Roulette Betting Odds

Roulette Odds Explained

Roulette has always been attracting casino enthusiasts who are looking to score big as it is a game, which provides high payouts. If you ask anybody to name one casino game that would be most probably roulette, and there is almost no country to which the popularity of the game has not carried over. Roulette is indeed a game, in which not only the house has an edge, but luck also has a fair share. The reason is that when the croupier tosses the ball, there is no strategy, which can control it.

• Calculations in Roulette
• Explaining the “Probability”
• Probability in All Variations of Roulette
• The Meaning of the Odds
• The Odds in All Variations of Roulette
• The Meaning of the House Edge
• Gambler's Fallacy
• FAQ

The actual spinning device is a wheel, which consists of divisions that are 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 all over the world across land-based and online gambling venues, and among experienced players and total novices alike. Nowadays, many people prefer online roulette, instead of going to land-based casinos. Thus, they can focus on their strategy and betting system without being bothered by all the noise or feeling hard-pressed to place their bet.

Roulette Calculations

Roulette Probability

Roulette Odds

House Edge

The main objective of the game is to place the right bet and make the right guess to get a return. Thus, players place their chips down on the betting layout of the table and wait for the dealer to announce the winning number. Please note that, to calculate your profit, you need to know the table, which you are playing on and its specific rules. Although roulette is governed by similar rules, there are some differences in rules that 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 house edge.

Why Are Roulette Spins Unpredictable

Roulette has been one of the casino staples for more than a century, and its popularity has easily not lessened throughout the years, as currently, it is one of the most widely used games in online and brick-and-mortar casinos.

There are numerous reasons why players gravitate towards the roulette tables, and the popularity of the casino classic can be best justified with its simplicity. Still, the question many gambling enthusiasts have been asking themselves throughout the years is whether the outcomes from previous rounds will have an impact on the subsequent spins of the wheel. Contrary to what most players believe, roulette is a game of independent events, and now we will explain why.

If we take as an example a toss of a coin, even you have already flipped it ten times, and the only result, which has come out is tails, this does not mean that the next flip will certainly be tails. Yet, some people still think that the coin might correct itself on the next flip, and heads will come up, this will not necessarily be the case.

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

The second law might sound a bit confusing for players, but let’s take a look at the toss of a coin again where heads will come 50% of the time. People are often misled when a shorter period of time or trial is taken into account, as one of the results might come up 0% or 100% of the time. Still, the percentage will get closer to 50% with each subsequent toss of the coin.

Now, let’s take a look at the roulette wheel and assume that the white ball has landed in red pockets four times in a row. Some players might fall prey to the belief that red will come up also in the next round because such numbers are in a hot run or will go for black because it is due to come up. This might make sense for some gambling enthusiasts, but what they fail to take into account is that outcomes from the previous rounds do not influence the present odds simply because the roulette wheel does not hold information about what has happened in the past.

No matter how many times avid casino fans have placed an even-money bet and, most importantly, how many times their bet has won or lost, the odds of making a winning such even-money bet will invariably be 48.64% in European Roulette and 47.37% in American Roulette. Since roulette is a game of independent events or trials, this is to say that what has happened in past spins cannot be used to determine what will happen next, and the odds of red becoming a winning number again will remain unchanged.

Roulette is indeed a game of chance, and as such, it is made of a series of events that are not related to each other, meaning that each time the roulette wheel is spun, the probability of the numbers to become winning ones will remain the same but this does not apply to the cases when the wheel is biased.

Guided by the belief that a number is due to win, players start increasing or doubling their bets, which often leaves them with an emptied bankroll. In spite of the fact that making bets based on patterns might not have such a serious effect on the bankroll of payers, this will only be the case if they keep their wagers the same size.

Calculations in Roulette

To better understand the notion of odds and their calculation, it is crucial for players to understand that there are three different main types of roulette games, while roulette wheels fall into two different categories. In fact, at its core, the game is of French origin, but it was developed in 2 more variants – European and American. French and European roulette share almost the same rules and the same wheel. But Americans love changes, especially when in favor of the house.

When the game was first introduced to the American gambling community, casino managers did not like the idea of the low profit to the house. In an attempt to increase it, they have added the double-zero pocket, which boosts the house edge to 5.26%. Unlike the American variation, the European one provides only a single-zero pocket, which is absolutely advantageous to the player. With the low house edge (only 2.70%) and the better chance to win, players prefer the European and French tables over their double-zero counterparts.

Explaining the “Probability” Term

In order for players to gain an understanding of probability in roulette, we would like to make it clearer with a simpler example from life. We all know the flip-a-coin game, where the chances to win are just the same as to lose. The coin has two sides, which represent two different outcomes – heads or tails. For instance, you bet on heads outcome and you are expecting that particular result, or in other words, you choose one out of two possibilities in total. Thus, we may say that the “probability” to win is 1 out of 2 possible. This ratio can be also expressed as 1 to 2, 1:2 or ½.

Based on that ground, it is safe to allege that the “probability” term is related to two numbers. The first one shows the possible chances for the particular event to occur and the second one – all possible chances in total (both for win or loss). These can be also converted into percentages by dividing the first number by the second, and multiplying it by 100. If we acquire the first number as an unknown X and the second – as an unknown Y, we may come up with the following formula: X / Y × 100. In our case, we have 1 / 2 = 0.5 × 100 = 50%. So, the “probability” for heads to win is 50%.

Probability in All Variations of Roulette

In a nutshell, the term refers to the number of possible cases that are favorable to the player. Now, it is time to put the knowledge into practice. With the European and French wheel, we have 37 numbers and you place your bet on one number (straight-up bet). To calculate the possibility for your “lucky” number to show, you need to divide 1 chance of a win by all 37 possible ones. Briefly, this means 1 / 37 = 0.027 X 100 = 2.70%. Let’s explore the situation with placing a bet on 2 numbers. You have 2 possible chances to win out of 37 in total. Talking in percentages, this equals 5.4%, so a better chance to win.

It is a well-known fact that the American roulette table is disadvantageous to the player. But this concept may appear to be incomprehensible to an amateur gambler. This article will explore the reason why it is better to avoid the American table. On the American wheel, you will spot 38 pockets in total. To compare the percentage of probability in both variations, we will give examples with the same bets as in European roulette. You place your bet on one number and you have only 1 chance to win out of 38 (37 chances to lose, plus 1 to win). Expressed in percentages, it means 1 / 38 = 0.026 X 100 = 2.63%. If the player decides to place a bet on 2 numbers, then the following situation is in effect: 2 / 38 = 0.053 X 100 = 5.30%.

Roulette Variations

European Roulette

American Roulette

French Roulette

The Meaning of the Odds

Many people consider that “odds” and “probability” are the same, but that is not the case. There is a slight, but essential difference between these two. The odds represent the possibility of a particular event to happening as opposed to the possibility of the same event not to occurring.

Similar to the probabilities, odds are also represented by two numbers. The first number reflects the possibility of the occurrence of the particular event (exactly the same as the function of the first number in “probability”). The difference between the two terms comes from the second number. With odds, the second number represents all the other possible outcomes, excluding the winning one.

The Odds in All Variations of Roulette

If we look back at our example with the straight-up bet, the odds with the European variation are 1 to 36 (1 possibility to win and 36 to lose). On the other hand, the odds of a straight-up bet on the American table is 1 to 37, or the odds for winning are 1:37.

In fact, it should be mentioned that there is a slight difference between the odds. There are odds for and odds against. When the numbers are everything but even, the difference is quite tangible. Every seasoned player has no problem making the distinction 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. Let’s assume that you are about to place a straight-up bet, which means you place your bet only on one particular number out of 38 possibilities (for the American roulette). Thus, your chances to win are 1 to 37 or 1:37, i.e. the odds for winning are 1 to 37 and the odds against winning are 37 to 1. But if you win the bet, you will get a 35:1 payout, because of the profit of the casino, also known as the house edge.

If you place an even-money bet, like red/black, then the chances to win are 18 against 20 possible chances to lose (18 black numbers plus 2 green zero-numbered pockets). Therefore, the odds for winning are 18:20. The payout, though, is 18:18, because the house takes 2-unit profit (1 for each zero-numbered pocket). The same is valid for the even/odd bets, because zero as a number is neither even, nor odd. If you place your bet on even numbers, you have 18 chances to win and 20 to lose (the odd numbers and the two zeroes). Thus, the odds for winning are 18 against 20 possible ways to lose. But the payout is again 18:18 after the house takes its 2-unit profit.

The Meaning of the House Edge

The house edge is the profit of the casino, which is determined by the presence of the zero-numbered pocket(s). That is the reason why in the American variation of the game, the house edge is higher than in the European one. The presence of the second zero pocket increases the chances for the player to lose.

The house edge is calculated in a very logical way, in fact. It is not just a random number, figured out by the casino managers. With double-zero pocket, the chances of the casino (against all the bets on the table) are 2 to 38, which is equivalent to 0.0526. To represent it in percentages, it means that the house edge is 0.0526 X 100 = 5.26%.

With the European and French variations of the game, the logic is the same. With only one single zero-numbered pocket, the chance of the house to gain the upper hand over all the players is only one. Consequently, we have 1 to 37, which is 0.027 or 2.70%.

Gambler’s Fallacy

Knowing how to calculate your possible win or loss is the core strategy of roulette. Many gamblers are entrapped by the so-called gambler’s fallacy. They believe that the long consecutive streaks of one winning number or group of numbers is very rare. For example, if the winning number was three times in the red section, it is not necessarily that on the next spin the winning number will be black. This is a game of chance and the players cannot be sure that a particular number or event will show up on the next spin. That is why the best strategy in roulette is to keep track of your bankroll and protect your bank account from bankruptcy.

FAQ