A craps player wrote to me recently to say he’d found an automated game that looked like it had better odds than he found at table games.
“Instead of 30-1 on 2 or 12, it pays 31-1 and instead of 15-1 on 3 or 11 it pays 16-1,” he wrote. “Hardways pay 10-1 and 8-1 instead of 9-1 and 7-1.”
I told him he needed to check the machine again. It was likely the machine was paying odds-for-1 instead of odds-to-1, and that the payoffs he was seeing were just normal returns expressed in a different way.
It’s common for machine games to pay odds-for-1 because the game has already taken your bet before the roll takes place.
On a table that pays 30-1, if you win your bet on 12, you keep your 1-unit bet and get 30 units in winnings, for a total of 31. On a machine that pays 31-for-1, the machine keeps your bet when you make it, but pays 31 units on a win — still a total of 31 on your side after a win.
So 31-for-1 is the same as 30-to-1, 16-for-1 is the same as 15-to-1, 10-for-1 is the same as 9-to-1, and so on.
What if the game really was paying 31-1 on 12, and not 31-for-1?
With the standard 30-1 you’d get at most craps tables, bets on 2, 12 or hard hop bets give the house a 13.89 percent edge. If the payoff is 31-1, the edge drops only to 11.11 percent. True odds are 35-1, so there’s a long way to go from 30-1 before these become viable bets.
What about the hardway payoffs the reader described?
When your payoff is 9-1 on hard 6 or 8, the house edge is 9.09 percent, and when you’re paid 7-1 on hard 4 or 10, the house edge is 11.1 percent.
If the pays were increased to 10-1 and 8-1. they’d match the true odds of winning these bets. The house edge would be zero.
That reinforces the likelihood the game is paying in odds-for-1. Any time the odds paid on a machine version of a table game look higher than the table version, check to see if the payoffs are for-1.
