Independent Trials, Odds, and Casino Edge in Roulette

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Written by Boris Atanasov
Boris Atanasov
With more than 4+ years of experience in the iGaming industry, Boris Atanasov writes exciting content about slots, video poker, roulette and blackjack.
, | Updated: September 26, 2025

The rules of roulette are easy to grasp despite the broad range of betting options the game offers. Whether you place a straight-up bet on a single number or a wager based on number properties such as color, you put money at stake and play against the house. If you lose, the casino collects your stake. When you win, the house pays you.

In principle, all you need to start playing roulette is some money and the ability to distinguish among the available bets. However, if you take the game seriously, you should gain at least a rudimentary understanding of probability in gambling.

To be more specific, you should understand how the house turns a profit from its roulette tables and become familiar with the concepts of independent trials, true odds, and the casino edge. We explain all of these concepts in this article.

Why the Odds Never Change in Roulette?

1Independent Trials

Ever since roulette first appeared on casino floors, there has been much debate over whether the outcome of a spin is affected by the results of previous spins. Indeed, many roulette players still base their decisions on past results.

First, they look for patterns and wait for a particular number, color, or parity to appear several times in a row. Then they either bet on the opposite result because they believe it is “due,” or they back the same outcome or number because it is on a hot run. Both approaches are flawed because they imply roulette wheels “remember” past events.

That simply is not the case. Roulette is a game of independent events, where the odds of upcoming trials are not influenced by the outcomes of previous ones. Each spin should be viewed as an isolated trial, having no impact on the spins that follow.

2How games of independent trials work?

Imagine you are standing in front of a fish tank filled with 50 red and 50 black marbles. You can wager any amount of money on the color of the marble you will randomly pick. You decide to stake $10 on a black marble.

You have an even chance of winning or losing because the number of red marbles equals the number of black ones. You pull out a black marble on the first try and win. Then you put the marble back into the tank and prepare for another attempt.

What are the odds of drawing a black marble the second time? If you answered 50/50, you are correct. By returning the marble to the tank, you effectively reset the odds so that your first pick has no impact whatsoever on the result of the second one.

This is an example of how games of independent trials work. The situation is much the same in roulette, with the only difference being that the chances of winning and losing are not equal because of the additional zero pocket. Nevertheless, the true odds remain unchanged, no matter how many times the same outcome occurs in a row – unless, of course, you are playing on a biased wheel.

3The Concept of Randomness

Ideally, roulette wheels produce completely random results that are not affected by previous spins. When true randomness is present, each item in a given set (in this case, the numbers 0 through 36) has an equal probability of being selected. In other words, it is impossible to predict with certainty which item will be picked.

Likewise, a roulette spin is an isolated – and therefore independent – trial unless the wheel itself favors certain numbers or sections, causing them to appear more often. Such biases can usually be detected only after several thousand trials.

4Biased Wheels

Let’s suppose you observe a series of 3,000 or 4,000 spins. If the results do not deviate from the mathematical expectations of the game, you are most likely watching a random wheel.

However, if you notice that 32 Red and 10 Black have failed to appear even once over those 4,000 rounds, the wheel likely shows some bias against them. Such a wheel does not produce truly random results.

Observant roulette players may exploit these biases, so casino operators do everything in their power to prevent this. Wheels are regularly tested to ensure they show no bias.

Modern roulette tables are usually equipped with scoreboards that display the past ten or twenty results. These scoreboards serve a dual purpose. On one hand, they enable trend bettors to discern patterns and bet accordingly.

On the other hand, they make it easier for floor personnel to detect biases and take the necessary measures to eliminate them in due time. When randomness is preserved, subsequent outcomes remain unpredictable and unaffected by previous results.

Probability and Odds – Two Sides of the Same Coin

Many inexperienced roulette players use the terms probability and odds interchangeably. Indeed, they can be seen as two sides of the same coin. However, there is a not-so-subtle difference between the two concepts, and it is best to learn to distinguish them if you are into casino gambling. Below, we explain odds and probability in the context of roulette.

Measuring Roulette Probabilities
blank The Concept of Odds

Measuring Roulette Probabilities

Probability is the likelihood of an event occurring, such as the number 32 red coming up during any given roulette spin. It can be expressed as either a fraction or a percentage. Assuming all possible results have equal chances because they are produced randomly by a device like a roulette wheel, we calculate probability by dividing the number of ways an outcome can occur by the total number of possible outcomes.

In roulette, there are two possible outcomes from the player’s perspective – you either win or lose. Therefore, the total number of possible results is the sum of all outcomes that lead to a loss and all outcomes that result in a win.

A single-zero roulette wheel contains 37 pockets numbered 0 through 36. Because only one number can hit on any given spin, the probability of winning with a straight bet is 1 in 37 (1 in 38 on an American wheel). You have one winning number and 36 losing ones. The exact percentage is calculated as follows: Pw = 1/(1+36) = 1/37 = 0.0270 x 100 = 2.70%.

With double-street bets, there are six winning numbers and 31 losing ones. Therefore, the probability of winning is 6/(6+31) = 6/37 = 0.16216 x 100 = 16.22%. The likelihood of winning with a color bet on red is much higher because you cover a larger portion of the wheel. There are 18 red pockets, 18 black ones, and one green zero. The calculation becomes 18/(18+19) = 18/37 = 0.48648 x 100 = 48.65%. You can determine the probability of winning with any roulette bet using this formula.

Because gamblers are prone to looking for trends, let’s examine the likelihood of the same outcome occurring three times in a row. To calculate this, raise the probability of a single number hitting to the third power: (1/37)^3 = 1/37^3 = 0.00001974217 x 100 = 0.001974217%.

The Concept of Odds

Odds differ from probability in that they express the ratio of winning to losing results, and vice versa. For this reason, they are not converted into percentages or decimals but are shown in fractional form, such as 2/3 or 2:3, spoken as “two to three”.

For example, in roulette, the odds of winning with a straight-up bet are 1 to 36 because there is only one winning number and 36 losing ones. In gambling, the ratio is more often stated in reverse. The house is practically betting against its patrons, so it lists payouts as odds against the player winning.

The odds against winning with a straight-up bet are 36 to 1; in a fair game you would collect 36 units in net profit on a 1-unit wager. In reality, the house always pays less than the actual odds against winning, which is how it secures its profit margin.

Casinos sometimes resort to subtle tricks to make their odds seem more appealing. One such trick is to list the odds as “2 for 1” instead of “2 to 1”. What’s the difference? If you are paid 2 to 1, you receive 2 units in net profit plus your original 1-unit wager. When the odds are listed as 2 for 1, you are paid 2 units in total, meaning your initial 1-unit bet is included in the payout.

How Casinos Gain an Edge Over Roulette Players

The House Always Wins

Understanding The House Edge

House Edge Calculation

Is Winning Consistently Possible in Roulette?

Turning a profit is the primary goal of any business, and gambling operators are no exception. You have probably heard the popular expression “The house always wins.” This is true, although not for the reasons most people think.

As mentioned earlier, the payouts – or the odds at which the casino pays you for winning bets – are smaller than the true odds against winning. This reduction ensures the house inevitably comes out ahead over the long run.

If casinos paid winning bets at true odds, roulette would be a fair game in which players break even over time. That would mean zero profit for gambling operators, which is why they always preserve an edge over their players.
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