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Roulette Numbers

While the game doesn’t really have such demonic origins, the numerology of roulette is of interest to players to this day. Here’s a quick look at the numbers and patterns underlying this classic casino favourite.

The Numbers on the Wheel

Roulette NumbersLet’s start with the basics: a roulette wheel can have either 37 or 38 numbers on it, depending on the game being played. In European Roulette (which you’ll most often encounter here in Australia), the numbers 1-36 are joined by a single zero (0). American roulette takes those 37 numbers and adds a 38th number, the double zero (00) to the mix.

You’ll often hear that the house gains its edge from the zero (or zeros) on the wheel. This is essentially true, as all of the bets on the table are designed to be fair bets between the casino and the player…if there were only 36 numbers on the wheel. By adding the zeroes, the casino unbalances the scales a bit, giving them an edge. That edge is exactly equal to the number of zeroes divided by the total number of numbers on the wheel: 1/37 in European roulette and 2/38 in American roulette.

The numbers are also tied to various colour pockets during the game. Of the numbers between 1-36, half (18) are coloured red, while the other half are coloured black. In both American and European roulette, the zeroes are coloured green, ensuring that both red and black bets lose when a zero is spun.

The wheel is designed so that all numbers are equally likely to win on any given spin. All pockets are the same size, and — assuming the wheel doesn’t have any bias in it — every number is just as likely to win as any other regardless of what numbers have recently been winning.

Number Patterns

One of the interesting facets of this game is the way in which the numbers are arranged on the wheel. The first thing that is obvious when you look at a wheel in motion is that black and red numbers alternate around the wheel, broken up only by the green zeroes. However, there’s more going on than that.

The way the numbers are distributed around the wheel is designed to provide a high degree of numerical balance. In other words, each section of the wheel has numbers that add up to approximately the same total, regardless of the size of the sections you choose. This is accomplished by pairing numbers together with a single number in between them. These pairs of numbers normally add up to 37 or 39, and include one odd and one even number (you’ll notice that two even numbers usually follow two odd numbers working around the wheel).

There’s also some interest in the way that the red and black numbers are distributed. If you look at the table layout, you’ll notice that red and black numbers usually alternate, but that the pattern of alternation changes a few times throughout the layout. For numbers between one and ten, the odd numbers are red, while the even numbers are black. From 10-18, the red numbers become even, and the black numbers odd. This pattern reverses again from 19-28, and one last time between 29-36. This means that there’s some level of balance of odd/even and red/black, though it isn’t perfect; for instance, there are ten odd reds and only eight even reds, with the opposite distribution for black numbers.

The Law of the Third

There are a number of different bits of trivia about roulette numbers, but our favourite may be “The Law of the Third.” This is a rule that can be very instructive to the probabilities involved in a roulette game — and also an example of how simple mathematics can be used misleadingly to sell systems that don’t really help you win.

Imagine that you were to spin a roulette wheel (European in this case, though this basically works the same with an American wheel) 37 times. We know there are 37 numbers on the wheel, so this is exactly one time for each number. At the end of your 37 spins, how many unique numbers will you have expected to hit during those spins?

Many players assume that the number is 37, or even if they realize there will probably be doubles at some point, they expect the number will be close to that. In reality, there will only be on average 24 different numbers that will hit during a 37-spin period. The math behind this is somewhat complicated, but the concept is simple: the more numbers you spin, the better the chances of hitting one that you’ve already spun earlier in the sequence. The same concept is behind the surprising fact that if you get even a moderately high number of people in the same room, you’ll usually find at least one pair with the same birthday.

While this is interesting, it’s important to note that you can’t use this fact to predict what numbers will come, or which ones are likely to be “double up.” The wheel doesn’t remember which numbers have happened recently in an effort to repeat them; it’s just a mathematical quirk that this will eventually happen. Using “The Law of the Third” to promote a system is another great sign that the person selling it is simply trying to confuse people rather than actually sell them anything useful.