Cash game. Black owns the cube. White on move.
White to play 5-1.
When bearing in against an ace-point or other low anchor game, you generally have two goals in mind. The first is safety; you want to create formations that are less likely to leave blots as you bear off. The second is winning a gammon; you’d like to maximize your chances of winning a gammon if you can.
It’s usually good practice to look at the gammon chances first. If your gammon chances are either very large or very small, then it’s not likely that any play you make will affect them enough to matter. In those cases, you just make the long-run safe play whatever that might be. But if the gammon is up for grabs (which in practice means gammon chances in the 15% to 40% range) then you may need to look for riskier plays which win more gammons at the cost of some extra losing chances. (Typically these plays involve piling checkers on the 6-point and 5-point, hoping to hold the prime as long as possible.)
So what’s happening in this position? Here it’s pretty obvious that White is going to win a gammon unless he gets hit. Black has one checker to enter off the bar, then four checkers to extract from the ace-point, and several checkers in the outfield as well. All told, he needs 20 crossovers to get his checkers home, even after he manages to enter. Any reasonable play leaves White with gammon chances in the 58% to 60% range, which is so large that White can forget about the gammon as an issue and just concentrate on safety. So now we can ask the interesting question: What’s the long-run safest play?
When playing strictly for safety, White has four goals. Here they are, arranged in order of obviousness:
(1) Don’t volunteer shots. Here this simply means that White won’t slot the 7-point with his ace. Giving Black even a single indirect shot from the bar means giving him an extra 5.5% to hit, which could easily be a game-winner.
(2) Try to ensure that 6-6 and 5-5 don’t leave shots. This won’t always be possible, and even when it is possible you may decide to leave one of these numbers in order to secure better distribution.
(3) Strip the 6-point for quick clearance later. In general, you want to place your spare checkers on the 3, 4, and 5-points, preparing to clear the 6-point when you get all your men in.
(4) Avoid phantom interior gaps. A real interior gap occurs when an interior point like the 3-point or 4-point is actually open when the bearoff starts. Interior gaps are very weak and those formations will leave many more shots than a completely made board. Less weak (but still a serious flaw) are what I call “phantom gaps”, where you have all the points made but some points lack spares. For example, if you have spares on the 6, 5, and 3-points, but no spare on the 4-point, you have a phantom gap on the 4-point. Most players ignore this situation, but it’s actually more serious than it appears, leading to awkward formations later and more shots.
Note that some phantom gaps are worse then others. The 2-point and the 5-point are the least serious. The 2-point is so deep that it generally gets filled later, and the 5-point isn’t too important because it’s sometimes an advantage to clear the 5-point before clearing the 6-point. The serious phantom gaps occur on the 3-point and the 4-point.
If we now put all these ideas to work, we can find a clear winner with the 5-1, namely 8/3 6/5! All criteria are met: no shot volunteered, 6-6 and 5-5 are both safe, the 6-point is stripped, and no phantom gaps.
Other plays don’t work as well. 10/5 4/3 blots on both 6-6 and 5-5 and leaves a phantom gap on the 4-point. 10/5 6/5 doesn’t blot but also doesn’t put a spare on the 3-point, which may prove useful.
