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In games where players are not competing against the house, such as poker , the casino usually earns money via a commission, known as a " rake ". The luck factor in a casino game is quantified using standard deviations SD.
Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold.
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 casino games.
Many casino games, particularly slot machines, have extremely high standard deviations. The bigger size of the potential payouts, the more the standard deviation may increase.
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.
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