Triple-zero roulette

Anna was a casual acquaintance in college, a friend of a friend of a friend who I used to run into at the odd party. I was more than a little surprised to receive a message from her via Facebook — and then I saw it was about gambling.

"At a charity casino night, they had a roulette wheel with three zeroes," she wrote. "That's worse odds, right? Could they make a wheel with no zeroes? What would that do to the odds?"

I told her that a wheel with three zeroes does indeed increase the house advantage. On a double-zero wheel of the type you usually see in American casinos, each number is one of 38 — 1 through 36, and the two zeroes. Single-number bets pay 35-1, while true odds are 37-1. That difference between the true odds and the actual payoff gives the house its edge of 5.26%.

Or take single number bets. If you bet on black, you have 18 winning black numbers, and 20 losing numbers — the 18 reds and the two green zeroes. That difference between the 20 losers and 18 winners gives the house its edge of, yep, 5.26%.

Adding another zero to the mix widens the gaps. Now there are 39 numbers, including three zeroes. True odds against winning a single-number bet are now 38-1, the payoff remains 35-1, and the bigger gap yields a house edge of 7.69%.

Betting on black on a triple-zero wheel leaves you with 21 possible losers against your 18 winning numbers, and that wider gap gives the house that same 7.69% edge it would have on single numbers, corners, columns or other bets on such a wheel.

I, too, have come across triple-zero wheels in non-casino roulette games. My advice is to limit losses to an amount you would be willing to donate to the sponsoring charity, and not take the play too seriously.

And while I've never seen a four-zero wheel, I have been told of wheels at street fairs in other countries where the zeroes are augmented by special symbols that act as zeroes. I read once of a wheel in Mexico that had two zeroes and two cactus symbols. You could bet on the zeroes, bet on the cacti, but other bets lost if the ball landed in any of those. That leaves true odds of 39-1, and a house edge of a whopping 10%.

But what about a no-zero wheel, as Anna asked. How would that work?

If no other changes were made, a no-zero wheel would be an even game, with no edge to either house or player. Of course, no one running a game would allow that to happen. The payoffs would have to change.

It'd be easy enough on some bets — a single-number bet that paid 33-1 on a no-zero wheel would give the house a 5.56%. But when you got down to bets that pay even money — red/black, odd/even, first 18/last 18 — you'd be dealing in fractions. The house would have to pay less than a dollar per dollar wagered to keep the game going.

Let's say that a $1 wager on black paid 89 cents on winning bets. In an average 100 bets on a no-zero wheel, you'd risk $100. On the 50 winners, you'd keep your $50 in wagers, plus take a total of $44.50 in winnings. So at the end of those $100 spins, you'd have $94.50. The house would keep $5.50 — a 5.5% edge that's not far off the 5.26% on a double-zero wheel.

It wouldn't be hard to design a no-zero game with something very close to double-zero house edges, but it'd be more trouble than it's worth. You don't want those 89-cent payoffs on winners, and the house doesn't want to make the change.

Payoffs like that would be more feasible on an electronic format, with the player wagering credits and eventually cashing out with a bar-coded ticket to redeem at the cage or kiosk. With live payoffs, the casino would either have to stock the table with pennies, nickels, dimes and quarters to make the odd change above standard casino chips, or put in special orders for chips in odd denominations.

Do casino operators then allow you to use those 89-cent chips at a blackjack or craps table? Not likely.

The payoff issues make it unlikely we'll ever see a 36-number, no-zero roulette wheel as a casino table game. It's far easier on both dealer and players to keep the zeroes and traditional payoffs. You're unlikely ever to see that combo zeroed out.

As for Anna, I told her I was surprised to hear from her after all these years. Her response: "That's YOU? I didn't realize."