Understanding Double and Take Theory

This week’s position analysis provides an excellent lesson in understanding the theory of the double and the take.  

In the backgammon position below, it is a money game, and Black is on roll and doubles.  Should White take or drop?  See what you think and then scroll down to see what the right answer is, why it is the right answer, and some “shortcuts” to determine the right answer.

The answer is: it is a take. In a money game, the take point is around 25%. It means that if you can win over 25% of the time, you are going to do better in the long run, than if you drop.   Of course, you also have to take in consideration the number of times you get gammoned and backgammoned, and reduce those by the number of times you win gammons and backgammons. 

As you can see from Insert 2 below, according to Snowie (a computer program) White wins this game 32 percent of the time. Now he does get gammoned 20 percent of the time, but he also wins gammons about 8 percent. When you factor in all the variables, White still comes out well ahead by taking as opposed to dropping.

But forgetting about gammons and backgammons for a moment, let’s pretend you are in a simple race where you win 30 percent of the time. If you played that game 100 times and you dropped every time, you would lose 100 points. But if you took every time, you would lose 70 times, and with a 2-cube that would cost you 140 points. But you would also win 30 times at 2, and that’s 60. So you would lose 140 points and win 60, so your net loss by taking would be 80. So you save 20 points, or 20 percent, over dropping. And that is why it is right to take a cube even though you are not a favorite to win. 

• In a game where you have a 30 percent chance to win once your opponent doubles, if you take the cube, your odds of winning immediately go up. That's because now you are holding the cube, and that has value.
• If the game turns around and you get the lead, you can double and end the game or force your opponent to play for 4. Also, once you have the cube, your opponent cannot end the game, so even if he gets further ahead, you still have the chance to make a comeback and win. 

 Now, once you know this theory, the real trick is to be able to look at a position, like the one above, and try to decide if you have better than 25 percent after considering gammons and all other factors. Unfortunately, I have no magic formula for that. It takes skill and knowledge and experience to look at complicated positions like the one above and know whether you are better off taking or dropping.  

I have been playing backgammon for 45 years and I am still often not sure, but every year I learn more and more concepts and strategies that help me make the right decisions, and I can tell you that they work. Using the strategies I have learned (and that I also teach online to my students) I am able to break down positions like the one above and make some pretty good estimation about wins, losses and gammons, which generally leads to the correct decision. There are pragmatic, mathematical approaches that can and should be employed, and these can be learned with study and coaching.