alanback: It is the only one as far as I can see. I can't think of any position where there is contact and a backgammon cannot possibly be lost.

But thinking again about single games vs gammons I now see that "one checker off" is not a necessary criteria for gammons to be impossible. If all your checkers are one away from bearing off, and the opponent has more than 5 checkers on the board, one will manage to bear at least two checkers off whatever happens.

So awarding a gammon unless there is one checker off is not 100% conceptually clean after all. It is still probably the best see-in-one-glance estimate. Who would like a sophisticated software to decide about the result of a game ?