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DMP Answer

As you can see from the ExtremeGammon rollout below, the best play is to move the back checker 1 and bring a checker from the 13 to the 10 point. 

This is a very tough play to understand and make, and even some of the greatest players in the world missed it.  Neil Kazaross got this one right, and he explained it well.  You are down in the race and you are not interested in playing "safe" in this position.  You need to take chances and maximize your chances to get and hit a shot.  The reason you should move the checker from 16 to 15, I found, was very fascinating.  If Red rolls his very best roll, which is 6-6, you get hit and you have a chance to hit him back and still win the game.  If you don't have a checker on that point, 6-6 will almost surely give Red that game.

I recognized the concept of taking chances, but in my match I made the 4th best move, 16/12.  My opponent rolled a 9 and I didn't come in and lost the game and match.