Probability Speaking

Get the low down.

Any Craps player worth a damn knows his or her probabilities. If you need a 4 to be rolled, do you know the probability of seeing a 2/2 or 1/3 or 3/1 coming out? If not, it's time to learn.

Elementary Class

Craps is played with two dice. Each die is numbered 1-6.

Simple math tells us that there are 36 possible combinations that can be rolled. Let's look at them.

Dice Combinations

2, 12 - These two numbers only have one combination each (1-1 and 6-6-), thus their probability is 1:36 or 2.77%.

3, 11 - These two numbers each have two combinations (2-1, 1-2, 5-6, 6-5). Their probability is 2:36 or 5.5%.

4, 10 - There's three combinations each (3-1, 1-3, 2-2, 5-5, 6-4, 4-6). The 4 and 10 have a probability of 3:36 or 8.3%.

5, 9 - Four combinations each (1-4, 4-1, 2-3, 3-2, 5-4, 4-5, 6-3, 3-6). There's an 11.1% (4:36) probability of seeing one of these two numbers come up.

6 - The six can be rolled five ways (1-5, 5-1, 2-4, 4-2, 3-3). There's a 13.8% probability of a six being rolled. At 5:36, it's tied with the eight for the second best number to show up.

8 - The eight can also be rolled five ways (2-6, 6-2, 3-5, 5-5, 4-4). As with the six, the eight is 5:36 or 13.8%.

7 - The bad boy, or good boy depending on your playing style. The seven can be rolled six ways (1-6, 6-1, 2-5, 5-2, 4-3, 3-4). The 6:36 probability translate to a 16.67% of seeing a seven on any roll.

Extras

Now that we know the combinations, we can do a couple fun things. Let's look at Hardway bets. There are four (2-2, 3-3, 4-4, 5-5). The Hard 4 and Hard 10 only have one combination. Therefore, they have a 2.77% chance of coming up. Since the 4 and 10 only have three combinations, you have a 66% of losing the bet if the 4 or 10 is rolled.

The Hard 6 and Hard 8 have a 2.77% chance of being rolled. However, there's five ways to make a 6 and 8. Therefore, you have an 80% chance of losing your bet.

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