Black trails 3-5 in a 7-point match.

(a) How do you play 6-2?
(b) Move a checker from the 24 point to the midpoint, now how do you play 6-2?

The main decision here is to hit or not.

XG says not to hit in (a) (hitting is -0.05 error), but to hit in (b) (not hitting is a -0.04 error). I used a 1296-game rollout, standard XG settings, over all legal moves (since there aren't that many).

Why is this?

If you do not hit, then White escapes and you are playing an ace-point game.

If you hit, then you can hope to contain the checker (probably after some more hits) and force White to release the prime. If White eventually escapes anyway, you are back to the ace-point game. But Black could also get hit, locking him out for a few turns that could have been spent building his board for an eventual shot.

The difference between (a) and (b) is that in (b), Black has an extra checker to play with. Can that really make that big a difference?

Here is one reason the rollout could go wrong. If Black hits now, then there will be many decisions in the near future about whether to hit or not. If XG gets any of those wrong, the rollout decision may end up wrong.

Have you tried it with different match scores? -4/-2 is one of those scores where there's a lot happening.

The only other thing I can think of is that with 11 checkers you can build a 5 prime with a spare to shuffle around, whereas with only 10 checkers you really have a 4 prime with two spares to shuffle around. Not sure if that explains anything.

I wouldn't have hit in either case and would have just focused on building a board for a hit later.

Match score doesn't seem to make much difference. I tried both positions at:

-7/-7, cube entered
-7/-7, Black owns cube at 2

In all cases, for (b), XG likes 13/11* 8/2 best while for (a), XG places the non-hitting moves at the top (they are very close) while 13/11* 8/2 is near the bottom.

Weird.

When you hit, you start to create numbers that crack White's prime. 33, for instance, is an immediate cracker. The more checkers you have in the outfield, the better a chance you have to make new points and create more cracking numbers after the first turn. The fewer checkers in the outfield, the less likely it becomes that this approach will work. Clearly, there will be some crossover point, and it looks like you found it in this position. Over the board, there would be no way to determine this and you'd just have to guess.

Are there shortcuts you would use to evaluate your ace point game equity? E.g., do you commit to memory: "My defense will produce X hits in the bearoff of a balanced board, giving me Y wins/gammons, etc. if my timing holds" ?

It seems the only reason to pass up a hit now is that I risk cracking my own board before I can hit...with the extra checker out I can stall better...

No shortcuts -- I just try to look at the different features of the position and see what they tell me.

I think the real question here is "What's the point of hitting?" After hitting, you've got five checkers trapped behind a 6-prime and a 2-point board with the 6-point and 2-point. If you're trying to trap White's checker, making the 2-point isn't much of a help. The fact that hitting is correct with only four checkers trapped is the surprising part.