In Part a), the best strategy is to forego the game, and try to save the gammon. Along the way, White may crack, but very few risks should be taken to force the issue. Black's tactics should be to let White move. Containing White's stragglers is a near impossible task, so anything that delays White is going to make it harder for Black to hold onto his own board. Hitting is counterproductive. Conversely, every additional Black checker that gets hit and sent back increases the odds that Black will lose a double game.
Unfortunately, Black must choose between these competing needs:
- Do not hit: 8/4(2)
After this play, White can hit with any one. This is eleven shots in thirty-six compared to only one shot with the alternative play. Still, this is the move I like. It is so important to keep White moving that Black must risk having another checker sent back.
- Hit, in order to minimize White's shots: 13/11*/7*, 6/4
From the bar, White can hit only with a roll of 1-1. The immediate safety of this move is offset by the increased likelyhood that Black's board will crash sooner.
In Part b), where Black has an escape hatch, his tactics are completely different. With the bar point open, Black should hit, 13/11*/7*, 6/4, and attempt to contain White's checkers. Black is playing a two-way game. He may go forward or backward, depending on the next few rolls.
Part c) could be played the same as Part b). Black has two numbers -- five and six -- with which to launch his back men into the outfield, so a two-way game plan is not out of the question. His triple anchor is so strong, however, that Black should forget about the two-way option, and go all out for the backgame. Some variation of the hara-kiri is in order. I like 9/7*/5, 6/2. I don't want to hit twice; that would slow White down unnecessarily.
My solutions:
Part a):
8/4(2)
Part b):
13/11*/7*
Part c):
9/7*/5, 6/2
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.
Grunch: I have been answering these problems without the use of a bot, and before checking the excellent solutions of others, since Problem 28. My record at this writing is 52%.