Typically, in the retroanalysis of a backgammon position (the explanation of "how we got here"), more is possible than appears at first glance.
For White's last move, Mike came up with an excellent list of candidates. As he implies, some possibilities are better than others (in terms of being able to retrace the position further), and as an example of that concept he first showed the position copied below:
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| XGID=a---bBCBBC--b-c--bBacA--a-:1:1:-1:31:0:0:3:0:10 | |||||
White plays bar/21, thereby reaching the target position | |||||
MIke added, That [31 possibility] is somewhat unsatisfying, however, because it does not explain why Blue did not double on his previous turn. Right. One feels obligated to achieve a believable, stable situation (both cube-wise and checker-wise), before concluding, "Okay, it looks like this position could be plausibly reached."
Suppose, for example, Blue had the position below, rolled double 1s, and played 8/7*(2) 6/5(2) [thereby reaching the position above].
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| XGID=----b-EaDC--b-c--bBacA--a-:1:1:1:00:0:0:3:0:10 | |||||
Blue should not redouble (of course) | |||||
The fact that Blue did not yet have his five-prime easily explains why he did not redouble. Moreover, it almost completely takes the pressure off the why-no-recube" conundrum as we attempt to deduce what checker plays might have gotten us here.
However, White's board (with blots on her 6pt and 1pt) is still hard to explain. As Blue no longer has a strong board or prime, White fears less being hit and it's therefore hard to justify White's having played 6/5 instead of 11/10 with an ace. Other resources must be tapped.
For example, imagine that in the early game, White owned her 5pt and hit two more checkers, leaving a blot on the ace point, which gave her a strong enough position to double. Subsequently, Blue anchored on White's 4pt, and White rolled double 1s at a time when her aces were blocked everywhere else, which forced her to break her 5pt. After that, Blue hit some checkers, White managed to make her 21pt and 11pt, and they reached the position below.
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| XGID=---ab-E-D---bCc-AcB-c---a-:1:1:-1:62:0:0:3:0:10 | |||||
White should play 22/16 8/6 | |||||
Here (with 62), White ran with 22/16 and (correctly) began the process of rebuilding her board with 8/6. Blue hit with a seven (16/9*), White hit back with 63, Blue rolled 44 and played bar/21 13/9*(3), and finally White rolled 61 and came off the roof with bar/18. That sequence leads to the position previously diagrammed (where Blue was about to roll 11, followed by White 31, which gets to the target position shown below).
This is a high-level reconstruction, necessary only because the penultimate move chosen was 31 played bar/21. Extra work is the penalty for being initially lazy and failing to address the most acute problem (White's peculiar board situation) more directly. Likewise, bar/21 9/6 (with 43) or bar/21 11/6 (with 54) would require a protracted retrofit.
Below is the target position (i.e., after White has played bar/21 in the first position of this post):
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| XGID=----cBCBBC--b-c--bBacA--a-:1:1:1:00:0:0:3:0:10 | |||||
What was White's last move? | |||||
Technically, bar/21 is a legitimate answer to the question (as is bar/21 9/6, or bar/21 11/6). However, Mike found four much better answers: Bar/21 6/5, 15/11 6/5, 13/11 6/5, and 14/11 6/5 (with rolls of 41, 41, 21 and 31, respectively). In these positions (shown in the final four XGR++ evaluations of Mike's post, White owned her 6pt just prior to the play, which makes it much easier to create a (perfectly played) sequence from the opening position (or from White's initial cube position).
I chose bar/21 6/5 was for White's last move. I'll demonstrate my full 15-move sequence in a separate post (or posts).
Nack