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Best of Donald Catlin

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Lay Bets

4 May 2007

A few weeks ago, Frank Scoblete forwarded an email from a reader, Stanley Whittaker, to me. It seems that Stanley had written asking for information about Lay Bets in Craps. The letter ended up in the hands of somebody named Fred whose title is Marketing Manager. Fred's response was the following:

Dear Stanley,

On the Golden Touch site (http://www.goldentouchcraps.com/oddsedges.shtml) are all of the edges of just about all of the bets.

Fred

Stanley wrote back the following:

Yes, they are there, but I don't understand how to compute 19-41 for example. I thought if a player bets wrong and lays the five or nine, he had to lay it at 2-3,or six and eight at 5-6 , likewise the four and ten at 1-2. Is this correct?

Thanks so much.

Sincerely,
Stanley

Frank thought I could help out Stanley, and perhaps other players, if I responded to this email with an article about Lay bets. So here goes.

Lay bets are a type of wrong bet, that is, the player is making a wager against the point. For example, if a player bets against a 5 then that player is betting that the 7 will occur before the 5. As Stanley correctly point out, the odds on this are 3 to 2 since there are six ways to make the 7 and four ways to make the 5. Thus if this were a fair bet one would have to offer three units to make two, a 2 to 3 proposition. But as one of my old pals from Brooklyn used to say: "Fair is for stickball."

Indeed! Don't expect a fair bet in a casino. So how does the casino get the edge on such a wager? Well, one way would be to pay the wager at incorrect odds; this is what is done using Place bets. The other thing that the casino can do is charge a fee to make the wager as is done in Buy bets. That is what a Lay bet is. The casino charges the player a 5% commission on winning totals. Here is how it works.

Since the casino doesn't want to deal with small change, the smallest total which produces a unit amount is 20; 5% of 20 is one unit. Now depending upon the casino this fee may only be levied if the player wins or it may be levied when the player makes his wager. Let's look at each of these.

Since a fair wager would be betting 30 to make 20, if the fee is only collected on winning bets the player is essentially laying 30 units to make 19. We would describe this as a lay of 19-30. The probability of making a 5 (before a 7) is 2/5 and the probability of making the 7 (before the 5) is 3/5. Thus, the house edge in this case, on a per unit bet basis would be

House Edge = (19/30) x 3/5 - 1 x 2/5 = (57 - 60)/150 = -1/50

or 2%. If the casino collects the 1 unit fee when the wager is made then the lay is 19-31 and the house edge would be

House Edge = (19/31) x 3/5 - 1 x 2/5 = (57 - 62)/155 = -1/31

which is approximately 3.23%.

I hope this clears things up for some of you. See you next month.


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
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