If you hang around backgammon players it will not be long until you hear a reference to XG, or the “bots” or something similar. These refer to programs that are designed to play backgammon and provide in-depth analysis of positions. These programs use neural network programming techniques and are “trained” by repeatedly playing themselves and developing a database based on the outcomes of millions of games.
There are several ways you can use one of these programs to improve your game. One is by using the program as a “sparring partner.” The programs have various modes that will provide information on your choice of plays either while you are playing or after a game or match is completed. If you play backgammon online against others most sites have a method for creating a log of your game or match. These can be downloaded and analyzed using the program giving you an assessment of your — and your opponents — overall play as well as detailed information about every play and cube decision. You can also set up a particular position in the program and have it analyze the plays and tell you which is best. It is common to see players photographing positions during tournaments, and quite a few are recording entire matches to analyze later.
The currently undisputed “champion” of the backgammon bots is eXtreme Gammon, often referred to as XG. This program is available for Windows (although you will see it on a lot of Macs using Windows emulators at tournaments). The PC version is $59.95 which most players consider a bargain. There are also Android and iOS versions of XG available, while not as strong as the PC version these still play a very good game. XG is available at eXtreme Gammon.
If you are not ready to pay for a program yet, an open source alternative to XG is GNU Backgammon. GNU Backgammon is slower than XG, especially when doing detailed analysis, and not quite as strong, but it is still a very good tool for improving your game. GNUbg is available for Windows, MacOS, and LINUX. Get it at GNUbg.
If you look around the App Store or Google Play you will find a large number of backgammon playing programs. Most of these are not neural network programs and are fairly weak opponents. I would advise you against using them as sparring partners as you can pick up a lot of bad habits playing against these weak programs. If you are looking for a mobile opponent stick with XG or alternatively Backgammon NJ, which is also a neural net based program that plays a strong game. Backgammon NJ also has provisions to play against other humans online.
Finally, ignore all the complaints in the reviews for XG and Backgammon NJ about cheating with the dice. There are many reasons why these complaints are not valid and many sound ways to show that the programs do not cheat.