The myth of the house advantage

Don’t let the title fool you, for I know quite well that in all casino games the house has a probabilistic advantage for any one play of a game. But an interesting mathematical phenomenon, sometimes named Gambler’s Ruin, suggests that precisely 50:50 odds should still make them money.

Let me sum it up in slightly more of a layman’s terms. Assume the house has infinite money (compared to an individual player, this is essentially true). If the player never quits, he’ll eventually get a down swing in his luck and lose all his money to the house. If, on the other hand, the house gets a down swing, then it will give the player some more money, just to take it back when it hits its up swing.

Mathematically, on equal odds, the player with more money has the odds to take the rest. The house has more money, so it takes the money. Believe it or not, you can’t take advantage of that by “knowing when to quit.” For every time you double your money, a fellow just like you has gone bankrupt with nowhere to go but home. And that is the story of gambling: you can’t make yourself win with “money management”1. If you can’t win with everything you’ve got, you shouldn’t be playing at all2.

1Not to be confused with “chip management” in a Poker tournament. That will in fact get you much closer to winning—but you still have to know how to play the hands.

2Unless you have some ulterior motive, which many people do. If you go to Vegas to have a good time, then you’re paying some fraction of your bankroll to have that good time. In that case, you should play with the minimum amount of money possible that will still allow you to have fun.

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