We'll probably have to agree to disagree at this point.
It seems to me that while I've provided examples illustrating the weakness of your definition, you have not done the same. The bkgm definition may be overly wordy, but it is precise and unambiguous, and you have not showed otherwise.
As I've attempted to argue, your definition is too vague to stand on its own without extra implied clauses. I'm gratified you've decided to remove implied restrictions in respect of "zero legal hits without using both dice" , but it seems to me you're still smuggling in at least one 'hidden' assumption. Something like:
"In a world where you play backgammon with one die only, you'd have to come in with that die before doing anything else."
Fine, but we don't live in that world. We roll two dice.
Your hidden assumption here leads you to extraordinary conclusions, such as maintaining that there are no direct shots in this position we've discussed:
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| XGID=-------------aaaaaaA-----A:0:0:1:00:0:0:1:0:10 | |||||
| Blue on roll, cube action? | |||||
eXtreme Gammon Version: 2.10
I am frankly flabbergasted that you can't see direct shots here. In the real world where we roll two dice, there is literally every possible direct shot on offer (as well as almost every indirect shot)!
In a situation where there is absolutely no impediment whatsoever to hitting a direct shot (you will come in every time, and you'll be able to hit directly with the other checker every time), it's astonishing to me you'd support a definition that makes all the shots indirect.
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| XGID=-----a--A---------------A-:0:0:1:11:0:0:1:0:10 | |||||
| Blue to play 11 | |||||
eXtreme Gammon Version: 2.10
A useful definition must guide us in the real world. If a newcomer asked whether the position above represents a direct shot, you'd say no because neither die has a 3 on it. I'd say no because you'd need to 'hop' a checker multiple times to hit. My answer is more congruent with the intent of the direct/indirect dichotomy (a shortcut to counting shots).
Your answer would be apt to confuse the newbie if you'd just taught him that a 11 is played 4 times. "But can't I use the one die 3 times and the other once to make my play?", he might very reasonably enquire.
Matt.