I had prepared this message last night, before the server went down (or at least it did for me). Now with the server back up, I see that you already discovered your own example.
I was aware of the potential logic loop, though I thought nobody would notice (wrong, lol) and I figured it would never arise in practice (that judgment still appears to be correct). Below are two examples from the E family (one doublet, one non-doublet). For familes other than E, examples are harder to contrive.
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- Play 1: 23/22 21/20 3/1*, Hit, Five points
Play 2: 24/23 21/20, 6/4, No hit, Six points
Play 3: 24/22 5/3, No hit, Five points (incl. an extra inside)
In the right-hand position, consider three plays with 32:
- Play 1: 21/18 3/1*, Hit, Five points
Play 2: 24/21 6/4, No hit, Six points
Play 3: 24/22 5/3, No hit, Five points (incl. an extra inside)
In each position, Nactation-wise, play 1 outranks play 2 by the hit, play 2 outranks play 3 by most points, and play 3 outranks play 1 by the extra-point-in-home-quadrant-overrides-the-hit exception.
Backgammon-wise, none of these plays are remotely competitive. On a quick evaluation, the closest of the three plays with a roll of 32 is ranked 20th (and a triple whopper, -.343), and the three double 1s plays are even worse.
It may be possible to fabricate a position in which one of the logic-loop plays isn't quite so terrible, but still it's hard to imagine anyone would ever make the play. Hence, I don't think a change in the hierarchic wording is necessary. However, if I can reword the rule simply and avoid the (practically impossible) logic loop without causing a different conflict, I will look to do so. I'm impressed you found the loop on your own and thanks for reminding me.
Nack