Roulette Probability/Statistics

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.