A Roulette Story

It was a Friday morning, and I was wandering through the new barge at Hollywood Casino in Aurora, Illinois, checking out the games. A white-haired gentleman introduced himself as Phil, and said we'd met before.

"I learned to play roulette at a seminar you gave a few years ago," he said. "I still play slots, but I like to get a little roulette in whenever I'm here.

"I'm glad I ran into you. I have a question. I was looking at the board at the roulette table, and three times in the last 12 spins, the number was 2. There also was a 1 and a 3."

I asked if he was betting on 2.

"I hadn't been, and then I couldn't decide," he replied. "I thought maybe 2 had come up a little too often, that maybe other numbers were overdue and there might be a dry spell on 2. Then again, with the 1 and the 3, that meant five of the last 12 numbers had been low ones, in the first row. I thought maybe it was a trend, that it would keep hitting the low numbers."

So what did you do?

"I decided to bet the street--1, 2 and 3. I stuck with it for about 10 spins, and none of them came up. So I went back to my usual numbers and then--wouldn't you know it?--another 2 came up.

"What do you think? Would you have bet the street, because the low numbers were hot, or stayed away because the 2 had come up so much already?"

Neither one.

"Neither one?"

To start with, a number that has been hitting frequently doesn't have to have a cold streak to "make up" on the odds of the game. Every trial is a fresh start. Even if 2 hit three times in a row, the odds of it coming up again on the next spin remain 1 in 38, the same as any other number. Never disregard a number because it's been "too hot." There's nothing in the game or the odds that would force it to turn cold.

Now then, the likelihood is that the cluster of low numbers was pure chance. Unless you've happened upon a biased wheel, past results have no value in predicting future results.

"What's a biased wheel?"

A wheel with an irregularity--a balance problem, or a slight path worn into the wheel, or frets between numbers a fraction too tall or short--that would cause some numbers to occur more often than by random chance.

"So it's possible that the wheel was biased in favor of low numbers, and I should have kept betting the street, right?"

Not quite. You have to understand that a dozen spins is nowhere near long enough to indicate a wheel bias. Truly biased wheels are not common, and finding one takes painstaking work, tracking results on a suspect wheel over thousands of spins.

That being said, it can be fun, and not at all harmful, to bet on numbers that have come up frequently on the off chance that the wheel is truly biased. It's probably not, but the worst that can happen if you bet as if it is biased is that you face the same 5.26 percent house edge as any other roulette player.

"So betting on 1, 2 and 3 wasn't such a bad strategy, even though it probably wouldn't give me an edge."

I'd have thrown out the 1 and the 3, and concentrated on the 2.

"Why? With five of the last 12 numbers, wouldn't the possibility of a low-number bias be stronger than just the 2?"

No, and for the reason, you need to look at the wheel itself and ignore where the numbers fall on the table layout.

On the wheel, there is no particularly close relationship among the numbers 1, 2 and 3. The 2 is on the opposite side of the wheel from the 1, and the 3 is four spaces away from the 1, and 15 spaces away from the 2.

There is nothing that would cause the ball to land on 2 more often than expected that would also cause a bias in favor of the numbers 1 and 3.

"Do you think single-number bets on 2 are the way to go in that situation?"

As part of a package, maybe. I'm not an all-or-nothing guy in roulette. Maybe I'd add 2 to my regular pattern of bets for a while. I'd also be on the lookout to see if the numbers that surround 2 on the wheel come up while the streak is fresh.

"And those aren't 1 and 3."

Correct. Next to the 2 on the left is the 0, and one more space to the left is 28. To the right of 2, the next space is 14, and one more space to the right is 35. I might even bet those five numbers as a package for a while--single-number bets on 0, 2, 14, 28 and 35. I might try to balance that with low volatility bets such as red/black or odd/even.

"Do you guarantee a winner that way?"

I laughed, and told him that I really still expected to face the same house edge as if I played family birthdays. If the same number hits three times in short order, it's fun to see if we can latch onto a longer streak, but finding a real wheel bias is far from as easy as 1-2-3.