Backgammon Dice Probability Laws
While it has been determined that backgammon is a game of skill and luck combined, we cannot ignore the fact that the dice and laws of probability play a big factor when considering the luck element. As such, it is important to be aware of how these laws of probability affect the dice that you throw during a game of backgammon and how they work.
Let us take the example of throwing three dice and work out the probability of one six appearing on that throw. Your first thought may be that your chances of throwing a six are approximately 50%. Your logic is such – you have 1 in 6 chances of throwing a six with one dice; so therefore you have 2 in 6 chances throwing with two dice. Unfortunately, that logic simply won’t work. It is illogical to expect that 3 dice will give you a 50% chance of throwing a six, simply because if we continue with that line of logic, we will eventually reach the idea that playing with 6 dice will give you a 100% chance of throwing a six. Nothing can ever give you a 100% guarantee of throwing a certain number with a dice. So this is where the laws of probability come in.
The probabilities are as follows:
When you throw one dice, it can land six different ways – 1, 2, 3, 4, 5 or 6.However, when you throw two dice, you are suddenly faced with 36 different ways that the dice can fall. This equation is reached by simply multiplying the number of ways that one dice can land (6) with the number of ways the second dice can land (also 6). Therefore 6 x 6 gives you 36 ways that the second dice can land.
If you count the number of times that the number 6 appears in the 36 options, you will see that it is 11 times – giving you a 30.5% chance that a six will appear when you throw two dice.
When working out how many times a six will appear when throwing three dice, you can use another method.
Ask yourself what the chances are of six not appearing on one dice.
The answer is 5/6. Multiply that number by the chances of a six not appearing on the second dice. That should give you 5/6 x 5/6 = 25/36.
Multiply that answer by the chances of a six not appearing on the third dice (ie. 25/36 x 5/6 = 125/216). What does this mean? In a nutshell, it means that out of the 216 options when 3 dice are thrown, 125 of them will NOT be a six. In other words, 91 times out of 216, a six WILL appear. If you translate that into percentages, you get 42.1%
Top backgammon players take the laws of probability into account when deciding on their moves during a match. At the very least, players should be aware of how these laws affect the numbers that they throw on the dice.
