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Casino Craps House Edge Per Roll

By: Adam Richards, Wednesday June 2nd 2010
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House edge is the proportion of each bet that the house expects to take in the long run. For example the Pass Bet in Craps has a house edge of 1.41%. This means that if a player wagers on this bet continuously, for every $100 wagered the house can expect to take $1.41 and the player can expect to get back only $98.59. What if a player wants to estimate how much he expects to lose in an hour? In most casino games this can be easily computed from the house edge per bet, but not so in Craps. This article first explains how it is done in other games, what problems arise in craps and how these problems are overcome through the concept of house edge per roll.

To be able to compute the expected loss per hour in any game the player has to be able to estimate how many events take place in an hour. For example in Roulette the player has to estimate how many spins of the wheel he can get per hour. This can easily be done by playing online for ten minutes and logging the number of spins and extrapolating the result. For the sake of convenience let us assume that there will be 60 spins in an hour. The house edge in any bet in European Roulette is always 2.70%. If the player wagers $100 in every bet he will expect to lose $2.70 per bet and with 60 bets in an hour he will expect to lose $162 in one hour.

The same method cannot be applied in Craps. Most of the commonly placed bets in Craps are not decided in a single roll, whereas in Roulette all bets are decided in a single spin. Theoretically a player can keep on rolling for one hour without the Pass Bet being settled if neither the point nor 7 is rolled again any time. Therefore even though the hose edge of the Pass Bet is known and the player estimates that he can make 60 rolls per hour he cannot estimate his expected hourly loss. However if the player is given the value of the house edge per roll for the Pass Bet he will be able to compute the expected hourly loss as described in the Roulette example.

Fortunately the house edge per roll can be computed. Using advanced statistics it is possible to compute the average number of rolls required to complete each bet in craps. For the Pass Bet this number is 3.38. What this means is that if a player places the Pass Bet 1,000 times and each time records the number of rolls it took to complete the bet, he will find that the average is close to 3.38. Now the house edge per roll is the house edge per bet divided by the average number of rolls required to complete the bet. Therefore for the Pass Bet the house edge per roll is 1.41%/3.38, which is 0.42%. If the player wagers $100 every time on a fresh Pass Bet he can expect to lose $0.42 on each roll and on 60 rolls he can expect to lose $25.20. Therefore his expected hourly loss will be $25.20.

The house edges per roll for some of the other bets in Craps are given below.

Don't Pass: 0.40%
Place 6, 8: 0.46%
Place 5, 9: 1.11%
Place 4, 10: 1.67%
Big 6, 8: 2.78%
Hard 4, 8: 2.78%

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