Craps Speak

13 December 2020

By John Grochowski

Rick is a craps player I first encountered when I was giving a seminar in the late 1990s. He's kept in occasional touch ever since, contacting me a time or two a year.

In early November, he emailed with an arithmetic question.

"I've always just accepted the listed house edges without really thinking about some of the whys," he wrote. "I buy 4 and 10 because the listed edges are lower than place bets, but place the other numbers because the listed edges go up when buying.

"Lately I've wondered why that should be. When you're placing 6 or 8 and 5 or 9, you're being paid at true odds just like when you buy 4 or 10. The payoffs are better, so why should the house edge be higher?"

The key is the commission you pay the house when you buy a number. Assume a $20 wager. Instead of placing 5 or 9 for $20, it'll cost $21 to buy those numbers, and in most casinos the house will keep the extra $1 regardless of whether you win or lose.

You're paid true odds of 3-2 on 5 or 9 winners instead of the 7-5 return on place bets, but that bigger payoff applies only to your $20 bet and not to the $1 commission.

The result is a 4.76 percent house edge when buying 5 or 9 vs. 4 percent on place bets.

On 6 or 8, when you place in multiples of $6, winners are paid at 7-6 odds and the house edge is 1.52 percent. The closest whole-number bet to our $20 wager above would be $18. If you buy instead, you no longer have to bet in multiples of $6 because you're paid at 6-5 odds.

Assume a $20 wager and a $1 commission. You're still risking $21, but the house keeps the $1 commission and only the $20 portion of your bet is paid at 6-5 odds. The house edge rises to 4.76 percent.

Imagine a series of $18 place bets on 8. You win if the shooter rolls 8, lose on 7.

In an average 11 decisions with total wagers of $198, you'll lose six times and win five. On each win, you'll keep your $18 wager for a total of $90 and get $21 in winnings for another $105.

At the end of the trial, you have $195 of your original $198. The house edge is your $3 loss divided by your $198 investment, multiplied by 100 to convert to percent -- 1.52 percent.

Now imagine you buy the numbers instead, betting $20 and adding a $1 commission. In 11 decisions, you'll risk $231, and the house keeps $11 off the top.

On each of the five wins, you keep your $20 wager and get $24 in winnings, leaving you with $220 of your $231. The house has an $11 profit, or 4.76 percent of your investment.

As long as the house keeps the commission on every bet, the edge on buy bets is 4.76 percent. That's better than the 6.67 on placing 4 or 10 but not as good as the 4 percent on placing 5 or 9 or 1.52 on 6 or 8.

If you find a casino that keeps the commission only on winning bets, then edges drop to 1.67 on 4 or 10 and 2 percent on 5 or 9, making those buys better than places. The edge on 6 or 8 drops to 2.27 on buys, but that's still not as good as the place bets without the cost of commission.

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