout not shown).
Position 3 and 4: I would guess that the magnitudes of the swings of these two of the six Mochy/Muchy comparisons are the biggest surprises to readers as a whole.
Position 5: Changing the score (to something where gammons pay extra) would have been too obvious, but it was a strain to find a single change in checker position that would overturn the robust 8pt/4pt improvement. I thought of omitting this one.
Bonus position: If White has as few as three checkers off, then 8/7 6/2 becomes right even at DMP (by .007) -- see below. With zero checkers off 8/7 6/2 is wrong by -.059 (per my Muchy rollout), a margin difference of .066 (or, naively, a .022 adjustment per checker off).
Nack
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| XGID=-BAbCCC-B----A----------j-:1:-1:1:41:0:0:3:0:10 | |||||
MUCHY Bonus position, | |||||
| 1. | Rollout1 | 8/7 6/2 | eq: +0.495 | |||
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| 2. | Rollout1 | 13/12 6/2 | eq: +0.487 (-0.007) | |||
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| 1 5184 Games rolled with Variance Reduction. Dice Seed: 28662935 Moves: 3-ply, cube decisions: XG Roller | ||||||