Oct

25

2016

# What Are The Chances of 1-2-3 Sequence in Roulette?

Events that are extreme long shots to you and me are certainties to casino operators.

Given thousands of plays a day, every day, rare outcomes and streaks are inevitable.

Take the roulette streak that prompted a reader to contact me via email.

“I’ve been playing roulette a long time, and I don’t think I ever saw this before,” he wrote. “There was a winner on 1, the next number was 2 and the next was 3. After that, it was something in the 20s, and the streak was broken. What are the chances of a 1-2-3 sequence? How big a stretch would it have been to go 1-2-3-4?”

On an American double-zero wheel, there are 38 numbers – 1 through 36 plus 0 and 00. To calculate the chances of any specific three-number sequence occurring on consecutive spins, you can cube 38.

So the chances of 1-2-3 coming up on consecutive spins would be 1 in 38 x 38 x 38, or 1 in 54,872.

That’s a big number, but not so big that it doesn’t happen pretty often. There are more than 1,000 casinos in the U.S. Not all have roulette, but even so, a 1-2-3 sequence happens somewhere just about every day.

Make it a 1-2-3-4 sequence, and the chances are more remote at 1 in 2,085,136, though even at that level it happens somewhere in the U.S. a few times a year.

There’s another way to look at the problem. What if the 1-2-3 sequence already has occurred, as it did at the casino where you were playing? How likely is it that the next number will be a 4, for a 1-2-3-4 sequence?

At that point, it’s a 1 in 38 chance. The odds of any given number occurring on any spin are 1 in 38. Before the sequence began, 1-2-3-4 was beyond a 1-in-2 million shot, but once the heavy lifting had been done and 1-2-3 was in the books, it was down to 1 in 38.