Roulette rules are fairly simple and yet important to know if you plan beating odds. Before I dive into discussion on roulette strategy and how to increase odds into your favor at roulette table I would like to provide some background history on Roulette Game.
It is said that first form of roulette for real money game was created by a french mathematician Blaise Pascal in 17 th century. Rumor is that creation was result of his fascination with perpetual motion devices. As everything else Game of Roulette was modified in 1842 by frenchmen Francois and Louis Blank. They have added numerical 0 to roulette wheel to increase house odds. US got its introduction to roulette in 1800s and another modification taken place, 00 was added to the wheel to even further increase house odds. This double 0 is something that is normally found in American Roulette and generally not present in European games. Roulette Game is one of the most known casino games and was brought to fame by many famous writers, including Russian Feodor Dostoevskiy.
Roulette is a straight forward game and roulette rules are simple. A croupier is responsible for turning roulette wheel, which has 37 or 38 numbered pockets. As wheel spins a ball will land into one of these pockets, which are numbered from 1 to 36 and each number has a color that alternates between red and black. Number 1 is always a red color and all roulette wheels have a green pocket numbered 0, US based casinos also have a second green pocket marked with numeric 00.
Players have option to make bets on numbers, colors, number combinations, number ranges and odd/evens. If bet is placed on a single number and that number wins – payout is equal 35 to 1. So the bet on a winning number is returned and gets multiplied by 36. Essentially a winning number bet has a prize that is equal 36 times the cost of the bet itself. Pretty good returns, wouldn’t you say? European and American roulette tables have different odds due to an additional 00 pocket. House advantage of European roulette is 2.7% while American Roulette has a house advantage of 5.3%
As in every casino game, knowing your odds and basic strategies will only help you make more a more educated decision on play and calculate you winning chances. For your convenience I have placed a Board Depiction and Bet Odds table for American Roulette. Original materials for the tables and strategy bellow are found on wikipedia.
↔ 
00 

1 
1st 
1 
2 
3 
← 
4 
5 
6 
← 

odd 
7 
8 
9 
← 

10 
11 
12 
← 

red 
2nd 
13 
14 
15 
← 
16 
17 
18 
← 

blk 
19 
20 
21 
← 

22 
23 
24 
← 

even 
3rd 
25 
26 
27 
← 
28 
29 
30 
← 

19 
31 
32 
33 
← 

34 
35 
36 
← 

↑ 
↑ 
↑ 
Bet name  Winning spaces  Payout  Odds of winning (against) 
Expected value (on a $1 bet) 

35 to 1 
37 to 1 
$0.053 

00 
00 
35 to 1 
37 to 1 
$0.053 
1 
1 
35 to 1 
37 to 1 
$0.053 
2 
2 
35 to 1 
37 to 1 
$0.053 
36 
36 
35 to 1 
37 to 1 
$0.053 
Row 00 
0, 00 
17 to 1 
18 to 1 
$0.053 
Row 3 
1, 2, 3 
11 to 1 
11.667 to 1 
$0.053 
Row 6 
4, 5, 6 
11 to 1 
11.667 to 1 
$0.053 
Row 9 
7, 8, 9 
11 to 1 
11.667 to 1 
$0.053 
Row 36 
34, 35, 36 
11 to 1 
11.667 to 1 
$0.053 
Column 1 
1, 4, 7, , 34 
2 to 1 
2.167 to 1 
$0.053 
Column 2 
2, 5, 8, , 35 
2 to 1 
2.167 to 1 
$0.053 
Column 3 
3, 6, 9, , 36 
2 to 1 
2.167 to 1 
$0.053 
First 12 
1, 2, 3, , 12 
2 to 1 
2.167 to 1 
$0.053 
Middle 12 
13, 14, 15, , 24 
2 to 1 
2.167 to 1 
$0.053 
Last 12 
25, 26, 27, , 36 
2 to 1 
2.167 to 1 
$0.053 
Odd 
1, 3, 5, , 35 
1 to 1 
1.111 to 1 
$0.053 
Even 
2, 4, 6, , 36 
1 to 1 
1.111 to 1 
$0.053 
Red 
1, 3, 5, 7, 9, 12, 
1 to 1 
1.111 to 1 
$0.053 
Black 
2, 4, 6, 8, 10, 11, 
1 to 1 
1.111 to 1 
$0.053 
1 to 18 
1, 2, 3, , 18 
1 to 1 
1.111 to 1 
$0.053 
19 to 36 
19, 20, 21, , 36 
1 to 1 
1.111 to 1 
$0.053 
five number bet 
0, 00, 1, 2, 3 
6 to 1 
6.6 to 1 
$0.079 
Note also that 0 and 00 are neither odd nor even in this game.
The house average or house edge is what is lost on average relative to the bet. If a player bets on a single number in the American game there is a probability of 1/38 that the player gets 36 times the bet (including the return), so they end up having on average 36/38=0.9474 times the bet. Thus the house average for American roulette is 1/19 (5.26%); the same applies for the other kinds of bets, except for the five number bet where it is greater than 7%. The house average is approximately halved in the European game.
Albert Einstein is reputed to have stated, You cannot beat a roulette table unless you steal money from it.
And yet, the numerous even money bets in roulette have inspired many players over the years to attempt to beat the game by using one or more variations of a Martingale betting strategy, wherein the gamer doubles the bet after every loss, so that the first win would recover all previous losses, plus win a profit equal to the original bet. As the referenced article on Martingales points out, this betting strategy is fundamentally flawed in practice and the inevitable longterm consequence is a large financial loss. There is no way such a betting strategy can work over the long term. Another strategy is the Fibonacci system, where bets are calculated according to the Fibonacci sequence. Regardless of the specific progression, no such strategy can ever overcome the casinos advantage; players trying them will inevitably lose sooner or later.
While not a strategy to win money, New York Times editor Andres Martinez described an enjoyable roulette betting method in his book on Las Vegas entitled 24/7. He called it the dopey experiment. The idea is to divide your roulette session bankroll into 35 units. This unit is bet on a particular number for 35 consecutive spins. Thus, if the number hits in that time, youve won back your original bankroll and can play subsequent spins with house money. If your number never hits well, it can take a great deal of time to spin the wheel 35 times; think of the fun youll have in that time! In practice, this dopey experiment often results in funny looks from the dealer at first; soon, however, every gambler at the table will be putting money on your number. This turns roulette into a group activity that can rival craps for cheers when the number hits. However, there is only a (1 − (37 / 38)35) * 100% = 60.68% probability of winning within 35 spins (assuming a double zero wheel with 38 pockets).
There is a common misconception that the green numbers are house numbers and that by betting on them one gains the house edge. In fact, it is true that the houses advantage comes from the existence of the green numbers (a game without them would be statistically fair) however they are no more or less likely to come up than any other number.
Various attempts have been made by engineers to overcome the house edge through predicting the mechanical performance of the wheel, most notably by Joseph Jaggers, the man who broke the bank at Monte Carlo in 1873. These schemes work by determining that the ball is more likely to fall at certain numbers. Claude Shannon, a mathematician and computer scientist best known for his contributions to information theory, built arguably the first wearable computer to do so in 1961.
To try to prevent exploits like this, the casinos monitor the performance of their wheels, and rebalance and realign them regularly to try to keep the result of the spins as random as possible.
More recently Thomas Bass, in his book The Newtonian Casino 1991, has claimed to be able to predict wheel performance in real time. He is also the author of The Eudaemonic Pie, which describes the exploits of a group of computer hackers, who called themselves the Eudaemons, who in the late 1970s used computers in their shoes to win at roulette by predicting where the ball would fall.
In the early 1990s, Gonzalo GarciaPelayo, realizing that most roulette wheels are not perfect, used a computer to model the tendencies of the roulette wheels at the Casino de Madrid in Madrid, Spain. Betting the most likely numbers, along with members of his family, he was able to win over one million dollars over a period of several years. A court ruled in his favor when the legality of his strategy was challenged by the casino.
One conceivable strategy would be to bet on the ball landing in a red space for a certain number of spins, for example, 38.
There are 18 red spaces on a roulette table with 38 total spaces. Dividing 18 by 38 yields a probability of landing on red of 47.37%. This probability can be used in a binomial distribution and made into an approximate standard normal distribution.
Doing so indicates that, if one were to spin the wheel 38 times, there is a 99% probability that the ball would land on red at least 10 times. There is a 83% probability that in 38 spins, the ball will land on red at least 15 times. Out of 38 spins, theres a 50% chance that 18 will be red.
However, the breakeven point is 19 spins, since the bet on red is 2:1, and the probability of 19 red spins in 38 is only 37%. This indicates the difficulty of winning by only betting on red.
The results occur because, as indicated by the 18 divided by 38 equals 47.37% figure, the ball will land on red less than half the time. This percentage applied in the binomial and standard normal distributions creates the vast divide in probability from 18 red spins to 19 red spins out of 38 spins. Basically, it is very unlikely for anyone to spin much more than 18 red spins out of 38 spins.