In the long run, the house always wins.

The old axiom, "In the long run, the house always wins." is usually right. "Long run" is the key part here and is linked mostly to the percentage edge the casino has on all it's games. That is, the longer a gambler plays, the more likely they are to lose to the mathematical advantage the house enjoys.

Therefore, it is only in the short run that the gambler has a chance to win. He never has the advantage over the casino because the math is still on the side of the house, but at least he has chance.

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