Backgammon Odds for Rolling the Correct Dice Combinations

Below, we’ve indicated the odds for rolling the correct dice combinations, which bring your checker back into the game, depending on the no. of points covered by your opponent. Remember this is when you have only one checker on the bar; when you have more than one the odds of re-entering two checkers increase significantly.

Number of Blocked Points Odds for possible re-entry
0 36/36
1 35/36
2 32/36
3 27/36
4 20/36
5 11/36
6 0/36
How to Use the Odds

You can employ the odds in any number of ways. Backgammon is a game that requires a lot of decisions. A solid understanding of the possibility of any particular roll occurring will give you a huge advantage over your opponent. To illustrate this, consider the following scenario:

It’s the late stages of a match and you have three checkers remaining: one each on the 2-, 4-, and 6-points. Your opponent has three checkers on his 1-point. You roll a 6 and a 1. Now, you would bear off the checker on the 6-point, but what do you do with the extra 1? Checkers on 3 and 2, or checkers on 4 and 1? A quick examination of the odds is all that’s necessary to make the best decision. If you leave checkers on 4 and 1, then you know that all you need to do is roll a 3, 4, or a 5 on my next roll, or doubles 2 or 3. The table illustrates this below:

1,1 2,1 3,1 4,1 5,1 6,1
1,2 2,2 3,2 4,2 5,2 6,2
1,3 2,3 3,3 4,3 5,3 6,3
1,4 2,4 3,4 4,4 5,4 6,4
1,5 2,5 3,5 4,5 5,5 6,5
1,6 2,6 3,6 4,6 5,6 6,6

As you can see, there are 29/36 combinations (80.1% chance) that will result in victory. Not bad. Now, let’s consider the alternative; leaving checkers on the 3- and 2-points.

1,1 2,1 3,1 4,1 5,1 6,1
1,2 2,2 3,2 4,2 5,2 6,2
1,3 2,3 3,3 4,3 5,3 6,3
1,4 2,4 3,4 4,4 5,4 6,4
1,5 2,5 3,5 4,5 5,5 6,5
1,6 2,6 3,6 4,6 5,6 6,6

Here the chances of getting a good roll are only 25/36 or 69%, so it is clear that the first option is better. If you think about it in percentages, by leaving the remaining checkers on the 4- and 1-point rather than the 3- and 2-point, you have increased your chances of winning by 11%!

As you can see, being familiar with the odds, which takes some practice, can make decision-making much easier and fruitful!

General Guidelines

You can’t draw or use a table like the ones above every time you need to determine the odds of any one combination occurring. So, a better idea is to devise and remember a shortcut that will allow you to make quick and accurate decisions. Check out the following breakdown:

The odds of rolling any particular number are:

1 (i.e., a 3) 11/36 (31%)
2 (i.e., a 5 or a 6) 20/36 (56%)
3 (i.e., a 4, 5, or 6) 27/36 (75%)
4 32/36 (89%)
5 35/36 (97%)
6 36/36 (100%)

Does that make it a bit simpler???

Calculating the Probabilities Hitting the Right Combination

This quick formula can be used in any situation where you are concerned with the probability of rolling productive numbers. This type of knowledge will help in your doubling decisions.

Chances of a successful roll = (the total of useable combinations/36) %

Whenever the useable combinations are greater than 18/36, then the probability is more than 50% that the outcome will be good for you. So, in this case, the player will know that there is a more than even chance of an immediately successful roll and that over a period of time (a game, for example) successful outcomes must occur more often than not.

With all of this in mind, you can see that your chances of success in backgammon can be greatly improved with a solid understanding of the odds involved. And, hopefully, you’ve seen here that such calculations aren’t too difficult to make and with a bit of practice, such an understanding can easily be added to your bag of skills.