In this position, White has been reduced to a deuce-point game, and Black is in the process of bringing his men home and trapping White behind a prime. Black’s made a lot of progress, but there are still a few hurdles to overcome:
- Black’s open 3-point needs to be filled in before he starts his bearoff.
- The open 7-point is a small nuisance.
- Black still has to clear the 16-point.
Are all these problems serious enough to stop Black from doubling? Or is the 2-point game so weak that White already has a pass? Before we answer these questions, let’s take a little look at the structure of the 2-point game itself.
Consider the typical 2-point game in Position A. Here things have gone pretty well for Black. He brought all his men home, formed a prime, didn’t leave any gaps, and now has about as good a position as he could want. (True, he’d be happier if the two checkers on his one-point were spares on his 4-point and 5-point, but let’s not quibble.)
If the cube were still accessible to Black here (an unlikely scenario) the cube action would be double/pass, and both actions would be clear. However, what’s important to note is that this position is much better for White than a similar ace-point game would be. In Position A White’s winning chances are around 20%, while Black’s gammon chances are about 10%. If we put White into an ace-point game while keeping his position on the other side of the board the same, and give Black spares on his low points, White’s winning chances remain about 20%, but Black’s gammon chances jump to about 20%, almost twice the gammon chances in the similarly structured deuce-point game!
Why is a 2-point game so much stronger than an ace-point game? Basically, it’s much easier for White to get off the gammon, while still retaining significant winning chances. The obvious reason for this is that the slightly higher inner-board point gives White more chances to release back checkers before Black gets all his men home. The more subtle reason is that Black’s ace-point acts as a kind of suction pump, pulling checkers to it as Black tries to clear higher points. Even when Black finally clears all the points in front of the 2-point, he’ll find himself with a bunch of checkers still on the ace-point, requiring a few more rolls to bear off.
Low gammon chances for Black means that White is much closer to a take with the deuce-point game than in other low anchor situations.
Take a look at the next position:
Here we’ve given Black’s game one flaw: the open 5-point. Now a take for White is trivially easy, and in fact Black’s doubling decision is the question. If White were playing an ace-point game instead, the open 5-point wouldn’t have much effect and the position would still be a big pass.
Now back to our actual position. Here the big problem is not Black’s open 3-point, but instead Black’s 16-point. If Black clears this point without being hit, the position will be a pass for White.
Black’s 3-point may look like a potentially big problem, but it’s not. Every turn for the next several rolls, Black will have a minimum of three useful builders bearing on the point, and if he can bring builders to the 8-point or 4-point he’ll have even more. The awkwardness of a gap is proportional to the length of time you have to make it. In Position B, Black has hardly any time to make the 5-point, so it’s a problem. But in the original position, Black has plenty of time to make the 3-point, so it’s a very minor problem.
Now our doubling problem becomes pretty straightforward. Black needs to double, because he’ll lose his market if he clears the 16-point. White’s going to take, because he gets solid chances from both the possibility of hitting Black in the outfield, and the long-run chances of winning a 2-point game. Neither possibility by itself is enough, but the combination of the two is plenty.
After doubling, Black needs to clear his 16-point as quickly as possible, so he can go to work on the 3-point with plenty of builders. He should run with any reasonable non-double, such as 65, 64, 61, 53, 52, or 43. He’ll stay with numbers that still play constructively on his side of the board, like 63, 62, 54, 51, and the various small numbers.