Craps Theories

"Hey, John. Do you have a minute?"

I turned back as I was about to descend the stairs and recognized a 40-ish man I'd seen shooting craps as I'd started making my rounds.

I was in no rush.

"I have a theory about craps, and I wanted to know what you think. Two theories, really. The silly one is really my brother's."

And...

"He likes to play all the goofy propositions. You know, he bets the 12 and the Yo (11). Any craps. Any 7."

The casinos must love him.

"Yeah, they comp him pretty good, at that. But his theory is that if he wins one more pass bet than average in a short time, he barely does more than break even. But if there's one extra 12, he makes a nice profit because of the 30-1 payoff."

I don't suppose he's considered that it's a lot easier to win an extra pass bet than it is to make an extra 12. Pass bets win 49.3 percent of the time. One-roll propositions on 12 win only once per 36 rolls, on average. Profitable sessions on the pass line come a lot more often than profitable runs on 12.

"I've tried to tell him that."

There's a flip side, too. Lose one more pass bet than expected in a short time and you have a small loss. If in 36 decisions you lose one more bet on 12 than average, you're left with zero wins and a big loss. In the long run, you'll lose $1.41 per $100 wagered on the pass line, but $13.89 on 12. And since the propositions are decided in one roll, instead of the average of nearly three on the line, your risk is higher on the props.

"I told you it was goofy."

So what about your own theory?

"Well, I've read that the house edge is 1.4 percent on the pass line and 1.5 percent on placing the 6 and 8, right?"

To be a little pedantic, it's 1.41 percent on the line, 1.52 percent on the 6 and 8.

"All right. And other than the 7, the 6 and 8 are the numbers that come most often, right?"

Right. There are 36 possible combinations of two six-sided dice. Six of those total 7, making it the most common number, followed by the five ways to make 6 and the five ways to make 8.

"So on the line, I'll win most often if the point is 6 or 8, right?"

Assuming a point is established on the comeout, yes.

"But to win on one of those numbers, the shooter has to roll it twice before he rolls a 7. He has to roll it on the comeout, then roll it again without a 7.

"So isn't it better to just place the 6 and 8? Then you have the most frequent winners, and the shooter only has to roll it once. Doesn't that make up for that little difference in the house edge?"

No.

"Why not?"

Because with a place bet, there is no comeout roll, and the comeout is the best part of betting the pass line. You win on the comeout, without having to worry about any number coming up twice, if the roll is 7 or 11.

"But you lose on 2, 3 or 12."

True, but there are six ways to roll 7 -- 6-1, 5-2, 4-3, 3-4, 2-5, and 1-6. And there are two ways to roll 11 -- 6-5 and 5-6. But there is only one way to roll 2 -- 1-1; one way to roll 12 -- 6-6, and two ways to roll 3 -- 2-1 and 1-2. So there are eight ways to win on the comeout, and only four ways to lose.

"And that's enough to overcome the problem of having to roll a number twice?"

Sure. The pass bet is going to be decided on the comeout a third of the time, and on those rolls, you're going to win twice as often as you lose. That's an awfully powerful advantage.

Think of the pass bet as two wagers in one. First, you're wagering on the comeout, where you win twice as often as you lose. If a point number rolls instead, your bet stays on the table, and what you're left with is similar to a place bet -- a little better because you can back it with free odds. At the point the pass bet becomes like a place bet, the shooter has already rolled the number once and needs roll it just once more to win.

So you have a two-part bet: the comeout, on which you have a big edge, and a potential place bet. If you could bet the portion on which you have the edge separately, wouldn't you do it?

"I guess I would. So you're saying always to bet the line instead of placing the numbers?"

No. The house edge when placing 6 and 8 is small enough to be acceptable to a player who wants to be certain of having the most frequently rolled numbers. There's no way to assure that on the pass line. But in the long run, pass bets will lose $1.41 per $100 wagered, while place bets on 6 and 8 will drop $1.52 per $100.

"Well, I still like my theory."

You pay your money and you take your choice.

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