Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.

This is a cute little technical problem which revolves around an unusual idea. White is clearly in serious trouble and has to find the best move to save the gammon.

The obvious play is 13/4, getting two crossovers. Maximizing crossovers is usually the right idea in getting off the gammon, but not always. If Black doesn’t roll a double in the next two turns, White will have two throws to get off the gammon. (If Black does roll a double, White’s play doesn’t matter much.) Playing 13/4 leaves White needing three crossovers to get off the gammon. Playing 13/7 10/7 leaves White needing four crossovers. But if White has two turns, there’s little difference between three crossovers and four crossovers; both will take two turns (barring doubles) to get off. So instead of crossovers, let’s look at individual rolls and see if there are any swing numbers.

After 13/7 10/7, all rolls get at least two checkers in next turn. White therefore will be a big favorite to get off the gammon on his second roll, no matter what he throws on his first roll.

After 13/4, however, a little inspection shows that White has a small problem: 2-1! If he plays 13/4 and then throws 2-1, he can’t bring in an outfield checker, so he’ll need a double on his last throw. That’s a huge swing on that number, a swing which can’t be made up by tiny improvements on other numbers.

Solution: 13/7 10/7