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# Mailbag

2 November 2007

Every now and then I receive a letter from a reader that is interesting but does not have enough substance to demand a whole column. Here are three such letters and I thank the writers - I'm sure my readers will enjoy them; I did.

Dear Don,

That article you wrote on Zzyzx Road. To my surprise there is a horse named Zzyzx Road that is running at Yonkers on 8/14/07 in the 7th race. I guess you should take credit for it.

John

Well, John, thousands of people pass the Zzyzx Road exit on I-15 every day so I don't think I can take credit for naming this horse. It is interesting though and I imagine a lot of people are curious about how this horse got such a strange name. Thanks for the info.

Dr. Cat,

I play the Don't Pass and lay odds - the 12 is barred.

I was wondering what the average wager would be when making a \$5 Don't Pass Wager and laying \$12 on whichever box number was the shooter's point.

I'm sure there is a formula for this.

Thanks,
Eddie

I don't know about a formula Eddie but this can be easily computed. Before I get to that, however, I have to settle the issue of the push on the 12. Some people insist that this should not be counted as the resolution of the wager; others think it should be counted since you can take the wager down when the 12 occurs. Whichever stand you take there will be critics so you can't win this argument. I am going to assume that the bet is resolved when the 12 occurs since it makes the calculations nicer.

In 36 rolls if everything happens as probability theory predicts, the 2, 3, 7, 11, 12 will occur 12 times and a point will occur 24 times. Thus 1/3 of the time the wager will be \$5 and 2/3 of the time the wager will be \$17. Hence the average wager will be

1/3 x 5 + 2/3 x 17 = 13

By the way, note why Eddie uses \$12 to lay the odds. This number pays out an integer amount no matter what the point is. Good thinking Eddie!

Dear Don,

I dropped by the Atlantic City Hilton the other day and saw Roulette "machines." They are SINGLE zero and payouts seem to be the same (36-1, etc., because they have to "give" you your dollar back.) Are the odds calculated as in a "hand-played" single-zero roulette game, i.e., half of the 5.26% on a double zero table? I assume there is a software program essentially like the ones in VP machines since they have to be true to the table game and not various hold percentages as in slots. Bets can be \$1 up to \$25 if I remember correctly. Don't know if the normal Atlantic City "en prison" rule is in effect. If so, it should be one of the first "table machines" to have a very low house percentage, correct? Thanks for any explanation you can offer. I did enjoy playing it, but the wheel is way too high up and you have a crick in your neck after about 15 minutes.

I hope you have an answer for me. I enjoyed the machines but not as much as being involved in a "real" roulette table environment. But if the percentage is cut in half with the single zero it would be worth switching. There is just something about roulette and I tend to gravitate to the table when I'm taking a break from shooting craps.

Thanks,
Suzanne

A single zero Roulette game has 37 outcomes. On even money bets there are 18 ways to win and 19 ways to lose. The house edge is

18/37 - 19/37 = -1/37 = -2.7%

Notice that this is not half of the 5.26% edge on the double zero wheel but is a bit more.

The en prison rule on a single zero game is as follows. It applies only to even money bets. If the ball lands on the zero the player's wager is not lost but remains on the layout (in prison). On the next spin if the ball again lands on the zero the wager remains. Otherwise, if the player's wager is a winner his bet is returned (a push). If it is a loser the player's wager is taken.

With the en prison rule in effect there are 18 winning numbers, 18 losing numbers and one number (the zero) whose expected return is -1/2 (half the time you lose and half the time you push). The expected return is

18/37 - 18/37 - 1/37 x 1/2 = - 1/74 = -1.35%

If this machine is a single zero game with en prison then this is indeed a good game, Suzanne.

I enjoy your letters so keep them coming. 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