Editing Roulette (section)

===Simplified mathematical model===
For a roulette wheel with <math>n</math> green numbers and 36 other unique numbers, the chance of the ball landing on a given number is <math display="inline">\frac{1}{(36+n)}</math>. For a betting option with <math>p</math> numbers defining a win, the chance of winning a bet is <math display="inline">\frac{p}{(36+n)}</math>

For example, if a player bets on red, there are 18 red numbers, <math>p = 18</math>, so the chance of winning is <math display="inline">\frac{18}{(36+n)}</math>.

The payout given by the casino for a win is based on the roulette wheel having 36 outcomes, and the payout for a bet is given by <math display="inline">\frac{36}{p}</math>.

For example, betting on 1-12 there are 12 numbers that define a win, <math>p = 12</math>, the payout is <math display="inline">\frac{36}{12} = 3</math>, so the bettor wins 3 times their bet.

The average return on a player's bet is given by <math display="inline">\frac{p}{(36+n)} \cdot \frac{36}{p} = \frac{36}{(36+n)}</math>

For <math>n > 0</math>, the average return is always lower than 1, so on average a player will lose money.

With 1 green number, <math>n = 1</math>, the average return is <math display="inline">\frac{36}{37}</math>, that is, after a bet the player will on average have <math display="inline">\frac{36}{37}</math> of their original bet returned to them. With 2 green numbers, <math>n = 2</math>, the average return is <math display="inline">\frac{36}{38}</math>. With 3 green numbers, <math>n = 3</math>, the average return is <math display="inline">\frac{36}{39}</math>.

This shows that the expected return is independent of the choice of bet.