Getting the edge at craps

9 July 2017

By John Grochowski

Last week, I mentioned that a number of readers had e-mailed recently asking for details on how the house gets its edge on various games. In response, I explored some of the arithmetic behind roulette.

This week, let’s focus on craps, which long has been the second-most-popular table game in American casinos, behind only blackjack. It has some of the best bets in the casino and some of the worst,

There are dozens of possible bets at the craps table. One of them, the free odds that you can take when you be pass or come or lay when you bet don’t pass or don’t come, carries no house edge. All of the other potential wagers pay at less than true odds.

Take the single-roll bet on 12. There are 36 possible combinations of two six-sided dice. Only one of them totals 12 – a 6 on each die.

That makes the true odds of rolling 12 35-1, but the usual payoff is 30-1. If you bet $1 on each of 36 rolls and 12 came up once, you would keep that $1 bet and get $30 in winnings for a total of $31. The house would keep the other $5, leaving a house edge of $5/$36, or 13.89%.

Some casinos pay 30-for-1, which is the same as 29-to-1. With that payoff, you have $30 total for your one win, and the house edge is 16.67%.

Some wagers are more complex because they involve multiple rolls. A place bet on 6, for example, could go several rolls before it’s decided. You win if the shooter rolls a 6 and lose if he rolls a 7. No other rolls matter.

Of those 36 possible rolls in craps, six total 7 and five total 6. That makes the true odds of winning the bet 6-5. The house pays 7-6, provided you bet in multiples of $6. If you bet $6 at a time on a streak of 11 decisions that include six 7s and five 6s, you risk $66. On each of the five winners, you keep the $6 wager and get $7 in winnings for a total of $13 per win and $65 for all five.

Since you risk $66 and have $65 at the end of the trial, that mere $1 difference is the house edge, and that comes to 1.52%.

So it goes through nearly all craps bets. The math is more involved with pass, don’t pass, come and don’t come, but the basics remain in place: The house takes an edge by paying less than true odds.

The exception is the free odds bet, which pays at true odds. If the point number is 6, where there are six ways to lose and five ways to win, the true odds are 6-5 against rolling a 6 before the next 7. If you’re on the pass or come side, your free odds bet pays 6-5. If you’re on the don’t pass/don’t come side, betting the 7 will come first, you lay 5-6 odds, betting $6 for the chance to win $5.

Either way, since the bet pays at true odds, there is no house edge. However, in order to make the free odds bet, you must first bet pass or don’t pass, come or don’t come, so you always have a wager with a house edge at risk.

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