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# The Fire Bet

13 February 2010

I've had a few letters from readers asking about a Craps wager called the Fire Bet. This wager is offered by the Golden Nugget in downtown Las Vegas and I've heard, but can't confirm, that the Orleans also offers the wager. This wager was created by Perry B. Stasi and was patented in 2003 and trademarked in 2004. Let me describe the bet for you.

The Fire Bet is made before the first role of a shooter's hand. The bettor is wagering that the shooter will make at least four distinct points during his hand. The payoff is according to a pay table: 25 for 1 for four distinct points, 250 for 1 for five and 1000 for 1 for six. (Another pay table is 10 to 1, 200 to 1 and 2000 to 1, respectively.)

In order to calculate a house edge for this wager one needs to calculate the probability distribution for the number of points made during a shooter's hand. It turns out that this is not easy to do. In fact, when I first looked at this I decided that I would obtain these by writing a simulation. Then I recalled that my friend Stewart Ethier from the University of Utah was the first person to tell me about the Fire Bet. Stewart is publishing a book entitled The Doctrine of Chances and I figured that he probably mentions this wager in his book. I wrote to Stewart and he sent back the section in his book where he analyzes the Fire Bet. It is a rather tricky calculation and is not suitable for this article. However, since they are exact, I will use his numbers. By the way, if you want to read Stewart's analysis, his book will be published on April 3, 2010 and the calculation is in Chapter 15; his publisher is Springer. I am grateful for his permission to use his numbers.

Here is the table one must construct to analyze the Fire Bet:

 Number Probability Payoff Product 0 0.593939393939 -1 -0.593939393939 1 0.260750492004 -1 -0.260750492004 2 0.101275355549 -1 -0.101275355549 3 0.033434212179 -1 -0.033434212179 4 0.008798178440 24 0.211156282560 5 0.001639933139 249 0.408343351611 6 0.000162434749 999 0.162272314251 Totals- 0.999999999999 --- -0.207627505249

The reason that (for example) the payoff corresponding to the number 4 is 24 is because the payouts were stated as 25 for 1 rather than 25 to 1. When the payoff is 25 for 1 the 25 includes the unit wager so you are really only winning 24 units.

From the above result we see that the Fire Bet has a house edge of approximately 20.7628%, not a very good wager for the player. See you next month.

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

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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
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