The issue of how to double non-contact 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, itís actually simpler than it looks.
First, letís talk about evaluating non-contact positions in money games.
Non-contact 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 8-9-12 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 wonít 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 isnít 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 isnít 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 6-points, but your 4-point is open, then youíll miss every time you roll a 4. Thatís very significant. When you roll a 4, youíll move a checker from your 6 or 5-point down to your 2 or 1-point, then later youíll bear him off with a number larger than the point heís on, so youíll 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 donít have to adjust very much. Take a look at the next position.
Money game. Black on roll.
Black leads in the pip count by 100 to 111, an 11% edge. Itís a double and a take, as we might expect.
Now suppose weíre playing a 21-point match and Black leads White 7-4. The cube is still in the middle. The correct cube action is still double-tale.
Suppose Black leads 14-4? Itís still double-take.
Suppose Black leads 17-4? Itís still double-take.
In fact, the cube action doesnít change until the score reaches 18-4 to 21. Now itís not a double. Black would need to lead by two more pips, either 98-111 or 100-113, in order to double.
Whatís different about the 18-4 score? Itís the first score where, if White takes and redoubles to 4, Black will take but he canít 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 19-4, the cube action changes a little more. Now Black needs a 15-pip lead, either 96-111 or 100-115, before he can make an initial double.
The lesson here is that for initial racing doubles, the leader doesnít have to adjust his strategy until he has less than 4 points to go in the match. Even then, he doesnít adjust by very much.
Recubes get a little trickier. If Black owned a 2-cube and was thinking about redoubling to 4, heíd have to worry about the re-redouble to 8, so heíd start making small adjustments a little earlier in the match. But thatís a story for another time.
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