The issue of how to double noncontact positions in a match is an interesting one. Although the match equity tables (METs) and the various racing formulas make the topic seem very complicated, it’s actually simpler than it looks.
First, let’s talk about evaluating noncontact positions in money games.
Noncontact positions come in two forms: races and bearoffs. A race is a position with some checkers still in the outer boards, ready to come home. Pip count in a race is usually somewhere between 60 and 120 for each side. For races, the 8912 formula is really all you need in a money game.
Make an initial double if you are 8% ahead in the pip count. Make a redouble if you are 9% ahead. Take a double if you are no more than 12% behind. These are good rules and ensure that you won’t ever be making a big error. I use them myself all the time, and in real play I never worry about the exceptions.
Bearoffs are a little different. When you get all your men into your inner board and start bearing off, the pip count isn’t the only thing you need to consider. The number of checkers remaining is important. If you have a pip count lead but have more checkers left than your opponent, your effective lead isn’t quite as great as the pip count would indicate. Roughly speaking, every extra checker decreases the significance of your pip count by about two pips.
Gaps also matter. If you have checkers on your 2, 3, 5, and 6points, but your 4point is open, then you’ll miss every time you roll a 4. That’s very significant. When you roll a 4, you’ll move a checker from your 6 or 5point down to your 2 or 1point, then later you’ll bear him off with a number larger than the point he’s on, so you’ll end up wasting pips.
The Thorp formula (Advanced Backgammon, volume 2, p. 190) was the first attempt to correct for these problems, and it works pretty well. Other formulas came along later that are more work but give slightly better results. For me, Thorp has the right combination of ease and power, but the other formulas have their fans too.
Now, what happens when we move from a money game to a match, where one side might have a big lead? How do we adjust?
Now for the good news. Where initial doubles are concerned, we don’t have to adjust very much. Take a look at the next position.

Position 1. Money game. Black on roll. Cube action?

Black leads in the pip count by 100 to 111, an 11% edge. It’s a double and a take, as we might expect.
Now suppose we’re playing a 21point match and Black leads White 74. The cube is still in the middle. The correct cube action is still doubletale.
Suppose Black leads 144? It’s still doubletake.
Suppose Black leads 174? It’s still doubletake.
In fact, the cube action doesn’t change until the score reaches 184 to 21. Now it’s not a double. Black would need to lead by two more pips, either 98111 or 100113, in order to double.
What’s different about the 184 score? It’s the first score where, if White takes and redoubles to 4, Black will take but he can’t use all the points now in play. The cube is dead at 4, but Black only needs 3. Only at that point does the cube action change.
At the score of 194, the cube action changes a little more. Now Black needs a 15pip lead, either 96111 or 100115, before he can make an initial double.
The lesson here is that for initial racing doubles, the leader doesn’t have to adjust his strategy until he has less than 4 points to go in the match. Even then, he doesn’t adjust by very much.
Recubes get a little trickier. If Black owned a 2cube and was thinking about redoubling to 4, he’d have to worry about the reredouble to 8, so he’d start making small adjustments a little earlier in the match. But that’s a story for another time.
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