Some mate of mine is some casino lover, and he usually says something like this to justify his hobby.
"Let's suppose we have a game, in which I gamble something, and if I win, I receive the double, and if I lose I don't receive anything. So I gamble 1 dollar. If I win, I stop gambling. If I lose, I gamble 2 dollars. If I win now, I stop gambling, but if I lose, I gamble 4 dollars, and so. Then in the end, when I win I will always have won 1 dollar".
I see a few problems with that reasoning. What if he keeps losing until he does not have more money? What does he do then?
Another way for me to think it is, let's suppose that the game is not fair, so he has a negative expected value for this game. Independently of how he gambles, he'll tend to lose, and if the only way for it to happen is just not winning even once, it will happen eventually.
So, is there any other problem with that reasoning?
Sorry, I don't know which tag to use here, I think probability may not be too appropiate.