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While some casino games have a skill element in the outcome, some casino games are purely according to chance. Because all online casino games are partly or completely driven by chance, all casino games rely upon a random number generator, or RNG in the software that powers the game. The RNG is a mathematical application that does precisely what it says: generates a completely random number. Not all RNGs are exactly the same, and they have to be tested extensively to ensure that the numbers they generate actually are random.
In certain games, the utilization of an RNG has an obvious role. In European roulette, as an example, the RNG generates a number from 1 to 37 (with 37 corresponding to "0") on the roulette wheel. The RNG generates a number, the casino stops, and bets are paid or forfeited.
In craps, the RNG must generate two random numbers simultaneously, and in single deck card games, the RNG must generate a number from 1 to 52, with each of those numbers corresponding to a specific card. During an individual deck card game, the RNG has to "remember" which cards it has already dealt to ensure that they won't be dealt again. With multiple-deck games like finding online casino blackjack, the RNG has an much more complicated mathematical algorithm driving it.
Some RNGs require the user to specify an initial "seed" value, which itself varies randomly. A number of them use the time on a clock as a seed, so that there is no human intervention at all within the RNG. There are some RNGs that really involve numerous RNGs running all at the same time, with one RNG picking from among the results, creating a sort of super-randomness to the calculation. Remember, they are very oversimplified ways of describing how RNGs work, but it provides you with some notion of the "brain" behind the many online casino games you enjoy.
To be deemed as fair, numbers spit out by any RNG have to be unpredictable and unbiased. To make sure that this really is the situation, internet gaming platforms have to be tested regularly by independent testing entities like eCOGRA. The testing groups have to test the RNG algorithms over millions of hands of card games or millions of throws of dice to be certain that the numbers are unpredictable and unbiased.
Within your online research about internet gambling, you could stumble across someone or site telling you that the specific slot machine has a "cycle" that is predictable enough that you could learn when it's "due" for a jackpot, or which will want to sell you some sort of system for predicting hits. These ploys aren't gambles at all: they're just good ways to throw away your hard earned money. Save those hard-earned dollars for another thing!