How to Mathematically Win at Roulette: Cracking the Code

Can math help people win at roulette? This is one of the doubts many people around me have. Generally speaking, nothing can help you win all the time. Even so, eventually, mathematical formulas can be pretty helpful. Things are connected here with probability and which outcome will most likely happen. You know I am not a genius at this science.

Yet, after years of exploring different roulette strategies, I have managed to make certain conclusions. 

The Mathematics of Roulette Odds 

Let’s start from the very beginning. People need to understand how math works with roulette. Otherwise, they won’t manage to implement the strategies in the best possible way. 

Calculating Probabilities 

You will soon realize why ocean wildlife is my passion and not math. There are different ways to display probability. They are:

• Percentage odds: As you can guess, this method defines the percentage of the time a specific outcome occurs. 
• Radio odds (X to 1): Whenever an unknown factor (X in this case) happens, the outcome will occur just once. 
• Fractional Odds (1/x): Things are opposite here. A certain event will happen once out of X number of trials. 

Keep in mind that the calculation is different for the American and European versions of the game. The reason is simple — the USD variant has single and double zero. 

The House Edge Explained 

There is a good reason why calculating probabilities does not provide clear results. 

Each casino game comes with a house edge. In other words, the algorithm supporting the roulette games is programmed to keep part of the losses made by players in the long run. For the EUR variant, it is around 2.70% on average, and for the American one, it is around 5.26%. 

Example: Let’s translate this into numbers.

If players lose $10k, the machine will keep $270 for European roulette and $526 for the American version. This explains why the EUR version is more suitable for me. Anyway, the remaining part of the money is given back to all the players. Someone may win $7000 while someone may lose everything. 

Expected Value (EV)

Suddenly, I feel like a math professor. 

Let’s imagine that you wagered $10 on red, and the ball falls in the pocket of the red number. In that case, you get $10, and the net winning is 1. Although, if the ball lands in the pocket of either green or black color, you lose everything, and the net winning is -1.

The previous explanation will make things easier for the players. Here is how to calculate the EV = P(Red) x (Value of X for Red) + P (not Red) x (Value of X for not Red).

The result of this is: 18/38 × 1 + 20/38 x (-1) = -0.053.

This explanation is for the US variant of roulette, and things are slightly different for the European one. 

So, what does this mean? If you find yourself in a winning strike, you will make a decent profit. Yet, in the long term, you will lose 5 cents on average each time you play. 

Statistical Strategies 

Indeed, statistics are like a bikini — what they reveal is suggestive, but what they conceal is vital. Be that as it may, I don’t recommend you neglect them. They can help you develop specific tactics.

The Law of Large Numbers 

Believe it or not, this law was invented in the 17th century. Logically, it didn’t have anything to do with gambling. Having said that, my fellow casino enthusiasts find a purpose in every formula and try to raise their chances of winning. 

Coin flipping is a good way to explain it. Chances for each outcome are 50%. In the short run, that percentage may not be exact. Even so, the proportion will draw nearer to 50% in the long run.

Let’s use European roulette as an example. The chances that a ball will land on either black or red color is around 48.65%. After a few sessions, the ratio won’t be as this definition suggests. Yet, after a longer period, the outcome will be closer to the theoretical probability. 

Variance and Standard Deviation

I am pretty sure that many gamblers haven’t heard about standard deviation. Well, this strategy aims to tell how far from the man the outcome lies. This calculation is marked with the Greek letter Stigma, so don’t be surprised if you see it. 

So, how to calculate the standard deviation? Trust me, it is pretty challenging to understand it. Instead, I would like to share a table with different standard deviation data.

Bet	Payout	Expected Value	Standard Deviation
Straight Up	35 to 1	-5.26	576
Split or 0/00	17 to 1	-5.26	402
Street	11 to 1	-5.26	324
Corner	8 to 1	-5.26	276
First Five	6 to 1	-7.89	94
Line	5 to 1	-5.26	219
Dozen and Columns	2 to 1	-5.26	139
Red/Black, High/Low, Odd/Even	Even Money	-5.26	100

Probability Distributions 

Wiser people than me have made these calculations, and I trust them. 

Let’s, once again, use European roulette as an example. There are 37 options in total. Math geniuses have studied 36 rounds by using the Binomial distribution where x → Bin (35,36/37).

So, the probability of winning nothing looks like this: P(X=0) = (35 35) (36/37)^35(1/37) = 0.3833.

Let me make things easier. This statistical invention suggests that betting on a single number 35 times in a row will ensure you win at least once. For such an outcome, there is a 62% chance. In other words, you can make a profit if you guess the number as early as possible during that process. 

Advanced Betting Systems 

Here comes the easier part of the article. I am not the type of guy who will read these formulas; I am only sharing them with those who love to do that. Here are three strategies I often use. 

The Fibonacci Sequence 

Have you heard about the Fibonacci sequence? It looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, etc. In other words, each stake is the sum of the previous two ones. 

So, how to apply it to roulette? Let’s say that you placed $50 on black, and you lost. Next round, you place $100, then $150, then $250, and so on. That rule only counts if you don’t guess the outcome.

If you did do that with $150, you get back to $150 – $100 = $50. 

Don’t forget you can get in a losing strike and lose money even with this advanced tactic. 

The Labouchere System

In my opinion, this is a responsible gambling roulette strategy. 

Players primarily need to determine how much they want to win. Imagine that is $100, a sum that won’t harm your budget a lot. Next, split that number into small sums. For example, $10, $20, $50, $10, and $20. 

Now, place the farthest left and right wagers (10 and 20 USD in this case).

• If you win, you cross those two sums and focus again on the furthest left and right, which would be $20 and $10.
• All the same, if you lose, don’t cross anything. Instead, add the bet you made, which would be $30 at the end of the sequence. Now, apply the same strategy I talked about before. 

Repeat until you win. 

The Reverse Martingale 

The marginal system suggests that a player should double the bet after failure. As you can guess, this tactic proposes quite the opposite. It suggests players should double their bet after a win. That way, they are actually risking the casino’s money. 

Limitations of Mathematical Approaches 

These strategies aren’t perfect. On the contrary, you need to be aware of certain obstacles. 

The House Always Wins

Please note that roulette is a game of luck. Each table is supported by a completely random algorithm. It is transparently explained how much players can expect to win. So, don’t expect to become a millionaire, even if you perfectly apply all the tactics. 

Randomness and Chaos Theory

Chaos theory recommends that everything can depend on the outcome of the game. It suggests that the humidity in a casino, which changes during the day, impacts the way roulette works. Moreover, it suggests that the temperature of the wheel changes when more people are playing, which automatically impacts the way the ball falls in any pocket. 

Honestly, I don’t believe in this.

Casino Countermeasures 

Imagine that everyone is using the statistical strategies we talked about. The outcomes would be ridiculous. 

Casinos are aware of that. That’s why they often set up certain limits and rules to prevent exploitation. Get familiar with them before depositing money, and ensure that you can freely use the selected gambling tactic. 

Ethical and Practical Considerations 

At the end of the day, everything depends on how you gamble. That’s why you need to pay attention to three things before even deciding on the method you will use. 

Avoiding Gambling Fallacies

You have probably heard about this. For instance, if five numbers in a row were even, the 6th one has to be odd. These are only myths, and don’t believe in them too much. Players regularly give up on their strategies because of them, believing their chances will grow that way. In the end, there is no one who ends up happy because of them. 

Responsible Gambling

I have discussed the ways to invest your money. A more important thing is how much money you can afford to lose. Making calculations is essential. That way, you will know how much you can wager from the very first moment. 

Knowing When to Stop

Don’t bother to make limits on your losses if your budget is small. Honestly, everything below $100 per session is considered low. However, define limits on what will be the maximal amount that will satisfy you. 

Doubling your initial budget per session is a great goal, and I consider it reasonable. Don’t chase millions if you can’t deposit at least $50k. Stay on the ground. Besides, this is a source of entertainment; it is not your job! 

And Now? 

This is probably the most complicated guide you will read on my website. I honestly tried to simplify each statistical tactic as much as I could. If something is unclear, read other articles related to mathematical topics. 

Most importantly, work on your self-control and organize your budget in the best possible way. Without that step, neither of the tactics I discussed will help you make a profit.

If they bother you, simply give up on them! There are other ways you can opt for when it concerns winning at roulette.