Roulette Betting Odds

Roulette Odds Explained

Roulette has always attracted casino enthusiasts looking to score big, as it is a game that offers high payouts. If you ask anyone to name a casino game, they will most likely mention roulette, and there is hardly a country where the game is not popular. Roulette is indeed a game in which the house has an edge, but luck also plays a major role. When the croupier releases the ball, no strategy can influence where it will land.

The actual spinning device is a wheel consisting of divisions, also called pockets. The whole structure has become so iconic that even those who have never been to a casino might instantly recognize the game. Thanks to its straightforward rules, the game has gained immense popularity worldwide across land-based and online gambling venues, attracting both seasoned players and complete novices alike. Nowadays, many people prefer online roulette instead of visiting land-based casinos. This allows them to focus on their strategy and betting system without being distracted by the noise or feeling rushed to place their bets.

Roulette Calculations

Roulette Probability

Roulette Odds

House Edge

The main objective of the game is to place the correct bet and predict where the ball will land. Thus, players place their chips on the betting layout and wait for the dealer to announce the winning number. Please note that to calculate your profit, you need to know the table you are playing on and its specific rules. Although roulette variants share similar rules, subtle differences can affect the odds and payouts.

The current guide reveals important information about the unpredictability of each roulette round, as well as the mathematics behind the popular game. Stay with us to learn more about probability and odds in all variations of roulette, as well as the meaning of the house edge.

Why Are Roulette Spins Unpredictable

Roulette has been a casino staple for more than a century, and its popularity has not diminished; today it is one of the most widely played games in both online and brick-and-mortar casinos.

Many factors draw players to roulette tables, but the game’s enduring popularity is primarily due to its simplicity. Still, many gambling enthusiasts wonder whether the outcomes of previous rounds influence subsequent spins of the wheel. Contrary to what most players believe, roulette is a game of independent events, and now we will explain why.

Take a coin toss, for example. Even if you flip the coin ten times and get tails every time, that does not mean the next flip will also be tails. Some people believe the coin will “correct” itself and land on heads, but that is not necessarily the case.

Many players are guided by the Law of Averages and the Law of Large Numbers. According to the first law, results average out over time, while the second states that as the sample size grows, actual outcomes approach the mathematical probability.

The second law may sound confusing, so let’s return to the coin example, where heads is expected 50% of the time. Over a small number of flips, you might observe heads 0% or even 100% of the time, but with each additional toss the percentage moves closer to 50%.

Now, let’s look at the roulette wheel and assume that the white ball has landed in red pockets four times in a row. Some players may believe red will appear again because the numbers are “hot” while others will bet on black because it is “due”. This reasoning might make sense to some, but what they fail to take into account is that outcomes from the previous rounds do not influence the present odds; the roulette wheel does not remember what has happened in the past.

Regardless of how many even-money bets a player has made, or how often those bets have won or lost, the probability of winning an even-money bet remains 48.64% in European Roulette and 47.37% in American Roulette. Since roulette consists of independent events, past spins cannot determine what will happen next, and the odds of red appearing again remain unchanged.

Roulette is indeed a game of chance, and as such, it is made up of a series of unrelated events, meaning that each time the wheel is spun the probabilities remain the same—unless the wheel is physically biased.

Believing that a number is “due” players often increase or double their bets, which can quickly drain their bankroll. Betting based on perceived patterns may be less harmful only if players keep their wager size constant.

Calculations in Roulette

To understand how odds are calculated, players should first know that there are three main types of roulette games, and roulette wheels fall into two categories. The game originated in France but later developed into two additional variants—European and American. French and European roulette share almost identical rules and use the same wheel. The American version, however, introduced changes that favor the house.

When roulette first reached the United States, casino managers were unhappy with its modest house profit. To increase revenue, they added a double-zero pocket, raising the house edge to 5.26%. In contrast, the European version has only a single-zero pocket, which is far more advantageous for the player. Thanks to its lower house edge (just 2.70%) and higher chance of winning, players prefer European and French tables to their double-zero counterparts.

Explaining the “Probability” Term

In order for players to grasp probability in roulette, let’s use a simple real-life example. We all know the coin-flip game, where the chances of winning are the same as losing. The coin has two sides that represent two different outcomes—heads or tails. If you bet on heads, you are choosing one of the two possibilities. Thus, the probability of winning is 1 out of 2. This ratio can also be expressed as 1 to 2, 1:2 or ½.

Based on that, it is safe to say that the term “probability” relates to two numbers. The first shows the number of ways the event can occur, and the second shows the total number of possible outcomes. These can be converted into percentages by dividing the first number by the second and multiplying by 100. If we denote the first number as X and the second as Y, the formula is X / Y × 100. In our case, 1 / 2 = 0.5; 0.5 × 100 = 50%. So, the probability of heads is 50%.

Probability in All Variations of Roulette

In a nutshell, probability is the number of possible outcomes that are favorable to the player. Now it is time to put this knowledge into practice. With the European and French wheels, there are 37 numbers, and you place your bet on one number (a straight-up bet). To calculate the probability of your “lucky” number showing, you divide the 1 chance to win by all 37 possible outcomes. Briefly, this means 1 / 37 = 0.027 × 100 = 2.70%. Let’s explore the situation when you bet on two numbers. You have 2 chances to win out of 37 in total, which equals 5.4%—a better chance to win.

It is well known that the American roulette table is less favorable to the player, though this may not be obvious to beginners. This section explains why it is better to avoid the American table. On the American wheel, you will spot 38 pockets in total. To compare the probability in both variations, we will use the same bets as in European roulette. If you bet on one number, you have only 1 chance to win out of 38. Expressed in percentages, this means 1 / 38 = 0.026 × 100 = 2.63%. If you decide to place a bet on two numbers, the calculation is 2 / 38 = 0.053 × 100 = 5.30%.

Roulette Variations

European Roulette

American Roulette

French Roulette

The Meaning of the Odds

Many people believe that “odds” and “probability” are the same, but they are not. There is a subtle yet essential difference between the two. Odds compare the likelihood of an event occurring with the likelihood of it not occurring.

Like probability, odds are expressed with two numbers. The first shows the number of ways the event can occur. The second represents all the remaining possible outcomes, excluding the winning one.

The Odds in All Variations of Roulette

Returning to our straight-up bet example, the odds on the European wheel are 1 to 36 (1 way to win and 36 to lose). On the American wheel, the odds are 1 to 37, or 1:37.

It is important to distinguish between odds “for” and odds “against”. When the numbers are uneven, the difference is significant. Experienced players easily differentiate between “odds for winning are 1:2” and “odds against winning are 2:1”.

The payout is always higher when the chances of winning are lower. Suppose you place a straight-up bet on the American wheel, wagering on a single number out of 38. Your odds of winning are 1 to 37 (or 1:37), while the odds against you are 37 to 1. If you win, the casino pays 35:1, keeping the difference as its profit, known as the house edge.

If you place an even-money bet, like red/black, then your chances of winning are 18 against 20 chances of losing (18 coloured numbers plus 2 green zero pockets). Therefore, the odds for winning are 18:20. The payout, however, is 18:18 because the house keeps a two-unit profit (one for each zero pocket). The same logic applies to even/odd bets, because zero is neither even nor odd. If you bet on even numbers, you have 18 chances to win and 20 to lose (the odd numbers plus the two zeros). Thus, the odds for winning are 18 to 20, and the payout is again 18:18 after the house takes its two-unit profit.

The Meaning of the House Edge

The house edge is the casino’s built-in profit, determined by the presence of the zero-numbered pocket(s). That is why, in the American variation of the game, the house edge is higher than in the European one. The second zero pocket further increases the player’s chances of losing.

In fact, the house edge is calculated logically; it is not a random figure devised by casino managers. With a double-zero pocket, the casino’s advantage over all bets on the table is 2 out of 38, which equals 0.0526. Expressed as a percentage, the house edge is 0.0526 × 100 = 5.26%.

The same logic applies to the European and French games. With only one zero-numbered pocket, the house advantage is 1 out of 37, which is 0.027, or 2.70%.

Gambler’s Fallacy

Knowing how to calculate potential wins or losses is at the core of roulette strategy. Many gamblers, however, fall victim to the so-called gambler’s fallacy. They believe that long consecutive streaks of one winning number or group of numbers are very rare. For example, if the winning number has landed in the red section three times in a row, it does not necessarily mean that the next spin will be black. This is a game of chance, and players cannot be sure that a particular number or event will appear on the next spin. That is why the best strategy in roulette is to keep track of your bankroll and protect it from depletion.

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