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The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
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The return of a slot machine is based on the published paytable, but also on the normally unpublished reels. For a five-reel slot machine, the player would need to know each symbol on each of the slot machine's five reels in order to calculate the odds. For a three-reel slot, the reels are normally weighted, and this would not be possible.
In statistics, this is called odds against. For instance, with a royal flush, there are 4 ways to draw one, and 2,598,956 ways to draw something else, so the odds against drawing a royal flush are 2,598,956 : 4, or 649,739 : 1. The formula for establishing the odds can also be stated as (1/p) - 1 : 1, where p is the aforementioned probability.
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