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## Calculating House Edges For Simple Craps Bets

By: Adam Richards, Tuesday July 28th 2009

Online craps has a large number of bets on offer. The player must know the correct criteria for choosing which is a favorable bet and which is a sucker bet. Some players go for bets that have a high probability of occurring. But if these bets have a measly payout then there is little worth in them. Other players go for bets that offer high payouts. But if the events have a low probability of occurring then the payouts are like a pie in the sky. The correct criterion for choosing bets is the house edge which combines the concepts of both probability and payout. Simply stated the house edge is the percent of a wager that goes to the casino in the long run. Therefore the higher the house edge the less favorable is the wager for the online craps player.

Before calculating the house edges for online craps bets, the probabilities of the outcomes must be known. In craps the outcomes are the totals of the numbers shown on the two dice. For example the outcome that leads to Any Craps bet winning is a total of 2, 3 or 12. In craps there are eleven outcomes, which are the totals from 2 to 12. These eleven outcomes can be achieved in 36 different ways. A total of 2 can be achieved in only one way, which is with 1 on each die. The probability of achieving a 2 is therefore 1/36. A total of 9 can be achieved in four ways. Therefore the probability of achieving a 9 is 4/36 or 1/9. The probability of the other totals can be similarly computed.

The next step is to understand the payouts. The payout for the Any Craps bet in most online casinos is 7 to 1. This means that if the player wagers \$1 and a 2, 3 or 12 is rolled the player will win \$7. If any other total is rolled then the player will lose \$1.

Now the house edge for the Any Craps bet can be computed. In the long run for every nine wagers the player will win once and lose eight times because the probability of winning is 1/9. Let us assume that he places nine \$1 wagers on the Any Craps bet or \$9 in all. He will win once and get \$7 from the online casino. He will lose eight times and give \$8 to the online casino. Therefore he will lose \$1 over the \$9 that he wagers. Therefore the house edge is 1/9 expressed as a percent or 11.11%.

Another common one roll bet in online craps is Any Seven. This bet wins if a 7 is rolled. A 7 can be rolled in six ways. These are 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, and 6 and 1. Therefore the probability of rolling a 7 is 6/36 or 1/6. Most online casinos offer a payout of 4 to 1 for a bet of Any Sevens. Assuming a player bets \$1 for six Any Seven bets. He will win once and lose five times in the long run. When he wins he will get \$4 and in his five losses he will pay \$5. Therefore on a total investment of \$6 he will lose \$1. Hence the house edge for this bet is 1/6 or 16.67%.

Many of the bets in craps are decided over multiple rolls and the procedure of calculating the house edge is slightly difficult.

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