I've noticed that XG likes 41 minor split here a bit better than Snowie or GNU used to. Maybe it prefers to split with 51 rather than slot. It seems like almost 20 years that I've been slotting with 21, 51, and 41 in reply to opening 65. I discuss my reasons in Backgammon Praxis. I probably won't change now.
For rollout results, Gnu has always been more slot-leaning than the other bots.
According to the best pre-XG data I know of for 65R-41, Gnu is [$ S8] /31 (see bgonline.org), but Snowie is on the fence with [$ S1] ~20. Similarly, XG1 was [S $1] '^46 (also rolled out by Neil but not posted), and XG2 is [S $0.6] "^46. However, even if we combine those to [S $0.8] ^92, the confidence interval is still two-and-a-half times the margin, so we can't ignore the currently-on-site 65R-41 [S $3.8] <=31 (checker 3-ply, cube Roller, 31k).
For 65R-51, slot-happy Gnu is [$ S6] /31. By "contrast," Snowie is [S $3] ~31 (but also [$ S9] ~5, so combine those to [S $1.7] ~36). Meanwhile, XG1 (4-ply) was [$=S] '^46, and XG2 (no 4-ply yet) is [S $3.4] "<=31 and [S $1.2] "<46.
In short, it is only Gnu that supports 65R-41$ and 65R-51$ a tiny bit. I think it is reasonable to conclude that for both positions, (Snowie and) XG favor S over $ by a whisker, though it's basically a toss-up and the choice should be determined by stronger/weaker player and/or match score.
By contrast, 65R-21$ is clearly right (by .025). A useful association is that it is the only slot position (of the three) against which one should NOT hit with 31. Paul and I discuss our reasons on pages 54–55 of Backgammon Openings. :)
Nack
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| XGID=-b----E-C---dFa--c-da---A-:0:0:1:31:0:0:3:0:10 | |||||
65R-21$-31 | |||||
| 1. | XG Roller++ | 8/5 6/5 | eq: +0.233 | |||
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| 2. | XG Roller++ | 24/20* | eq: +0.213 (-0.020) | |||
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eXtreme Gammon Version: 2.10