Right, I have never heard "mean" being used in the context of casino games. I get what they are trying to say though, at some point the variance should start e

Right, I have never heard "mean" being used in the context of casino games. I get what they are trying to say though, at some point the variance should start evening out to reflect the odds of the game. But we should be practical and remember we're in a casino. A red/black bet on roulette is one of the few games where you're going to get that low of variance. With slots, you have to play a ton of games before you can get an idea of what the variance is just from your game play. In poker, the rule of thumb is 10,000 hands before the player can be confident of having an idea of how effective a change of strategy is. Overall, whoever wrote this article is out of their element. Like this bit... > So we think we can use our amazing powers of pattern recognition to determine that black is “due” and use that power to win big. Casinos love this delusion, because they know that math wins out in the end. This is contradictory. They're saying the player is wrong, because of math. By that line of thinking, the casino would also be wrong to love it, because of math. In a typical casino game, gambler's fallacy won't make your choice more or less correct, unless the choice is to keep playing or to walk away. The author doesn't specify why the casinos would love this though. As an aside, gambler's fallacy could affect more decision making in poker, but poker is a game of skill and the casino doesn't have a house edge on poker (they take a rake.)