It is essential to differentiate between systems of playing Roulette and strategies of playing Roulette.
Systems that would guarantee you a profit from playing Roulette do not exist. Strategies in the game of Roulette are more like recommendations than rules. No mathematically sound playing strategy would allow you to constantly win at Roulette, as Roulette is primarily a game of chance and luck, and probability theory cannot help here.
The only thing we can use probability theory for is calculating the probability of each game outcome and the mathematical expectation, in other words, the casino advantage.

Do not take the systems of playing Roulette seriously.
Systems give tangible results in other games, such as Blackjack, and Video Poker, where using basic system strategies, the player even gets an advantage over the casino.
Roulette, however, is an exciting game for entertainment, and you should treat it as such. Play responsibly, and always remember that the casino’s primary goal is to make a profit and not to entertain you.

The outcome in gambling games usually depends on luck, but it is still necessary to thoroughly know the rules of the game that can increase your chances.
It also applies to Roulette, where your best strategy is choosing the proper game guidelines. What are the chances of winning in Roulette? If you flip a coin 100 times, it will land on “heads” about 50 times.

“The result in gambling games usually depends on luck, but it is still necessary to thoroughly know the game rules, which can increase your chances. This also applies to Roulette, where your best strategy will be the correct choice of rules by which the game will be played.

What are the chances of winning at Roulette?

If you flip a coin 100 times, it will land on “heads” approximately 50 times. If, theoretically, “tails” comes up 20 times in the first 20 tosses, then there is a huge chance it will land on “heads” the next time.

As for Roulette, many also try to determine a “trend.” For example, red numbers appear several times in a row, so it is reasonable to bet on a black number. In reality, there is no law. You may lose or win several times in a row. In a very long game, the balance will always be zero.
The player and the casino take turns losing and winning. But how long can you lose? It seems short, as money will eventually run out. The same is true for the casino, except it has much more money.

Play European or French Roulette.”

“The casino’s mathematical expectation (advantage) when playing American Roulette is 5.26%, in European Roulette – 2.7%. This is why Roulette has become the most popular in Europe. You cannot eliminate or change the casino’s advantage in Roulette. If you try to do this, you will only slowly lose your money. Your goal in the game of Roulette is to win as much money in as few spins as possible while having clear boundaries on when to end the game. This will help you with a successful betting system and financial planning.”

The theory of probability for mathematical analysis of Roulette.

In the game of Roulette, all 37 numbers come up with an equal probability. If we assume that the zero sectors (“0”) is absent, then in this case, the player would have an equal chance of winning and losing, and the presence of the zero sector makes Roulette a profitable game for the casino.

In other words, the expectation of winning for the casino is equal to 1/37 of the bets made. Each player who makes bets on numbers loses 1/37 of their bet on average. In this case, the probability of winning is 18/37. This value is almost the same, but all casinos profit from the difference between 1/2 and 18/37.
When betting on simple chances on French Roulette (red, black, even, odd, small numbers (1-18), large numbers (19-36)), the player’s probability of winning is even greater because, according to the rules of the game, if zero comes up, the player loses only half of their bet. But even in this case, the probability is less than 0.5%.

Roulette enthusiasts have long come up with countless game systems that help players beat the casino. Some recommend betting on losses (if black comes up, bet on red), others – on wins.
The alternating strategy is quite popular: betting on red and black, even and odd. They also advise increasing bets in case of a success and decreasing in case of a loss and vice versa. The player is left to choose which strategy will help him win. But most importantly, if you are not sure of your financial superiority over the casino, the only way not to lose everything is to be able to stop in time.

PS: GPT-3 artificial intelligence opinion (from “Generative Pre-trained Transformer 3”, the third version of the Generative Pre-trained Transformer model that was created by OpenAI) on roulette odds:

 The chances of winning at French Roulette depend on the specific bet that is placed. The game of Roulette is based on the principle of a spinning wheel with numbered pockets and a ball that is dropped into the wheel. Players can place bets on the numbers or different combinations of numbers, and the game’s outcome is determined by where the ball lands on the wheel.

 The most common bet in French Roulette is the single number bet, which offers the lowest odds of winning and the highest payouts. The odds of winning a single number bet are 1 in 37 (or 2.70%) on a European wheel and 1 in 38 (or 2.63%) on an American wheel.

 Other bets, such as even/odd, red/black, or high/low, offer better odds of winning and lower payouts. The odds of winning these types of bets are 1 in 2 (or 48.65% on a European wheel and 47.37% on an American wheel).