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 long-term 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 casino’s 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, you’ve 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 you’ll 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 house’s 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 Jagger, 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 1990’s, Gonzalo Garcia-Pelayo, 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.
In 2004, it was reported that a group in London had used mobile cameraphones to predict the path of the ball, a cheating technique called sector targeting.  In December 2004 court adjudged that they didn’t cheat because their special laser cameraphone and microchip weren’t influencing the ball – they kept all £1.3m. 
Betting Only on Red
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 an 83% probability that in 38 spins, the ball will land on red at least 15 times. Out of 38 spins, there’s a 50% chance that 18 will be red.
However, the break-even 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.
Betting multiple times
This type of bet is a combination of the red bet and the martingale system. Except this bet also includes the odd. What you do is you start off with a bet of 1 on each the red and the odd (or you can do the black and even). You treat each bet seperately. When one bet loses, you double it. When one bet wins, you set it back to 1. The reason that this technique keeps you in the game so long is that there is a 25% chance of you winning both the red and the odd and theres a 50% chance that you will break even. Of course in order for this method to last, you would need an unlimited source of money.
- In 2004, Ashley Revell of London sold all of his possessions, clothing included, and brought US$135,300 to the Plaza Hotel in Las Vegas and put it all on “Red” at the roulette table in a double-or-nothing bet. The ball landed on “Red 7” and Revell walked away with his net-worth doubled to $270,600.
- In the 1942 film Casablanca, Rick’s Café Americain has a trick roulette wheel. The croupier can cause it to land on 22 at will. Rick (Humphrey Bogart) urges a Bulgarian refugee with whose case he becomes sympathetic to put his last three chips on 22 and motions to the croupier to let him win. After the man’s number dramatically comes up, Rick tells him to let it all ride on 22 and lets him win again. Although the details are not mentioned in the film (the croupier only notes that they are “a couple of thousand” down), it appears that Rick has given the man 3675 (3*35*35) francs.
- In the music video for Palace & Main by Kent, guitarist Harri Mänty goes to Las Vegas and bets the entire video budget on black. He wins, and the profits were donated to charity.
- In the third part of the 1998 film Run, Lola, Run, Lola uses all her money to buy a 100-mark chip. (She is actually just short of 100 marks, but gains the sympathy of a casino employee who gives her the chip for what money she has.) She bets her single chip on 20 and wins. She lets her winnings ride on 20 and wins again, making her total winnings 100,000 marks.