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# Pass Versus Place

3 July 2011

I recently received the following letter from one of my readers named Dave.

Mt. Airy casino in Mt. Pocono, Penna. has the 3-4-5 free odds at the craps table. During the course of the game I realized that my pass line (\$10) and max free odds always worked out to a \$70 win. No matter what the point number was. That's if I won!

Driving home and thinking about the whole thing, I figured that I could place bet the equal amount of the pass and free odds and receive the same payoff. Ex. Point 6, pass line \$10 + max free odds \$50 = \$60; pay off is \$70. However a place bet of the same \$60 equals a \$70 pay off also. The \$70 pay off works for the other numbers also EXCEPT the 4 and 10. Buying the 4 or 10 even with the vig would gain \$8 with a \$78 pay off (total \$40 bet).

Since I always believed that the pass line and free odds were the best wager, I'm wondering if my math is fuzzy.

This place betting can be removed at anytime while the pass line cannot. Forgetting the pass line and placing the "point number" now seems to be the better wager. Am I missing something? I would like your thoughts or the math that justifies the often touted pass and free odds as the better bet.

Dave

Well, Dave, there is nothing wrong with your math; your calculations are correct. But you are missing something. You are ignoring the come out roll. When the dice are coming out you are twice as likely to win as you are to lose. If a point is established you have the worst of it but can partially make up for this by using the free odds.

The bottom line in any gambling game is the house edge. Placing the 6 or 8, for example, produces a house edge slightly less than 1.52%. You can check this in any of the several books on craps that have been published.

The house edge for the pass line is somewhat more complicated. You might like to check out my October 2003 article in the archives before reading further. The following table assumes that the player makes a \$10 line bet and then places \$50 on free odds for the 4, 6, 78, and 10. I'll assume that the most the house will let you place on the 5 and 9 is \$40, although some casinos will let you take \$60 in odds in this situation. Here is a table that assumes that the player makes 1980 line bets.

 Event Freq. Line Tot. Line Odds Tot. Odds L pay O Pay Nat. 440 10 4400 0 0 4400 0 Craps 220 10 2200 0 0 -2200 0 4 made 55 10 550 50 2750 550 5500 4 not 110 10 1100 50 5500 -1100 -5500 5 made 88 10 880 40 3520 880 5280 5 not 132 10 1320 40 5280 -1320 -5280 6 made 125 10 1250 50 6250 1250 7500 6 not 150 10 1500 50 7500 -1500 -7500 8 made 125 10 1250 50 6250 1250 7500 8 not 150 10 1500 50 7500 -1500 -7500 9 made 88 10 880 40 3520 -880 5280 9 not 132 10 1320 40 5280 -1320 -5280 10 made 55 10 550 50 2750 550 5500 10 not 110 10 1100 50 5500 -1100 -5500 Totals 1980 -- 19800 -- 61600 -280 0

If we add the total of the line bets and the odds bets we get 81400. The total amount lost is 280. The ratio 280/81400 is approximately 0.00344 so the house edge here is approximately 0.344%. This is much better than placing either the 6 or 8. If we could put \$60 on the 5 or 9, the house edge would be even smaller. I hope this settles things for you, Dave. See you all 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