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Poker is quite different. In roulette, the house advantage is probabilistic. As the linked page shows, that advantage is overwhelmingly likely to materialize, and rather quickly at that. But the probability that you play a million rounds of roulette and end up ahead isn’t exactly zero, just such a ridiculously small number you might as well call it zero for real life purposes.

Casinos make money on poker play differently, and in a few ways. The simplest is “rake”. They take a fixed percentage of every pot. This is different because it’s not probabilistic. The casino isn’t gambling its own money. It’s just a tax.

Money only comes in from players. So the EV of all players is negative, because a little is flowing out to the casino every hand. The chance players as a whole end up ahead isn’t near zero, it is zero.

If everyone was playing theoretically perfect poker every hand, all individual players EV are also negative. But, no one is playing perfect all the time. So you can get ahead because you’re not beating the odds. You’re beating other players.




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