Craps House Edges

Craps offers a wide range of bets with house edges varying from about 1% to over 16%. The house edge represents the amount that is expected to go to the casino in the long run. Bets with high house edges are generally a losing proposition. Therefore it is essential that players are aware of the house edges of the different craps bets.

For beginners the simplest option is to be aware of the bets with the lowest house edges and stick to those bets only. The more adventurous players will want to play the bets with the higher house edges occasionally because they offer larger payouts. One way out for such players is to look to memorizing the house edges of all the bets. But this is not the correct way because different casinos offer different payouts and as a result the house edges for the same bets vary from casino to casino. Hence expert players know how to calculate the house edges.

The first step to calculating the house edge is calculating the probabilities. When the two dice are rolled in craps the outcome varies from 2 to 12. These outcomes can be achieved in thirty-six ways. For getting a 2 the first dice has to show a 1 and the second dice has to show a 1. Therefore there is one way of getting a 2. For getting a 3 either the first dice has to show a 1 and the second dice has to show a 2 or the first dice has to show a 2 and the second dice has to show a 1. Therefore there are two ways of getting a 3. The probability of getting a 3 is 2/36 or 1/18. Similarly the probabilities of getting all numbers from 2 to 12 can be calculated. The final probabilities are given below.

• For an outcome of 2 the probability is 1/36
• For an outcome of 3 the probability is 1/18
• For an outcome of 4 the probability is 1/12
• For an outcome of 5 the probability is 1/9
• For an outcome of 6 the probability is 1/7.2
• For an outcome of 7 the probability is 1/6
• For an outcome of 8 the probability is 1/7.2
• For an outcome of 9 the probability is 1/9
• For an outcome of 10 the probability is 1/12
• For an outcome of 11 the probability is 1/18
• For an outcome of 12 the probability is 1/36

For an outcome whose probability is P and which pays out at Q to 1, the house edge can be calculated as follows:

• Expectation E = P*Q - (1 - P)*1
• House Edge = -E*100

An illustration will explain it better. The Any Seven bet wins if the outcome is a seven. It pays 4 to 1. The probability of rolling a seven is 1/6. Therefore P = 1/6 and Q = 4.

• Expectation E = (1/6)*4 - (1 - 1/6)*1 = -0.1667
• House Edge = -(-0.1667)*100 = 16.67%

If a casino offers a payout of 4.5 to 1 (9 to 2) for this bet the house edge will be halved to 8.33%