The following consideration appears somewhat paradoxical to me, in the sense of defying one's intuition. As far as I know, it's an original idea. Suppose that a casino offers all games at fair value (and doesn't have any other charges such as an entry fee etc.) For example, there are games where you have a 50% chance of winning an amount equal to your stake etc. Suppose also that all the customers are compulsive gamblers who always gamble everything they have until they lose all their money. My immediate intuition would be that, of course, the casino wins money -- the customers are determined to throw their money away. However, that can't be true because for every transaction, the casino makes an expected gain of zero. So the casino will make zero profit in the long run no matter how hard the customers try to lose. I suppose it's a bit similar to the St. Petersburg paradox. Every once in a while you'd get a customer who keeps winning until the casino closes and that would wipe out the profits.