Roulette Probability/Statistics
Original version at http://www.knowyourluck.com/roulette.html
Roulette is a simple game played in most casinos around the world. It contains a fixed set of probabilities with no real skill required to play the game.
There a two styles a roulette tables, one with a single zero and the other with two zero. We will examine the probabily of both tables.
Single Zero Roulette Table
There are a total of 37 different possible outcomes and each outcome is independant of the previous one.
| Aim | Successful | Not Successful |
| Single Number | 2.70%
(1/37) | 97.30%
(36/37) |
| Two Numbers | 5.41%
(2/37) | 94.59%
(35/37) |
Three Numbers
A Row | 8.11%
(3/37) | 91.89%
(34/37) |
| Four Numbers | 10.81%
(4/37) | 89.19%
(33/37) |
Six Numbers
Two Rows | 16.22%
(6/37) | 83.78%
(31/37) |
Nine Numbers
Three Rows | 24.32%
(9/37) | 75.68%
(28/37) |
Twelve Numbers
Four Rows
A Column
A Third | 32.43%
(12/37) | 67.57%
(25/37) |
Eighteen Numbers
Black or Red
Even or Odd
High or Low | 48.65%
(18/37) | 51.35%
(19/37) |
Double Zero Roulette Table
There are a total of 38 different possible outcomes and each outcome is independant of the previous one.
| Aim | Successful | Not Successful |
| Single Number | 2.63%
(1/38) | 97.37%
(37/38) |
| Two Numbers | 5.26%
(2/38) | 94.74%
(36/38) |
Three Numbers
A Row | 7.89%
(3/38) | 92.11%
(35/38) |
| Four Numbers | 10.53%
(4/38) | 89.47%
(34/38) |
Six Numbers
Two Rows | 15.79%
(6/38) | 84.21%
(32/38) |
Nine Numbers
Three Rows | 23.68%
(9/38) | 76.32%
(29/38) |
Twelve Numbers
Four Rows
A Column
A Third | 31.58%
(12/38) | 68.42%
(26/38) |
Eighteen Numbers
Black or Red
Even or Odd
High or Low | 47.37%
(18/38) | 52.63%
(20/38) |
How Casinos Make Their Money
Simply put, a casino makes its money by paying you back a value less than your true probability of winning is.
As an example if you bet on a single number your chances of winning is 1 in 37 or 1 in 38 (depending on the table). However the casino will only pay out to you
35 to 1 or 36 to 1.
A second example would be if you placed a $10 bet on red and win the casino will give back to you $20. However the probably of a red appearing is
18 in 37 or 18 in 38 (again depending on the table) which means to provide a fair payout for your bet you should have been paid approximately $20.56 or $21.11 respectively.
By payout out less than what the true odds dictate, the casino obtains the favourable monetary balance.