As a concept, the expected value in roulette is similar to the desired value in statistics. In many ways, the expected value is just as it sounds – the most expected outcome/value (usually monetary) from a random trial in any financial experiment. In the case of roulette, the expected value provides us with a general approximation of how much money we can envisage earning from the game or how much we can expect to lose. This article aims to examine roulette along the lines of odds, probabilities, and discrete random variables. With these tools, players choose strategies that help them win at roulette – in the long and short term.
First off, let’s quickly review how roulette works.
An American roulette wheel has 38 pockets or spaces on it. Thirty-six of these pockets are numbered 1 to 36 and colored either red or black. The two remaining pockets are colored green and numbered 0 and 00. The croupier spins the wheel, and simultaneously, a ball goes in the opposite direction. Once the wheel slows down or stops, the ball settles in one of the pockets. The pocket could be red, green, or black and has numbers 1-36 or 0 or 00—the entire object of roulette betting to predict where the ball lands. There are different payouts for different predictions, with the more difficult forecasts attracting more significant profits. Difficult forecasts have lower probabilities of occurring, while the opposite is trustworthy for more accessible forecasts.
Probabilities And Expected Value In Roulette
One of the most popular bets in roulette is the Red/black bet. This bet is an example of an outside chance with even money payout – commensurate with the approximate probability of getting the prediction correct. Have a mental picture of the layout of the American wheel, as discussed above. Since the wheel has a uniform probability distribution, the probability of the ball landing in any of the 38 pockets is the same – precisely 1/38. Let’s assume we are betting on BLACK. Since half of the non-green spaces are red and the remaining half are black:
- The probability of hitting black is 18/38. Based on the fact that the payout is 1:1, the black bet, if successful, would result in a net return of $1 from a stake of $1.
- The probability of not hitting black equals the possibility of red or green, which is 20/38. It would mean a lost bet, leading to a net return of -$1.
The net return from the bet is our discrete random variable. Let’s assign it “X.”
To calculate the expected value for X, all we need to do is obtain the product of every probability and its respective value and sum them up. In this case, we will get the value development of the lost bet and its likelihood and add it to the product of the value of the success chance and its probability.
P(of Getting Black) x (Value of X for Black) + P(Not Getting Black ) x (Value of X for Not Black) = 18/38 x 1 + 20/38 x (-1) = -0.053.
Therefore, the expected value of betting on Black with a stake of $1 is -$0.053.
Frequently Asked Questions About Online Roulette
The odds of hitting a specific number on a roulette wheel depend on the type of roulette being played. In American roulette, which has a double-zero wheel, the odds of hitting a specific number are 37 to 1 (or 38 to 1, depending on how the casino structures its payouts). This is because there are 38 possible outcomes, with numbers 1 through 36, a single zero, and a double zero. In European roulette, which has a single-zero wheel, the odds of hitting a specific number are 36 to 1. This is because there are 37 possible outcomes, with numbers 1 through 36 and a single zero.
It's important to note that the odds of hitting a specific number are different from the odds of winning a specific bet, such as a straight-up bet on a number. The odds of winning a straight-up bet are lower than the odds of hitting the number, as the player will lose if the ball lands on 0 or 00 (in American roulette).
It is highly unlikely that a reputable online casino would manipulate the outcome of a spin in an online roulette game. The online casino industry is heavily regulated and monitored by various gaming commissions and organizations that ensure fair play for all players. Additionally, reputable online casinos use a random number generator (RNG) to determine the outcome of a spin, which ensures that each spin is completely random and unbiased. It is worth noting that there have been some instances of unregulated or illegal online casinos manipulating the outcome of their games in the past, but these are rare and tend to be quickly shut down by authorities.
It is always recommended that players only play at reputable and licensed online casinos, to ensure that the games are fair and that their personal and financial information is protected.
It is highly unlikely that a reputable online casino would manipulate the outcome of a spin in an online roulette game. The online casino industry is heavily regulated and monitored by various gaming commissions and organizations that ensure fair play for all players. Additionally, reputable online casinos use a random number generator (RNG) to determine the outcome of a spin, which ensures that each spin is completely random and unbiased.
It is worth noting that there have been some instances of unregulated or illegal online casinos manipulating the outcome of their games in the past, but these are rare and tend to be quickly shut down by authorities. It is always recommended that players only play at reputable and licensed online casinos, to ensure that the games are fair and that their personal and financial information is protected.
The odds of winning in online and physical roulette are generally the same, assuming the game is being played at a reputable and licensed casino. Both types of roulette use the same basic rules and have the same types of bets available, with the same corresponding payouts. Online roulette games use a random number generator (RNG) to determine the outcome of a spin, which ensures that each spin is completely random and unbiased. This is similar to the physical roulette wheels which are also unbiased and random. The only difference in odds may come from the type of roulette wheel being used. American roulette, which has an extra pocket (00) on the wheel, has slightly worse odds than European roulette, which only has one green zero.
Overall, the odds of winning in online roulette are the same as in physical roulette, but online roulette has the added convenience and flexibility of being able to play from anywhere and at any time.
It is possible to develop betting strategies for online roulette, but it is important to understand that no strategy can guarantee a win. Roulette is a game of chance, and the outcome of each spin is determined by a random number generator (RNG). This means that no amount of strategy or skill can change the odds of the game, and each spin is independent of all previous spins. Some popular betting strategies for roulette include the Martingale strategy, in which players double their bet after each loss to eventually recoup their losses and make a profit, and the Fibonacci strategy, which follows a specific sequence of bets determined by the Fibonacci sequence.
It's important to keep in mind that these strategies are not a guarantee of winning and can lead to significant loses, specially in the short term. The best strategy for playing roulette is to set a budget for yourself, and stick to it. It's also important to be aware of the various types of bets and their corresponding payouts, and to only make bets that you can afford to lose.
Ultimately, the key to enjoying roulette is to remember that it is a game of chance, and to approach it with a sense of fun and entertainment rather than as a way to make money.
Online roulette games generate random numbers for the spin using a technology called random number generator (RNG). An RNG is a software program that uses mathematical algorithms to generate a sequence of numbers that cannot be predicted or influenced. The RNG generates a random number, which corresponds to a specific outcome on the roulette wheel, such as a specific number or color. The number generated by the RNG is then used to determine the outcome of the spin.
It is important to note that the RNG used by reputable online casinos are regularly tested and certified by independent auditing companies to ensure that they are truly random and unbiased. Additionally, many online casinos use a protocol called cryptographic hashing, that ensures that the RNG's output is truly random and cannot be predicted or influenced by any third-party.
In summary, online roulette games use a RNG to generate random numbers for the spin, ensuring that each spin is unbiased and independent, and the outcome is truly random.
In general, the payouts for online roulette are the same as in a physical casino, assuming the game is being played at a reputable and licensed online casino. The payouts for different types of bets in roulette are based on the mathematical probability of those bets winning, and these probabilities are the same whether the game is played online or in a physical casino. However, there may be some variations in payouts depending on the specific rules of the game and the casino. For example, some online casinos may have different payouts for the same type of bet, or they may have slightly different rules for the game.
It's always recommended to check the rules and payouts of a specific online roulette game before playing. It's also important to keep in mind that the payouts for some types of bets may be different between American and European roulette, due to the additional pocket on the wheel in American roulette. In general, players should expect the payouts to be similar to those in physical casinos, but it's always good to double check the rules and payouts before playing.
Yes, many we do offer bonuses for playing roulette, such as welcome bonuses, referral bonuses, and loyalty bonuses.
Yes, there are different types of online roulette games such as European roulette, American roulette, French roulette, and more. Each game has its own set of rules and variations.
Some online casinos may offer progressive jackpot roulette games, where a small percentage of each bet is added to a growing jackpot which can be won by hitting a specific combination of numbers or by triggering a bonus round.
