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# Gaming Guru

### Laying the Odds - Again

1 July 2012

I recently received the following e-mail from one of my readers named Dave Beck.

Don, This question concerns the Don't Pass wager. My numbers are rounded from what I remember.

A Pass Line bet on the Come Out has a 22% chance of winning and an 11% chance of losing.

A Don't Pass bet on the come out must have a 22% chance of losing and barring the twelve around a 9% chance of winning.

So I'm thinking approximately 66% of the time my Don't Pass bet would be alive on a number.

Since the Don't Pass has a lower house advantage, here is my question.

My normal average outlay on Pass Line and Place betting 6 & 8 is \$40.

If I bet the Dark Side and bet the \$40 alone on the Don't Pass instead of \$10 Don't and laying free odds, does the 66% of the time I'm on the point number and actually getting even money on my \$40 Don't Pass negate the 22% loss on the come out?

I know that the numbers say this and that but my personal experience is that the come out sevens and elevens are less than 22%. That's because I haven't played two million Craps games. Rationale is not my strong suit, but laying free odds on the Don't makes me ill.

Well, Dave, your question is a bit cryptic but I think I know what you're driving at and I'll address it shortly. First, a few general remarks about your e-mail.

Your figures of 22% and 11% are only approximations. When you say that your average outlay on the Pass Line and Placing the 6 & 8 is \$40, I'm not sure what you mean. For the benefit of other readers, however, I should point out that place bets on the 6 or 8 must be made in multiples of six units.

I think that before you read this you should go into the archives on this site and read my November 2003 article entitled Laying the Odds; it will make reading this article much easier.

Now let me rephrase your question into what I think you meant. Many players feel that once you are on a number with a Don't Pass bet you have a better than even chance of winning, so why lay odds? Does laying the odds make up for the lousy chance of winning on the Come Out? Yes, it does and here are the details. Your e-mail infers that you are playing at a casino that allows the odds wager to be three times that of the line wager. If the line bet is an even number then the odds wager will be in multiples of six, which is necessary to get integer payouts.

Before I begin let me mention that in the following table I state that the line bet for the twelve is zero. This is because, like my friend and colleague Stewart Ethier, I am firmly in the camp that feels that a tie should not be treated as a resolution of a bet. Doing so can lead to bizarre results. (See my article Mensa Mystery in the archives.) By inserting a zero for the twelve this treats the twelve as a non event.

Suppose now that we roll the dice 1980 times with a \$10 wager on the Don't Pass and \$30 on odds when possible. We then have the following table.

 Event Freq. Line Bet Tot. Line Odds Bet Tot. Odds Line Pay Odds Pay Natural 440 10 4,400 0 0 -4,400 0 2 or 3 165 10 1650 0 0 1,650 0 12 55 0 0 0 0 0 0 4 Made 55 10 550 30 1,650 -550 -1,650 4 Not 110 10 1,100 30 3,300 1,100 1,650 5 Made 88 10 880 30 2,640 -880 -2,640 5 Not 132 10 1,320 30 3,960 1,320 2,640 6 Made 125 10 1,250 30 3,750 -1,250 -3,750 6 Not 150 10 1,500 30 4,500 1,500 3,750 8 Made 125 10 1,250 30 3,750 -1,250 -3,750 8 Not 150 10 1,500 30 4,500 1,500 3,750 9 Made 88 10 880 30 2,640 -880 -2,640 9 Not 132 10 1,320 30 3,960 1,320 2,640 10 Made 55 10 550 30 1,650 -550 -1,650 10 Not 110 10 1,100 30 3,300 1,100 1,650 Totals 1,980 --- 19,250 --- 39,600 -270 0

The total amount at risk is the sum of 19,250 and 39,600, which is 58,850. Dividing this into 270 we get the house advantage at approximately 0.4588%. Had we put all of the \$40 on the Don't Pass, our total loss would have been 1080 and our total at risk would have been 77,700. Dividing 77,700 into 1080 we have an approximate house edge of 1.39%. Dave, I hope this answers your question. See you next month.

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

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Best of Donald Catlin
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