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7 Point 7

7 November 2008

By Donald Catlin

The Orleans Hotel and Casino introduced a new Craps bet on Friday, September 19th. The bet is called 7 Point 7 and was developed by Casino Gaming, LLC. Here is how it is played.

The player can place the 7 Point 7 bet on the come-out roll. If a 7 is rolled on the come-out the 7 Point 7 bet wins 2 to 1. If 2, 3, 11, or 12 are rolled on the come-out, the 7 Point 7 loses. Otherwise a point is established and the 7 Point 7 bet remains in action. Once the point is established the very next roll determines whether the bet wins or loses. If a 7 is rolled on the next roll the 7 Point 7 bet wins 3 to 1; otherwise the wager loses.

The house edge can be determined as follows. The probability of rolling a 7 on any roll is 1/6. Similarly the probability of rolling a 2, 3, 11, or 12 is 1/6. This means there is a 2/3 chance of rolling a point. Once a point is established there is a 1/6 chance of rolling the 7. Since the come-out and the next roll are independent events, the probability of establishing a point and then rolling a 7 is 2/3 x 1/6 or 2/18. This is the same as 1/9. There is a 5/6 chance of not rolling a 7, so the chance of establishing a point and then rolling a non 7 is 2/3 x 5/6 or 10/18. This is the same as 5/9. With these probabilities in hand, it is easy too calculate the house edge using the following table:

Outcome

Probability

Payoff

Product

7 on come-out

1/6

2

6/18

crap or 11 on come-out

1/6

-1

-3/18

Point then 7

1/9

3

6/18

Point then no 7

5/9

-1

-10/18

Totals

1

---

-1/18

The player's expected return is -1/18 or -5.5555…%. Thus the house edge for the 7 Point 7 wager is approximately 5.56%. See you next month with a super proposition bet.


Don Catlin can be reached at 711cat@comcast.net

Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers