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The calculation of the Roulette house edge was a trivial exercise; for other games, this is not usually the case.

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In games which have a skill element, such as Blackjack or Spanish 21 , the house edge is defined as the house advantage from optimal play without the use of advanced techniques such as card counting or shuffle tracking , on the first hand of the shoe the container that holds the cards. The set of the optimal plays for all possible hands is known as "basic strategy" and is highly dependent on the specific rules, and even the number of decks used. Good Blackjack and Spanish 21 games have house edges below 0. Online slot games often have a published Return to Player RTP percentage that determines the theoretical house edge.

Some software developers choose to publish the RTP of their slot games while others do not. The luck factor in a casino game is quantified using standard deviation SD. The standard deviation of a simple game like Roulette can be simply calculated because of the binomial distribution of successes assuming a result of 1 unit for a win, and 0 units for a loss. Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold. After enough large number of rounds the theoretical distribution of the total win converges to the normal distribution , giving a good possibility to forecast the possible win or loss.

The 3 sigma range is six times the standard deviation: three above the mean, and three below.

There is still a ca. The standard deviation for the even-money Roulette bet is one of the lowest out of all casinos games.


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Most games, particularly slots, have extremely high standard deviations. As the size of the potential payouts increase, so does the standard deviation.

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Unfortunately, the above considerations for small numbers of rounds are incorrect, because the distribution is far from normal. Moreover, the results of more volatile games usually converge to the normal distribution much more slowly, therefore much more huge number of rounds are required for that. As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over.

From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played. As the number of rounds increases, the expected loss increases at a much faster rate. This is why it is practically impossible for a gambler to win in the long term if they don't have an edge. It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win. The volatility index VI is defined as the standard deviation for one round, betting one unit.

Therefore, the variance of the even-money American Roulette bet is ca. The variance for Blackjack is ca. Additionally, the term of the volatility index based on some confidence intervals are used. It is important for a casino to know both the house edge and volatility index for all of their games. The house edge tells them what kind of profit they will make as percentage of turnover, and the volatility index tells them how much they need in the way of cash reserves.

The mathematicians and computer programmers that do this kind of work are called gaming mathematicians and gaming analysts. Casinos do not have in-house expertise in this field, so they outsource their requirements to experts in the gaming analysis field. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

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