Problems with this reasoning (Gambling) 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.
 A: This is certainly not formal, but maybe it will help you understand the system flaws a bit better. 
Consider $X$ to be the waiting-time random variable representing the time until you finally win a bet and profit. 
If (as mentioned in the comments) you have an infinite supply of money to bet with, then so long as $X$ is a proper random variable, i.e.
$$P(X < \infty) = 1$$ you will eventually profit with a net gain of 1 unit. With an infinite supply of money, no casino limits, an unlimited amount of time to continue gambling, etc. one could theoretically win as much money as they desired with this strategy given any game where $X$ is a proper random variable, simply by adjusting their first bet (representing their unit). 
Realistically however, it doesn't work out so nicely. In order for an individual to assure themselves a profit, they would need $X$ such that 
$$P(X<k) = 1$$
where $k$ represents the limiting number of gambles before they either 


*

*run out of money to gamble with

*run out of time in which to gamble

*...any other constraint on how long they can gamble that may apply


You can begin to now see the flaws with this system. Finite supplies of money and time as well as other constraints render $P(X<k)<1$, and expose the gambler to the risk of losing many more units of money than the 1 that they are attempting to win with this system. 
Even if an individual has enough money and time such that they can assure themselves a profit, their first bet (i.e. unit they are attempting to gain) is more than likely so small that by the expected time at which they win their returns will be minimal, either as a result of how small they were forced to make their first bet, or how long it took them to finally win. 
So in short, I presume unless your friend is incredibly rich, or attempting to win some small, small amount of money, or some combination of the two, the odds are still against him. 
