Backgammon probability tables
August 4th, 2006
Backgammon is essentially a game of mathematics, more precisely probabilities. Your success in backgammon therefore relies primarily on how well you can judge the chances of something happening in a given situation - the probability of X. From that we can conclude that in backgammon your decisions are only as good as your judgement of the situation.
Backgammon and probability
Novice players often find it extremely difficult to form a clear overall picture of a backgammon game. Duplications, diversifications, pip-counts, timings, wastage, strategies, backgammon, holding games - it is all very confusing in the beginning. I am no genius and chances are that your neither. So we need something that helps us getting started with understanding what’s going on and through that make better calls. The answer is probability tables.
For those interested in the mathematical aspects of probability, there is an excellent book called Introduction to Probability. The book is a scientific publication but contains many easy-to-understand examples that are very educative and useful.
Probability tables are overlooked in most of backgammon literature for novice players and hidden among the last pages just before the appendix or glossary so that you can easily forget about them. However, they should get the credit they deserve as they really can speed up the understanding and level of your game. See, if you know what is the chance of something happening after your move you might not even make that move but do something else that will either increase your chances or decrease your opponents chances. It’s up to you how you want to see it.
Below we go through the three most common and useful probability tables for novice players. You might want to print them and keep them near to you. Don’t worry, soon you can leave them alone for the bigger part of the game and the time will come when you can do without. The basic tips after each chapter will help you how memorize the essence of the probability tables.
Chances of hitting
The most used probability table deals with the probability of hitting a direct shot when when it is a given amount of pips (points) away. By studying and understanding this will help you to position your checkers in the best way, minimizing the chances of getting hit.
|
Points away |
Chance of hitting | |
| 1 2 3 4 5 6 7 8 9 10 11 12 15 and above |
11/36 12/36 14/36 15/36 15/36 17/36 6/36 6/36 5/36 3/36 2/36 3/36 1/36 |
31% 33% 39% 42% 42% 47% 17% 17% 14% 8% 6% 8% 3% |
By far the biggest chance of hitting is when the blot is 6 points away. That’s why in the beginning it can sometimes be so difficult to make the bar point for both players. However, the chance of hitting suddenly takes a nosedive when when the blot is 7 or more pips away. That’s good to keep in mind for example when either you or your opponent played a deep holding game and it’s time to bear in.
From this table, remember two things
1. If you leave a shot within 6 points away from your opponent, leave it as close to him as possible.
2. If you leave a shot more than 6 points away from your opponent, leave it as far away as possible.
Chances of entering from the bar
The reason why it is soooo important to make home board points as early in the game as possible is that the more points you make the harder it is for your opponent to enter from the bar. It might not seem much but three made points as opposed to two makes it suddenly much more difficult for your opponent to enter from the bar on his next turn. The probability table below highlights the chances of entering from the bar when the opponent has from 1 to 5 points made in his board:
One checker on the bar
| Points | 1 roll | 2 rolls | 3 rolls | 4 rolls | 5 rolls |
| 1 | 97% | 100% | 100% | 100% | 100% |
| 2 | 89% | 99% | 100% | 100% | 100% |
| 3 | 75% | 94% | 98% | 100% | 100% |
| 4 | 56% | 80% | 91% | 96% | 98% |
| 5 | 31% | 52% | 67% | 77% | 84% |
Two checkers on the bar
| Points | 1 roll |
| 1 | 69% |
| 2 | 44% |
| 3 | 25% |
| 4 | 11% |
| 5 | 3% |
From this table, remember two things
1. Make home board points always when you can.
2. Hit as many checkers as you can.
Chances of winning in a 5-point match
when you play money games online a very common match length is 5 points. Many tournaments also have match lenght of 5 and therefore it is important for you to know what your chances are of winning at a given score. This is important for doubling cube action as you need to take your chances into account when deciding to accept the doubling cube or not.
In the probability table below your score is on the left and your opponent’s on the right. Your chances of winning the game at that score are next to the it. The table below assumes that both players are of equal level.
| 0-0 50% | 0-1 42% | 0-2 34% | 0-3 25% | 0-4 15% |
| 1-0 58% | 1-1 50% | 1-2 41% | 1-3 32% | 1-4 17% |
| 2-0 66% | 2-1 59% | 2-2 50% | 2-3 40% | 2-4 25% |
| 3-0 75% | 3-1 68% | 3-2 60% | 3-3 50% | 3-4 30% |
| 4-0 85% | 4-1 83% | 4-2 75% | 4-3 70% | 4-4 50% |
1. If you are the first to reach score of 3 or 4 you are looking very good. Play solid, don’t take silly risks.
2. Whenever you are two points behind in the score, don’t hold back. You need to play aggressive to win.
