Craps Mathematics

Craps is a popular casino game that is played with two dice at a special craps table. The table is laid out into three areas: two side areas and a centre area. In each side area are sections for Don’t Pass line bets, Come and Don’t Come bets, Odds bets, Place bets and Field bets, while the centre area is where Proposition bets can be placed. Winnings are calculated from the outcome of either one roll or a series of rolls of the two dice. It’s important to be aware of the mathematics of craps, such as the probabilities and odds involved, as this can help you to make astute decisions as to what to bet on.

Mathematical Strategy in Craps

As the rolls of the dice in a game of Craps are not dependant on each other (see the independent and dependent events page), i.e. the outcome of one roll does not affect the outcome of the next roll, nor is it influenced by any previous rolls, it is not possible to develop a long-term strategy to win at Craps. As with all casino games, there is always the house advantage to take into consideration, which means that over time the house will always be favoured to win the majority of bets. In other words, all bets in Craps have a negative expected value.

Instead of trying to predict the outcome of a roll or sequence of rolls, which is not possible for the reason given above, a better idea is usually to “ride” the table, i.e. vary your bets according to the payout frequency from roll to roll. If the table is “hot”, i.e. paying out nicely, then bet more, but if it’s “cold”, lower your bets. There are no mathematical explanations to back this up, but try your luck and it may pay off.

Probability in Craps

The following table shows how many ways exist to reach a certain sum in Craps. For example, there is only one way of throwing the two dice to reach a sum of 2, while there are six ways to throw them to reach a sum of 7. The more ways that exist to arrive at a certain sum, the higher the probability of attaining that sum, and therefore the lower the payout ratio for that particular sum. View our page on the theory of probability for more details about this.

Sum 2 3 4 5 6 7 8 9 10 11 12
Frequency 1 2 3 4 5 6 5 4 3 2 1

View the Gambling Mathematics Glossary or see our other pages on the mathematics of casino games.