Independent Trials, Odds, and Casino Edge in Roulette

The rules of roulette are quite easy to grasp despite the broad range of betting options the game offers. Whether it is a straight up bet on an individual number or one on number properties like color, you put some money at stake and play against the house. If you lose, the casino collects your stake. When you win, the house pays you out.

In principle, having some money and learning to differentiate between the available bets are pretty much the only requisites to start playing roulette. However, if you take the game seriously, you should gain at least a rudimentary understanding of probabilities in gambling.

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

Why the Odds Never Change in Roulette?

1Independent Trials

Ever since roulette was first introduced to the floors of gambling houses, there have been hot debates as to whether the outcomes of subsequent spins are affected by those of previous spins. Indeed, many roulette players base their decisions on past results.

First, they look for a pattern and wait for a given number, color or parity to appear several times in a row. Then, they would either bet on the opposite result because they think it is due or they would back the same outcome/number because it is on a hot run. Both lines of reasoning are flawed because they infer roulette wheels “remember” past events.

This simply is not the case here. Roulette is a game of independent events where the odds of the trials to follow are not affected by the odds of the trials that have previously occurred. Each spin should be considered an isolated trial and as such, it has no impact on the spins that come next.

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 as much money as you wish on what colored marble you will randomly pick from the fish tank. You decide to stake $10 on a black marble.

You stand even chances of winning and losing your money because the number of red marbles in the tank is equal to the number of black ones. You pull out a black marble on the first try and win. Then you put the marble you have just picked back in the tank and prep up for another try.

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

This is an example of how games of independent trials work. Things are pretty much the same in roulette, the only difference being the chances of winning and losing are not equal because of the additional zero pocket. Nevertheless, the true odds remain the same regardless of how many consecutive times the same outcome has occurred. 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 the past. When randomness is at hand, each item from a given set (in this case numbers 0 through 36) has an equal probability of being picked. In other words, it is impossible to predict with certainty which item from the set will get picked.

Similarly, a roulette spin is an isolated, and therefore, independent trial unless the wheel itself shows bias toward specific numbers or sections of numbers causing them to occur more frequently. Potential biases can be detected within several thousands of trials.

4Biased Wheels

Let’s suppose you go through a set of 3,000 or 4,000 spins. Assuming the results you witnessed do not deviate from the mathematical expectation of the game, you are most likely observing a random wheel.

However, if you happen to notice 32 red and 10 black have failed to turn up even once over the course of 4,000 rounds of play, the wheel likely shows some bias against them. One such wheel does not yield truly random results.

Observant roulette players are prone to exploiting such biases. Casino operators do everything within their means to prevent this from happening. Wheels are tested on regularly to ensure they show no bias.

Modern roulette tables are usually equipped with scoreboard where the past ten or twenty results are displayed. These scoreboards serve a double-sided purpose. On one hand, they enable trend bettors to discern patterns and bet accordingly.

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

Probability and Odds – Two Sides of the Same Coin

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

Measuring Roulette Probabilities
The Concept of Odds

Measuring Roulette Probabilities

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

In the context of roulette, there are two possible outcomes from the perspective of the player – you either lose or win. Therefore, the overall number of possible results is the sum of all outcomes that lead to a loss and all outcomes that can yield a win.

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

With double street bets, there are 6 winning numbers and 31 losing ones. Therefore, the probability of winning in this case is equal to 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 1 green zero. The calculation will be 18/(18+19) = 18/37 = 0.48648 x 100 = 48.65%. You can easily determine the probability of winning with any roulette bet with this formula.

Since gamblers are prone to looking for trends, let’s see what is the likelihood of the same outcome occurring three times in a row. To calculate this, you need to raise the probability of a single number hitting to the third power like so: (1/1+36)3 = 1/373 = 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. Because of this, they are not converted into percentages or decimals but are expressed in a fractional format like 2/3 or 2:3, spoken as “two to three”.

To give an example with 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. The ratio is more often expressed in reverse in the context of gambling. The house is practically betting against its patrons and therefore, lists the payouts as odds against the player winning.

The odds against winning with a straight up bet are 36 to 1, i.e. you should collect 36 units in net profits with a bet of 1 unit if you play a fair game. In reality, the house always pays less than the actual odds against winning, which is how it secures its profit margin.

Casinos would sometimes resort to subtle tricks to make their odds appear more appealing than they are. One such trick is to list the odds as “2 for 1” instead of “2 to 1”, for example. What’s the difference? If you are paid 2 to 1, you receive 2 units in net profits plus your original one-unit wager. When the odds are listed as 2 for 1, they pay you 2 units but your initial one-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 up a profit is the primary concern and purpose of all businesses and gambling operators are no exception to this rule. You have probably heard the popular expression “The house always wins”. And this is true, albeit not for the reasons most laymen think.

Provided that you have read carefully, you probably remember we mentioned earlier the payouts (i.e. the odds at which the casino pays you for winning bets) are smaller than the true odds against winning. This reduction is what causes the house to inevitably win in the long run.

If casinos paid winning bets at true odds, roulette would have been a fair game where players inevitably break even in the long term. This translates into zero profit for the gambling operators, which is why they ensure they always maintain an edge over their players.
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