Exploring the Probability of Roulette

And then there is probability, without which a player can’t fully appreciate roulette’s geometries and idiosyncrasies – or calculate the expected value of a bet. Probability distils complex ratios of risk to reward into a single number.

Opportunities to witness 30 red-black, or odd-even misses in a row are very, very slim; players and spectators will better understand when to bet (and cut their losses) if they are cognisant of this.


On its side, today’s gambler loves to spread the word about remarkable success and fabulous failures at the roulette table, but its origins are lost in time.

Hippodrome accounts from Constantinople attest to the game’s existence (via an Arab feminine variant called ‘al-fleh’), and its extensive whispers across the Orient tell the tale of its origins: one theory goes that Roulette was modeled on an ancient Tibetan board game. In this game, players picked and arranged 37 animal figurines that must total 666.

American gamblers began to take to this European favourite, and by the turn of the century it established a foothold here, and its popularity would last until the Second World War, which in turn displaced it with craps and blackjack.


On the opposite side, you find casino games that require lots of experience, in a way that you cannot just “jump in” and expect to enjoy them – or at least enjoy them well. Roulette is a perfect example of an easy game, arguably the easiest casino game of them all. I would say that all levels of players can count on it to have fun and learn something new while losing or winning money. Since roulette is mainly a game of chance, there are no new strategies or betting approaches that can influence the outcome in any way. Still, seemingly inexperienced players can focus on some sort of betting strategy (like Martingale, D’Alembert) to feel they can control the bankroll and potentially increase their winning chances.

Roulette also offers other bets, known as outside bets and inside bets, with a lower edge but a higher house cut; inside bets pay off less often, but with a higher return on your investment, while outside bets have a lower payout but they come with less risk. à Betting-system purveyors are one of the oldest hustles in the world, and they’re still peddling their wares Despite the apparent structural logic of the house edge, novice gamblers may experience an emotional letdown as their money is siphoned away.


Roulette is a maths game. If you play on an American double-zero wheel, which has compartments numbered 1 through 36, plus 0 and 00, then player odds are based on the chances those players have of seeing their number appear on the wheel.

This could be more common than previously thought: gamblers are trying to beat the house edge through betting systems that aim to control their bankrolls. However, such strategies are likely to be negated by further extreme results arising from the spinning of the wheel.

Outside bets tend to offer smaller returns, but win more often. And repeating numbers or sectors are almost certainly pure coincidence, and not an indication that the wheel has been tampered with.


Roulette odds are an important element in reckoning whether or not a player will win his wager. They are obtained by calculation, in the proceeding manner: one adds up the figures of negative cases, followed by division of the sum by positive ones, and states the result as a ratio or fraction, e.g. straight bets have a ratio of 35:1.

While an awareness of probability will help you to devise a good roulette system, keeping in mind that each turn of the wheel is also subject to luck is just as important for you to play successfully. Being aware of this teeter-totter effect, and how it impacts each spin of the wheel, will help you to make better decisions at the table, just as a basic grasp of probability will prevent costly mistakes that can be made by mistakenly assuming that our calculus of chance bears some fixed relation to the real world.


In roulette, there are many options for betting. ‘Inside bets’ betting on one number, and ‘outside bets’ betting on groups of numbers such as red or black numbers, odd/even numbers, high/low odds pay out differently.

You have 18/37 chances of winning that bet, assuming it was red. In fractional probability or ratio odds, roulette probability is capture; but neither by itself offer the complete picture, which also entails total return or payout odds.


Roulette is one of the oldest games in casinos, even up to this day, it is widely popular. The main element of roulette is luck, and luck rules over each spin; however, over the long term, it is probabilities that determine results. Understanding the impact of probabilities can help players to come up with a good winning strategy.

Whether you’re playing for fun or trying to make money, play responsibly. Know the odds on different bets before placing them, and make a profit target for yourself.

A common betting system used for gambling on roulette is that of the Martingale, in which you double your bet after each loss – it works quite well if applied correctly.

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