Was that a biased roulette wheel?

6 December 2015

By John Grochowski

QUESTION: I usually play craps, but when I was walking from the table, the roulette wheel caught my eye. The board showed black 31 had come up four times in a row.

I got some chips and started to bet 31 and the numbers around it, 29, 28, 32, 34 and 35. It never came up again while I was there. I won a couple of corner bets when the 28 and 35 came up, but 31 was my only single number.

Good thing it was only a $5 table. I wound up losing $55 and walked away.

Did I play it right? Should I have avoided 31 instead, figuring for the odds to even out, some other numbers had to start rolling?

ANSWER: Assuming the wheel is in balance, the odds in roulette are the same on every spin. Streaks happen, and the same number coming up four times in a row is just part of normal probability. It’s bound to happen once in a while, and you just happened to be there when it did.

If I’d been walking past and seen the four 31s on a board, I’d probably have said, “Cool, four in a row,” kept on walking and forgotten about it. Past results have no impact on future outcome, and there’s no edge to be had by either betting or avoiding the streaking number.

However, if I did play, I’d probably have bet on 31 and surrounding numbers – but not on the numbers that surround it on the layout. Instead, I’d have bet on 18 and 19, which are left and right of 31 on the wheel, and 6 and 8, which are the other numbers adjacent to 18 and 19.

The theory is that if there is a balance problem causing the ball to gravitate toward 31, or if the dealer happens to be in a rhythm that is directing the ball to that area, it could increase the likelihood of the ball landing on the numbers nearest 31 on the wheel. There’s no particular reason for the ball to favor numbers that are close to 31 on the layout, but not on the wheel.

Still, the extreme likelihood is that there is no such wheel bias or dealer rhythm, and the streak happened by chance.


QUESTION: How does having five reels, like on video slots, instead of three reels affect your chance of winning? It seems like the odds would be a lot longer against you with three reels.

ANSWER: If we assume same-sized number sets per reel, than there would be many more possible combinations on a five-reel game. If we assume 100 virtual stops on a mechanical reel, and 100 symbols on video reel, and a single payline, then three reels yield 1 million possible combinations and five reels yield 10 billion.

However, slot games are not all designed with equivalent number sets per reel, and other than a few three-reel machines, games don’t have only one payline. On a five-reel video slot, you’re going to see at least 20 paylines, and you’re more likely to see 30 or 40, and sometimes 100. Alternatively, you might find yourself playing a Reel Power, 243 ways to win game.

The odd also are affected by the number of winning symbols. On some video slots, there are winning two-symbol combinations. On three-reel slots, we see blank spaces that don’t win, while every symbol is a potential winner on five-reel video slots.

There are many, many factors that go into slot odds – slots are the most mathematically complex games in the casino. The number of reels alone tells us nothing about our shot to win.