Backgammon Dice Theory

Good backgammon players know that part of the charm of backgammon games is the element of luck in the toss of the dice. The important thing is to know how to make even the part that's just luck into a part of your strategy, and that's where knowing the probability of rolls comes in.

In a standard backgammon game, you have, for each roll, two dice, on which there are six faces. For the first die you have six options, and for the second die you have six options. Multiply six times six, and you'll realize that there are 36 possible outcomes for each roll of the dice. If you think that 1,2 and 2,1 are the same, then there are 21 possibilities, but fifteen of the possibilities occur twice as often as the other six. Since that makes the math a lot more complicated, it's better to consider 36 possibilities.

When playing backgammon, it's important to know that the dice are fair. If you're playing land-based backgammon, you should feel your opponent's dice, take a good look at them, even roll them a few times off of the board to see what happens. If you're playing in a tournament, there are probably standards. The dice probably need to be transparent, and the pips on each face of the die need to be filled in to make the dice flat. If you suspect, for any reason, that your opponent is playing with unfair dice, request that your opponent switch to a different pair of dice or ask a judge to check them. In a friendly game, if your opponent is playing with unfair dice, your opponent may not be playing as friendly a game as you are.

If you're playing backgammon online, check the internet site. It should have a symbol from an independent auditor such as iTech Labs. If the site's random number generator has not been authorized by an independent auditor, find a different site. Since almost all online backgammon software has been properly tested, there's no need to waste your time on a site you aren't sure of.

Assuming that the dice are fair, and that there are 36 possibilities, imagine the following scenario; you have to choose between two moves, one in which you will leave a blot that is one point away from your opponent, and another move which will leave a blot nine points away from your opponent, how do you choose which is the less risky move? Using the theory of probability, you can calculate the chance that he will hit either of these blots on the next roll.

If your opponent throws any combination of dice that shows a 1, he will be able to hit a blot which is one point away. There are 11 such possible rolls; 1-1 (only one combination of the dice produces 1-1), a 1 on the first die, and any other number on the second die: 1-2, 1-3, 1-4, 1-5, 1-6, an/or a 1 on the second die and any other number on the first die: 2-1, 3-1, 4-1, 5-1, 6-1. That makes the probability of getting hit 11 out of 36 possible rolls.

If, on the other hand, your other possible move would leave a blot nine points away from your opponent, he would have to roll one of the following combinations: 4-5, 5-4, 3-6, or 6-3. The probability of this event is 4 out of 36, a lower chance of being hit. Now it is clear which is the less risky move, right?

You can see why it's important to know how to calculate the statistical probability of any particular roll being thrown, and it's not all that difficult, either.

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