Sometimes I think theoretically it is profitable. Take a dice game. How many times in a row you might have reds with 50% winning chance? At first I thought not more than 7 times. Played with that strategy, was winning some, but lost in the end having 12 reds. Then I thought well it couldn't be more than 12 reds. Played with that strategy, was winning some, but lost in the end having 16 reds. ... After that I stopped. )
What makes you think there is a maximum to the reds you can get? The next roll doesn't depend on the previous roll. So if you have had 16 reds, chances of the next one being red are exactly the same as after having 16 greens.
The more bets you place, the longer your win/loss-streaks will be.
Assuming 50% chance and 2 bets, chances are one is red, one is green.
With 2^10 bets (1000 bets) chances are pretty big you hit 10 red or 10 green in a row.
Place 1 million (2^20) bets, and 20 in a row becomes very likely.