If you even considered some form of the hara-kiri play involving 6/4 (as I did), it's a sure sign you've been reading too many books by Barclay Cooke (as I have)! Although Black trails by a ton (190 to 122), and sooner or later may find himself playing a backgame, it's way too early to commit to one now. For one thing, he has only one anchor point. Moreover, this 22 gives him a fair chance to win going forward.
This is one of those positions where Black does best by preserving both forward and backward options. He should reject any play that doesn't put at least two White checkers up on the roof.
- Play A, Make the Five Point: Bar/23, 11/9*/7*/5
Black's safest move leaves White with only a few doubles to regain any balance, but also leaves a pile of checkers buried on the twenty-four point. During the next couple of turns, Black figures to be fighting for front position, and may not get back to making an advanced anchor until it's too late. This play also leaves an awkward distribution of builders up front, with the blot on the eleven point bearing only on outfield points.
- Play B, Make an Advanced Anchor: Bar/23, 24/22*(2), 11/9*
Making the twenty-two point gives Black better balance in the back board, but leaves White any five, along with doubles, to swing the momentum his way. The twenty-two point works well for Black in both forward and backward options. In forward games, it gives him a launching pad to leap over White's block, and in any backgame Black might play from here, it gives him one of his best anchors.
- Play C, Triple Hit: Bar/23, 24/22*, 11/9*/7*
If White misses the return shots, the triple hit gives Black his strongest attacking options. His outfield checkers are nicely diversified, and he's got a man in place to escape with any six. If his attack fails, Black may still be able to anchor up and form some sort of backgame.
- Play D, Make the Nine Point: Bar/23, 24/22*, 11/9*(2)
This play gives Black the double hit, but is probably weaker than the other alternatives. If Black wants to make a point somewhere, either the anchor on the twenty-two point, or the five point in his inner board is a better choice.
If not for the stack back on the twenty-four point, Play A would be Black's best. Of the others, Play B gives Black a balanced, two-way game plan more than Play C or D.
My solution:
Bar/23, 24/22*(2), 11/9*.
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. My record at this writing is 55% correct.
Correct: 28(a), 29, 30, 32, 35, 36
Incorrect: 28(b), 31, 33(a), 33(b), 34