This question is of course endlessly debatable, and I can easily imagine myself being persuaded to change my mind. However, if I had to cast my vote today, I would nominate post-blitz cubes as the most difficult problems in backgammon.
By a post-blitz cube, I mean a position in which one player is playing on for the gammon, but then encounters a speed bump—e.g., the opponent hits. Now comes what is very often a tough cube decision. For example:
| White | 145 |
|---|---|
| |
| Blue | 131 |
| GNUBg Id: hufBAUJzdgECUQ:cAkAAAAAAAAA XGID=aB-CaBCA----c--A-d-d-A-bAA:0:0:1:00:0:0:0:0:10 | |
According to a rollout, this is a 0.920 take, but you just have to shift Blue's 15pt blot to the 13pt to push it to the take/drop borderline. In general, two things make this kind of cube decision very difficult in my mind. First, they can be very sensitive to seemingly small changes. For another example, according to the computer, in Position A below, Blue is too good, but in Position B, it's a whopper with cheese to hold the cube. Rollout
Position A
| White | 159 |
|---|---|
| |
| Blue | 130 |
| GNUBg Id: 4PPgAUHbWIWAUA:cAngAAAAAAAA XGID=aBBB-aBAAA--dA---d-eA---AA:0:0:1:00:0:0:0:7:8 | |
Position B
| White | 159 |
|---|---|
| |
| Blue | 139 |
| GNUBg Id: 4PPgAUHbWAVAUg:cAngAAAAAAAA XGID=aBBB-aBAAA--d----d-eA-A-AA:0:0:1:00:0:0:0:7:8 | |
Secondly, the positions that arise can be very diverse, making them very difficult to categorize and master. In one of Mochy's seminars, he offered the following reference position, which he said was a borderline take/pass:
| White | 172 |
|---|---|
| |
| Blue | 32 |
| GNUBg Id: 4HPwABV/AACAAA:cAkAAAAAAAAA XGID=-Gaaa-------d----c-e-----A:0:0:1:00:0:0:0:0:10 | |
This is clearly a good position to know, but it hardly scratches the surface of the kinds of post-blitz situations that can arise. Not long ago, David Levy posted a request for help with what I would call a post-blitz cube, and nobody piped up with any general tools for approaching such positions.
If I had to also pick a type of checker-play decision, I would be hard-pressed to come up with a clear winner. Trice's suggestion of prime-versus-prime is a strong contender, but there are others. In my files, I have a lot more containment errors and blitzing errors than priming errors, though this may be because they come up a lot, not necessarily because they are most conducive to whoppers. I also like Bob Koca's suggestion of decisions that involve choosing between different game plans, e.g., attack or prime? attack or run? pay now or pay later? buy now or buy later? But this is a bit too broad.
I looked through my ten coolest checkerplay problems of 2012 and I noticed that 7 out of 10 involved giving up a (seemingly) good point, and an 8th involved forgoing making a good point (the 5pt). I think that this is indeed a common theme underlying many of the most difficult plays in backgammon. But unfortunately, it's a little too broad a category, including anchor breaks and banana splits and many other types of decisions that could be categories in their own right.