Roulette volatility

21 April 2016

By John Grochowski

A reader named Bill contacted me to ask about betting options at roulette.

“Everything I read tells me the house has the same edge no matter what bet you make,” he wrote. “So if all bets are created equal, why have all those different bets?”

The house edge is the same, 5.26% on all bets but one on a double-zero wheel, with the exception being the five-number bet on 0, 00, 1, 2 and 3.

That’s not the same as saying all bets are created equal. The difference comes in volatility.

Spreading your bets out over many numbers gives you many chances to win on a given spin, but each win will bring a relatively low return. Concentrating more of your wagers in fewer numbers gives you a larger potential payback, but it gives you fewer chances to win.

Let’s take an extreme situation and say you and I are at a $5 minimum table and I choose to focus my full $5 per spin on a single number. You bet your $5 on black.

Per 38 spins, you and I each wager $190. On the average, my single number will come up once and the other 37 spins will be the other numbers. On my one win, I get a 35-1 payback. That’s $175 in winnings plus I keep my $5 bet on the winner, so at the end of the 38 spins I have $180.

With average results, you’ll win 18 times on black. On each, you win $5 and keep your $5 wager, so you also have $180 at the end of the trial.

The house has kept $10 of my money and $10 of your money. We’ve both faced the same house edge.

However, not every trial will bring average results. Sometimes we win more than expected; sometimes we lose more. If things didn’t work that way, there would never be the winning days that keep us coming back. Nobody would play.

What if we each have one more winner than expected? Then I pick up another 35-1 single-number winner, and have $360 at the end – a $170 profit. You pick up another 1-1 winner on black, and have $190 after 38 spins – you break even.

What if we each have one more loser than expected? Then I have no winners. I lose my whole $190. You still have 17 winners, and have $170 of your original $190.

Betting on single numbers, it takes only a small deviation from the norm to turn me into a big winner, while your bets on black would need 36 winners in 38 spins to turn the same profit I get with two single numbers.

However, I’m busted with just one fewer win than usual. You would need 18 fewer wins than normal to go bust.

Single-numbers are high-volatility bets, and black is a low-volatility bet. There’s a continuum of high to low volatility throughout the roulette layout, both on inside bets and outside bets. A two-number split has high volatility, but not as high as single numbers and higher than three-number streets, four-number corners and six-number double streets.

Twelve-number bets such as dozens and columns have low volatility, but not as low as 18-number red, black, odd, even, first 18 or last 18.

To maximize chances of winning big, focus on bets with fewer numbers, but recognize that also maximizes chances of losing fast. To extend playing time with minimum chances of losing fast but also minimum chances of winning big, bet more numbers at a time.

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