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For example, if a game is played by wagering on the number that would result from the roll of one die, true odds would be 5 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that the player gets the original amount wagered back.

However, the casino may only pay 4 times the amount wagered for a winning wager. In games such as blackjack or Spanish 21 , the final bet may be several times the original bet, if the player double and splits.

In American roulette , there are two "zeroes" 0, 00 and 36 non-zero numbers 18 red and 18 black. This leads to a higher house edge compared to the European roulette.

Therefore, the house edge is 5. After 10 spins, betting 1 unit per spin, the average house profit will be 10 x 1 x 5.

The house edge of casino games vary greatly with the game, with some games having as low as 0. The calculation of the roulette house edge was a trivial exercise; for other games, this is not usually the case.

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 , 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. Traditionally, the majority of casinos have refused to reveal the house edge information for their slots games and due to the unknown number of symbols and weightings of the reels, in most cases this is much more difficult to calculate than for other casino games.

However, due to some online properties revealing this information and some independent research conducted by Michael Shackleford in the offline sector, this pattern is slowly changing.

The luck factor in a casino game is quantified using standard deviations SD. The binomial distribution assumes a result of 1 unit for a win, and 0 units for a loss, rather than -1 units for a loss, which doubles the range of possible outcomes.

Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold.

After 10 rounds, the expected loss will be 10 x 1 x 5. As you can see, standard deviation is many times the magnitude of the expected loss.

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However, due to some online properties revealing this information and some independent research conducted by Michael Shackleford in the offline sector, this pattern is slowly changing.

The luck factor in a casino game is quantified using standard deviations SD. The binomial distribution assumes a result of 1 unit for a win, and 0 units for a loss, rather than -1 units for a loss, which doubles the range of possible outcomes.

Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold. After 10 rounds, the expected loss will be 10 x 1 x 5.

As you can see, standard deviation is many times the magnitude of the expected loss. The standard deviation for pai gow poker is the lowest out of all common casinos.

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

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 impossible for a gambler to win in the long term.

It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win.

It is important for a casino to know both the house edge and variance for all of their games. The house edge tells them what kind of profit they will make as percentage of turnover, and the variance 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 outsource their requirements to experts in the gaming analysis field.

From Wikipedia, the free encyclopedia.

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