Probability in Backgammon

In the game of backgammon, there are eleven ways to roll a specific number.

Given this, you would most likely believe that there are twenty-two ways to roll one of two numbers (for example, one and two). However, in actuality there are only twenty ways to roll a two number combination, because one/two and two/one will not be counted twice. Sounds a bit confusing, until you understand further the concepts of probability.

Woman Playing Backgammon

When you gather this knowledge, you then realize there are twenty-seven ways to roll one of three specific numbers, followed by thirty-two ways to roll one of four, and thirty-five ways to roll one of five numbers.

When you understand the complexities behind probability in backgammon, this allows you to be more strategic in your play. For example, you can figure out what the risk is for leaving blots, as well as your chances for hitting and/or covering points. You will also be able to assess how to move your various pieces around the backgammon board in order to make the most dice rolls work well for you. If you have ever played against a seasoned backgammon player who seemed to get better rolls than beginners, you can chalk it up to the odds of probability.

To break down probability into percentages, let's look at it the following way.

Your odds of directly rolling a specific number are 30.55%, while rolling a particular double combination translates into 2.77%. Subsequently, your odds of rolling a specific non-double are 5.54%, while the probability of rolling any double is 16.66%.

As you can see, the probability that you will roll any specific number with two dice are not necessarily what they seem. By learning the concept of probability as it applies to backgammon, players can use this to their advantage to move their pieces around the board into the most advantageous positions for them.