Thanks, Pierre, for the clarification. I thought your "preamble" was just an explanation of the difficulties that you encountered as a consequence of your 3-or-more interpretation of White's roll caveat, and then you went on to describe your variant (in the form of three changes to mine).
If I understand correctly now, the puzzle you are proposing does retain minimum x + y as the primary objective, but with the following four changes:
- all wins are bargammons
- same Blue starting position for minimum and maximum pipcount difference
- same sequence of dice for both sides in both configurations.
- White never rolls smaller than a 3 (instead of 2) on either die.
For your variant (the 3+ instead of 2+ being the pivotal difference), I couldn't find a 16 value for x + y either. (Almost, but not quite.) Indeed, I believe I can prove 16 impossible. So, 18 it is.
I slightly prefer the solution pair below, because the smaller pipcount difference is closer to zero. (However, the difference in differences is 71 in both cases, so I can't claim it to be a clear improvement.)
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I was unable to reduce that last pip (from 1 to zero) in the pipcount difference of the left-hand position while maintaining the 71 diff/diff, but it was fun trying. :)
Nack