I know there are lots of formula's for races when to double and when to take, but they all seem to be based on like when 8% ahead in pipcount double, or with an adjusted pipcount of Thorp, then use the 10% minus 2 rule etc etc etc.

All these methods share in common that they tell you when to double, pass or take. Which is good for money games and in early match situations.

But what about late match situations? where your doubling points and take points are diffrent, one cannot use this methods. So one needs another method.
Best Method would be a formula where your winningchanges /game-equity are expressed in % or something.
Does anybody know a method like this.

I know about a Lamford formula:

CPW = 50 + (900+PC+400L)/(PC+7L+25)

where
CPW = cubeless probability of winning the game expressed in percent,
PC = pipcount for the player on roll,
L = number of pips lead he has in the race


But this is to minddazzling to do over the board.

I know there is a formula by Kleinman too which involves remembering some tables.

question is, are there any other methods, which are practical in over the board play?

thank you.

Kleinman is probably the best formula you can find, especially if you learn the adjustments (for holes, stacks and crossovers), and seems to be fairly accurate in medium and long races, but yeah it is pretty extensive especially if you're not pretty decent at doing math in your head.

An intermediate player would probably be better off not worrying too much about making an occasional mistake in these situations and work on other aspects of his game (and I think there are many world class players, who go by feel and experience instead of hard math in these situations as well).

If you just use one of the standard percentage rules and then adjust as best you can, you're probably not gonna be off by much unless it's a really lopsided score.

Worth knowing is that one pip usually is worth somewhere between 1-1.5% increase/decrease in your winning chances (in mediumlong - long races) and that your takepoint in a moneygame is roughly 22.5%.

The 1-1.5% is only when you're reasonably close to the takepoint for money, I should add.

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, it’s actually simpler than it looks.

First, let’s 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 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 6-points, but your 4-point 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 5-point down to your 2 or 1-point, 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 Thorpe formula (Advanced BG, 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, Thorpe 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.



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 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? It’s still double-take.

Suppose Black leads 17-4? It’s still double-take.

In fact, the cube action doesn’t change until the score reaches 18-4 to 21. Now it’s not a double. Black would need to lead by two more pips, either 98-111 or 100-113, in order to double.

What’s different about the 18-4 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 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 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 2-cube and was thinking about redoubling to 4, he’d have to worry about the re-redouble to 8, so he’d start making small adjustments a little earlier in the match. But that’s a story for another time.