Backgammon Math

[the alex]

I just learned the basics of Backgammon. What maths am I looking into when making decisions on a beginner, intermediate, and advanced level?

[chris_a]

I'd say for intermediate level play and up you should definitely learn a few things:

1) How to count shots.
2) How to count pips.
3) About the tradeoff between wins and gammons.
4) Doubling in matches
Counting shots is probably the most important one as it will buy you almost immediate equity in lots of positions. You should learn how many shots are possible to hit checkers with 1 other check unobstructed, then with obstructions, then with two checkers. These have already been worked out and you can find them in tons of places. It's also a great exercise to work them out for yourself because eventually you'll have to do problems that you won't be able to memorize when you're over the board.

The next is counting pips. Lots of beginners intermediate and even a few advanced players eyeball this, but you can definitely buy yourself a lot of equity again by learning how to count pips. You can either do this directly (adding up the value of each checker) or by a more cute method. Notable methods that are good and fast and easy to learn with some practice are Jack Kissane's cluster counting, Doug Zare's half-crossover pip count, and Nack Ballard's NAccel.

For money games you want to be able to understand money equity and the probability of winning and getting gammoned or gammoning. This affects cube decisions directly (when you should take and pass). It also effects checker play in two ways... the first is pretty direct, that is understanding the tradeoff between winning a game and winning a gammon. For a gammonish move to be better than a non-gammonish move that wins more often, the gammonish move needs to win twice as many MORE gammons than the non-gammonish move wins in EXTRA games. The second and more subtle reason is that sometimes you'll want to make plays that bring you closer to your opponents take point so that your doubles can be more efficient.

For match doubling strategy you should learn about match equities, take points and doubling points at different match scores, and gammon prices. Lots of information on this can be found at http://www.bkgm.com