At a casino there is a game where the player bets some amount of money X and then spins a wheel. If the wheel says they win, they get X dollars....

At a casino there is a game where the player bets some amount of money X and then spins a wheel. If the wheel says they win, they get X dollars. Otherwise they lose and pay X dollars to the casino. I have the perfect gambling strategy to guarantee that I win this game. On the first round I bet X1. If I win, the payoff is X1 dollars. If I lose, I go "double or nothing" and bet X2 = 2X1 on the second game. I repeat this strategy, doubling my bet every time until I win. If I win on the first round, my payoff will be X1. If I win on the nth round, my payoff will be 2 nX1. Aside from the practical fact that I may run out of money before I win, this sequence of payoffs/losses doesn't satisfy the assumptions of the law of large numbers. Which assumption(s) does it violate?