Roulette Mathematics

Roulette mathematics – Can math help you win on roulette?

Roulette is a totally random game – at least as far as automated online roulette is concerned – and many players have been studying the game for ages in an effort to find a mathematically correct way to play it, that would guarantee a win and avoid bankruptcy. Let’s have a look at how math can help you win roulette. Or can it?

Choose your game wisely.

The first and the most important aspect of roulette is which game are you actually playing, as they can be very different and offer you a very different chance of winning. American roulette, with its two zeros, is the worst version and it should be avoided whenever possible as it has a house edge of 5.26%. European roulette, with one zero, is the golden standard and it has a house edge of 2.70%, which is tolerable.

There is a version of it called French roulette which has some favorable rules for situations where the ball lands on zero, and this version can have a house edge as low as 1.35% so it’s obvious you should play this version whenever you can. Take a look at all roulette game variations.

By choosing the game wisely, you’re already using math to help you win more, as you do want to play a game that gives you a better chance of winning and will then use that to build on top of it with some betting system or something.

Betting strategies

The way you bet will have a profound effect on the outcome of your playing session. Using flat stakes, betting the same amount with every spin, is the basic way to bet on roulette, and it is a conservative way to play. Betting strategies attempt to boost this to the point where you either win more when you do win or lose less when you do lose.

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No system actually increases the chances of winning, and you might as well put your bet on the same number with every spin and hope the number lands more often than it should. Roulette math is cruel, and it will always, always, give the house a house edge. Any player who tries to tinker with it by choosing a betting system is, in fact, increasing the variance. Although there are some good strategies, none of them is a foolproof system for winning. On our website, you can find some of the best roulette strategies.

Decreasing or increasing variance

The player can, however, directly affect the nature of his game by choosing to place bets on mathematically more probable outcomes for a low reward, or on mathematically less probable outcomes for a big reward. By covering almost the entire wheel with his bets, say, 35 numbers, the player will make a small 2.80% profit on most spins. On the other hand, betting on one number will only have a 2.70% chance of success, but the reward will be 36x your bet.

Some players say roulette shouldn’t be played only with two-sided bets such as red/black and odd/even as that makes sure you’re playing a coin flip game in which the house has the edge, and you will likely encounter long losing streaks as they’re a real possibility in coin flips. Adding a progressive betting strategy to this is a recipe for disaster since the variance is simply too high.

On the other hand, by choosing to play two out of three options, for example, 1-12 and 13-24, your chance of winning on that spin rises to 24/37 or almost 65%, so losing streaks will get shorter and your risk of bankruptcy will decrease compared to the two-sided bet.

But there’s the problem of not being able to win enough money with that kind of play, so some people opt for only one side of a three-sided bet, in which case they only have a 32.40% chance of winning but when they do win, they win more. It’s all about the risk and reward, and it’s important to decide what kind of game do you like to play – the risky one or the relatively safe one. This is when a math decision you make will directly affect your game.

Bold strategy – is it any good?

Some game theorists have stated that the bold strategy is the mathematically correct way to play roulette. It’s a strategy in which you always bet the maximum amount that lets you win your target amount of money. In essence, that means you should bet all your money on red or black and walk away in either case, if you win or lose. If you got close to your goal, you should only place a small bet that lets you reach the goal, not more. This way of thinking ensures that you don’t accumulate negative expected value by playing a lot of spins, and you’re also avoiding the biggest problem in roulette, which is winning too small when you do win.

It’s quite possible that playing a bold game is the best solution, as most other solutions seek long-term commitment, during which the house edge and losing streaks will eat up your bankroll. Many people say it’s actually wiser to just use the randomness to your advantage, bet big, and potentially walk away with your money doubled, as there are no strategies that are capable of leading you towards doubling your initial bankroll.


Roulette is definitely a game of math, so math must be considered when playing the game. It’s important to decide what kind of a game do you want to play – a low risk or high risk – and it’s quite possible that high risk is the way to go. The most famous betting system of all, Martingale, is not only bad because your bets can grow to incredible amounts, but because the system forces you to always win only 1 unit, never more than that. That’s far too little to make playing roulette a worthwhile exercise, so gamblers who study roulette math might just be better off if they gave themselves a chance to win big, at cost of greater risk.

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