This article is about roulette wheels, but first let’s take a step back. One of my earlier blog postings was about dart boards. Where is the best place to aim on a dart board? This is not a trivial question because a dart board is cleverly designed. On a dart board, high scoring regions are located adjacent to low scoring regions. If you manage to hit a high scoring segment, great, but if you miss, you are penalized heavily. Other regions have lots of medium scoring regions as close neighbours. Maybe it is better to aim for one of these middling areas? You’re not going to hit big scores, but you are not going to get low scores either.
It depends on how skilful you are. You’ll hit these most of the time, and maximize your expected score. At the other end of the scale, if you are a really bad player, you should just aim for the bullseye at the center of the board. For you, getting any score from your dart is a win! Just hitting the board is an achievement! If you are interested in learning more, I encourage you to read my earlier article. Roulette Wheel We can see that there’s logic to the arrangement of scores around a dart board. Why then, are the numbers in a roulette wheel arranged in a pseudo-random way? It’s not as if a roulette player has any input as to where the balls lands. Why not place all the numbers in numeric order and be done with it?
Why not just label them ordinally? Before we attempt to answer this, first let’s take a look at how they happen to be arranged. American and European The name ‘roulette’ comes from the French, and the name means ‘small wheel’. There is some indication that the invetor of the wheel was none other than the mathematician Blaise Pascal. You cannot beat a roulette table unless you steal money from it. There are two major styles of roulette wheel in use: European and American. A European wheel has 37 pockets into which the ball can land. These are numbered 1-36, plus one numbered zero. The non-zero numbers are half red, and half black. Here is the ordering on an American wheel.
Here is what the two wheel variants look like. The European, with the single zero, is shown on the left. The American, with the a double zero, on the right. On both wheels, if you sum up the values of all the numbers on the wheel you get the total 666. The only place this does not happens is where 5 is next to 10. The distribution of red and black varies. On an American wheel, numbers opposite each other differ by just one.
The numbers alternate red black on the American wheel up until the two zero pockets. There is the same color pocket on each side of a zero. Here are the distributions in graph form. This is how these data look as radar plots. In the diagrams below, the radius shows the value of the pocket at that location. The plot of the American wheel looks a little more structured. With no bias or favouritism for any pocket, the ordering of pockets should not be important. We come to the conclusion that the ordering is therefore psychological in nature.