Winning big at roulette

29 July 2018

By John Grochowski

When my longtime Jim and I get together, talk usually centers on family, kids and a lot of baseball.

Gambling rarely comes up. Jim doesn't play much, and when he does, it's Hold'em if the casino has a poker room and blackjack if it doesn't.

Imagine my surprise at our June lunch outing when Jim wanted to talk roulette.

"I'd been reading about Charles Wells, the man who broke the bank at Monte Carlo in the 1890s, and I got curious," Jim said. "He supposedly won 23 of 30 spins, and no one's sure if he was cheating, found a biased wheel or was just really lucky.

"I looked for other incidents, and found Joseph Jagger, who found a biased wheel in Monte Carlo in the 1870s. Pretty much all of the other big wins I could find were one spin, short-term things you can put down to luck.

"Longer streaks all seem to be in Europe, especially Monte Carlo. I couldn't find any in the United States. Any idea why?"

I told Jim some long streaks may have been for small enough money they didn't catch anyone's attention. Players who have found a biased wheel may have kept sessions short but frequent to avoid alerting operators. Besides, casinos are well aware of the dangers of wheel bias and take pains to properly maintain equipment.

Plus, the nature of the single-zero European game makes winning streaks more likely than in the American double-zero game.

We can see how that works with a little arithmetic, using single-number bets as an easy example.

Regardless of whether a single zero or double zero is used, winning single-number bets are paid at 35-1 odds. But the American wheel has 38 numbers, including 0 and 00, making the true odds 37-1, while the European wheel has only 37 numbers, making the true odds 36-1.

Imagine you've found a wheel with a bias that makes the number 17 more likely to come up than the usual odds would suggest. Perhaps a nearly invisible track has been worn down the wheel surface, or the frets are a hair higher or lower, or looser or tighter than on other numbers.

How much more often than average would 17 have to come up to make it profitable for players?

On either a single-zero or double-zero wheel, the break-even point would come when 17 came up an average of once per 36 spins. Then, in an average 36 spins in which you bet $1 per spin, you'd bet a total of $36. You'd win once, keep your $1 bet and get $35 in winnings for a total of $36 — you'd have just as much money at the end of the trial at the beginning.

If 17 came up more often than once per 36 spins, it would be a profitable number for players. Less than once per 36, it remains profitable for the house.

Averaging one hit per 36 spins means 17 is the number on 2.78% of spins. Without a bias, 17 would show up once per 38 spins, or 2.63%, on an American wheel, or once per 37 spins, or 2.70%, on an European wheel.

It takes less of a gain via bias to get to the breakeven point and beyond on a single-zero wheel than on a double-zero wheel. That's true of every available bet — splits, streets, corners, all of them.

That's not to say bias-based streaks can't happen here. They can, if casinos don't take proper care. But a smaller, less noticeable bias can take you farther on a single-zero wheel.

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