The odds at craps is a great bet

7 February 2013

By John Grochowski

Craps players have long known that the combination of a pass line bet backed by free odds is one of the best bets in the casino. The pass line alone is no slouch, with a 1.41% house edge. But the free odds themselves have no house edge, so the overall edge on the pass-odds combo drops to 0.8% with single odds, 0.6% with double odds, 0.3% at 5x odds, 0.2% at 10x odds and 0.02% at 100x odds.

The entire edge on the combo is attributable to the line bet, and that edge can never disappear entirely. Per $1,000 in pass line wagers, the house expects to keep $14.10. It expects to keep that same $14.10 if those pass bets are backed by $1,000, $10,000, $100,000 or any other amount in free odds.

So if the free odds can’t move that piece of the bottom line, what do they do for you?

One obvious thing is that they lead to much bigger wins when the shooter is hot. Free odds are paid at true odds, and the wins add up with those 6-5 payoffs when the point is 6 or 8, 3-2 on 5 or 9, and 2-1 on 4 or 10. And there’s a huge benefit in keeping your line bet to the minimum and putting the larger part of your wager in the no-edge odds.

Perhaps less obvious is that winning sessions are more frequent with free odds than without. Let’s set up an example using $10 pass wagers without odds, and with 10x odds.

Just so I have a whole number of each possible point, I’m going to 55 sets of 36 trials. In each set of 36, there will be six come-out winner 7s, two winner 11s, one loser 12, one loser 2 and two loser 3s, for a total of 440 winner 7s or 11s and 220 loser craps numbers. As for the point numbers, each set will have five each of 6 and 8, four each of 5 and 9 and three each of 4 or 10. That leaves 275 each of 6 or 8, 220 each of 5 or 9 and 165 each of 4 or 10.

Betting $10 on each trial leaves a total risk of $19,800. On the come-out winners, you keep your $4,400 risked and win another $4400, while on the losers you have $2,200. That leaves 1,320 trials with a point number, and there have $13,200 riding.

On the 6s, you’ll win 125 of the 275 trials and lose 150. Same deal on the 8s. On each of 5 and 9, you win 88 times and lose 132. And on each of 4 and 10, you win 55 and lose 110.

Overall, you win 536 times and lose 784. On the 536 winners, you get back your $5,360 in wagers and add $5,360 in winnings, for a total of $10,720. Add that to the come-out winners, and you have $19,520 of your original stake, and the house has $280 -- the 1.41% house edge.

To get back to your full $1,980, you’d need 14 more winners than the normal expectation.

What if you’re backing your pass wagers with 10x odds? They come into effect only after a point has been established, so they add $132,000 to your total risk, bringing it to $151,800. If the results come up in average proportions, you break even on the odds, and your average loss is the same $280 as when betting only the pass line.

Each free odds bet here is $100, and winners bring $120 on 6 or 8, $150 on 5 or 9 and $200 on 4 or 10. So including keeping your odds wager, each win swings the bottom line by $220, $250 or $300.

What that means is that with 10x odds, it takes only a single extra win to overcome that $280 pass-line loss if the extra win is a 4 or 10, or two extra wins if it’s any other point number.

There’s a downside, of course. In a cold streak, the pass-only bettor loses $10 per extra loss, while the odds bettor loses that, plus an additional $100 with 10x odds. The losses can get very large, very fast.

But when it takes only one or two extra wins instead of 14 to swing the bottom line from a $280 loss to break-even or better, winning sessions are going to be more frequent.

That’s not a reason to over-bet your bankroll. If you can’t bet the odds without using money you can’t afford to lose, then skip ’em. But for those sufficiently bankrolled, win frequency is one more reason to keep line bets to the minimum and shift the bulk of your wager into the odds.


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