In Problem 54, Black can hit with twenty-five shots: direct fours and sixes, as well as indirect fours, sixes and eights (22, 51, 53). In addition, Black can make an inner-board point with ten rolls (11, 21, 22, 34, 44, 56, 66). The doublets 22 and 44 are jokers, allowing him to do both. Things don't look very good for White. The gammon threat is real, and even when he enters, White has few immediate chances to make an anchor. Black has good double.
He really has no choice. Black must double to activate his gammon chances.
The decision to take or drop is much harder. It will be several turns before Black can bring his attack home. With only three checkers in the zone, Black cannot close White out before bringing down more wood from the midpoint. His attack could easily stall, and in a few turns, Black might find himself stranded in White's home board without any outfield points to support him.
Still, White should not be anxious to take. Seven times in ten, he will be facing a three-point board, with two checkers in the air. The other three times, he'll have only one man up, but might find Black has made a fourth inner-board point. Reluctantly -- or otherwise -- White should pass.
My solution: Double/pass
For the Record
I am so often wrong that I like to post my record in these messages. It's kind of a truth-in-advertising thing. I have been answering these problems without the use of a bot, and before checking the excellent solutions of others, since Problem 28. Including the 39a tossup, my record at this writing is 56% correct.
19 Correct: 28a, 29, 30, 32, 35, 36, 38, 39a, 39b, 42b, 43, 44, 45, 47, 48a, 48b, 50, 52b, 53. 15 Incorrect: 28b, 31, 33a, 33b, 34, 37, 40a, 40b, 41, 42a, 46, 48c, 49, 51, 52a.
Last edited by Taper_Mike; 03-16-2010 at 12:50 AM.