Most intermediate players, and many championship level players, do not truly understand how gammons affect their cube decisions. Maybe this will help shed some light on the subject for you.
We take or drop cubes based on the relative risk of winning and losing the game, and the relative risk of winning and losing gammons and backgammons. Basically, when we are doubled, we have two jobs: first, to make these estimates based on the position of the checkers on the board, and second, to factor in the match score to determine if this is a time we should take more or less risks than normal because of the score.
At any match score, every opponent has a “take-point.” The take point is that number that separates the proper takes from the drops. Since money game is always the same…around a 25% take point, most players use that as their basis for comparing cube decisions.
In a money game, the reason your take point is around 25% is because if you play 100 games where you are doubled, and you take them all, you will break even if you win 25% of the games you take. So if you are in a position that you think you would win 33% of the time, you are much better off taking than dropping…in the long run, you’ll lose less money.
The 25% number, however, does not consider gammons and backgammons. If you will win 25% of the games from a given position, but many of the 75% that you lose will be gammons, then it is foolish to take the cube. It is a big drop.
There is a “price” you pay for gammons, and in a money game, statistically, that price is .5 times the cube. In other words, if you think you would win 33%, but you get gammoned 26% of the time when you lose, you have to multiply the 26 by .5 to get 13, and that is your net loss from gammons. So you subtract 13 from 33, and that gives you 20, and since 20 is less than 25%, you should drop.
It’s not quite that simple, because you have to add back the price of gammons for the number of times you migh gammon your opponent. So in the above example, let’s say that you might win a gammon 10% of the games, you multiply that times .5 and that’s 5, and when you add the 5 back on to the 20, you are right at 25% and you can take the cube. (Most of the time we don’t estimate backgammons unless there is a clear, serious backgammon threat, because they are so rare.)
So that is the calculation that really top players do in their heads when they are doubled. Often experts don’t have to go through all of the estimates and numbers and match because most of the time they are doubled, the position is not that unusual and they can get a pretty good idea as to whether it is a take a drop just from having experienced playing similar positions so many times in the past. They have “reference” positions that help them decide.
Match play gets much more complex, as the take points vary depending on the score, and the price of gammons also vary depending on the score. Many top players do not know all these numbers…they are fairly complex and there are many numbers to learn, and even when you learn them, it is often tough to make accurate estimates of wins and losses and gammons over the board. But the very top players know these numbers and do these estimates very well…that’s one of the major reasons they are top players.
The secret is out…top backgammon players aren’t just people who are truly gifted at playing the game of backgammon—they are people who have studied the game and learned the numbers and also have the skills to remember them and apply them accurately over the board. Do you want to be a top player some day? You will have to study. No matter how talented you are, you need to have an excellent understanding of take points and the price of gammons in order to be a top player.