Wondering “what are the odds of winning at roulette”, are you? You’re not alone. Many a beginner and pro player alike have sought to discern the likelihood of their lucky number ending up as the resting place of the bright white ball. While you cannot forget that roulette is a game of chance, it is still crucial to be aware of your chances of winning vs. losing to determine what to risk, when to risk and what you’ll gain or forgo as a result. A definitive understanding of roulette betting odds and how they’re calculated is the only way to do that.
Odds can be defined in two ways. Roulette table odds refer to the chance of each outcome occurring while payout odds refer to the amount paid back for a win, after the house edge has been factored in (more on this at the end).
As you’ll see shortly, there are a variety of bets you can place, each with their own unique roulette odds that pay at differing amounts. Do keep in mind that although the European variant has better roulette odds than the French version and some roulette bets do give you a chance at a decent win, in the long-term you will lose a fraction of your bankroll.
In short: no, and the fact that the two are not interchangeable terms is a common misconception.
In reality, odds refers to the ratio between the amount staked based on the expected probability which are represented as odds against in gambling (i.e. the payout odds). On the other hand, probability is the possibility of an event occurring expressed as a ratio of favourable cases to the whole number of cases (i.e. the table odds).
In mathematics, the probability of an event is expressed as:
So, if Event A were the probability of hitting a red number on the roulette wheel, it would be expressed as:
Conversely, calculating the odds against red is equal to:
You could go on and calculate the odds for any bet using the method explained above but there’s no need. You’ll find them all listed in roulette odds tables a bit further down but first let’s take a closer look at each bet type.
There are three main types of roulette bets that you can make, each with varying odds and payouts which are coming up next. But if you’d like to see them defined with an explanation on how to place your chips, check out the Roulette Bets page.
Below you will find handy roulette odds charts split by outside and inside bets. They’re a great reference guide as you play online and essential to know before you undertake understanding how roulette odds work.
As we hinted at earlier, there are bet types that are only found in variants of the game. These include racetrack bets in the French variant and the Surrender bet in the American one. Furthermore, innovative game providers harness cutting-edge 21st century technology to create never-before-seen tables with new betting possibilities such as Evolution Double Ball Roulette odds that payout of 1300:1. Again, you’ll find these detailed on the Variants page.
We’re putting our statistics professor cap on now, but don’t feel intimidated by the terms such as the expected value and factorials, we’ll go through things step-by-step. After all, mathematical proficiency isn’t a prerequisite to being a good player and many great minds have already created roulette odds calculators that do all the work for you.
Nevertheless, there’s something to be said about individuals who go the extra mile and learn how to calculate roulette bets. So, if you’re ready to take things to the next level, let’s go through some examples.
You’ll be calculating table odds (hence the word probability can be used here) and the formula to use is:
P(e) = the probability of an event
n = the number of spins
x = the number of times the bet wins
P(A) = the probability of our bet winning in one spin
Say you’ve got a hunch that the black 5 will hit consecutively. In this case,
P(e) = two consecutive black 5
n = 2
x = 2
P(Black 5 in one spin) = 0.0270 (based on the probability formula shown at the top)
Here the values would be:
P(e) = 10 black numbers in a row
n = 10
x = 10
P(Black number in a single spin) = 0.4864
Putting these values in the formula gives:
Calculating your roulette win for any type of bet is simple. The odds against format (defined above) is the coefficient by which you are to multiply the stake of your winning bet. For example, if you place a straight-up bet of €1 with odds of 35:1, you’ll receive €1 x 35 = €35 back plus your original €1 stake. Likewise, if you place a split bet of €10 with odds of 17:1, a win will result in €180 added to your bankroll, €10 x 17 = €170 and your initial bet of €10.
Since roulette odds are often thought of as part and parcel with the house edge, it deserves its own section.
This term is defined as the difference between the true odds of a bet and the actual odds the casino pays you when you win. The reason you’re not paid at the true odds is simple – casinos need to earn a profit to remain in business, and this is one of the ways they do it.
To comprehend the thought behind the house edge, you’ll first need to understand mathematical expectation, also known as the expected value. In gambling terms, it is the amount of money you can expect to win or lose in the long term. In other words, it is the sum of all potential wins and losses, multiplied by the probability of their respective occurrence.
It is presented as:
Let’s look at this is practice.
As we revealed in the table, the payout odds of a single number on the European wheel is 35:1. So, if you were to bet €1 on every roulette number on the wheel, you’d end up winning €35 (w) with a probability of 1/37 (p) such that you’d lose €1 overall based on a loss probability of 36/37 (l). It’s calculated as,
To derive the value of the European roulette house edge, multiply -0.027027.. by 100, to obtain 2.7%.
Similarly, the American roulette house edge is:
For the most part, the value of the casino edge remains consistent for every type of inside, outside or special bet you can choose to place in any variant of the game but there are some exceptions.
Given its similarities to its continental counterpart, you’ve not heard much about French roulette yet. However, if you’re thinking of the little wheel in terms of its house edge, this variant’s La partage rule affects it significantly. As half of your stake is returned to you on even money bets when the ball lands on 0, the casino edge is reduced to 1.35%.
In the American variant, the basket bet has an increased house advantage of 7.89%. Since it’s a bet on five numbers, it has a probability of 5/38, a payout of 6/1 and odds against success of 33/5. To express the house odds in terms of the total amount of numbers you’ll be betting on, the house odds are multiplied by 5/5 such that:
Multiply this number by 100% to obtain 7.89%. Needless to say, this is a roulette bet to avoid as it seldom works out in your favour.
You made it, and luckily you needn’t memorise any of those formulas for some statistics exam. This information on the odds of roulette and their calculations will still take some time to sink in, so give the page a few rereads and pat yourself on the back for expanding your knowledge of this world-famous casino game! You’re ready for the next phase.
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