Comment by kbolino

As cbr pointed out, the two sets are equinumerous (y_n = 2 * x_n puts them into 1:1 correspondence). As long as you gamble a finite number of times, and your losses are finite, you will always have exactly as much money as you started with, if you started with infinite money. Since there is no such thing as infinite money, this model is only a practical approximation when your losses are greatly dwarfed by your starting capital.