Yes, the theory is right for the long run.
If you make 1 million bets of 10 cents, and the casino takes 1% house edge, you will end up losing about 1000$ which is equal to 10K bets or 1% from the total bets you did.
But if we talk here about a the very short term then the chances of you to lose/win more is much higher because there are less hits in total.
Personally this theory comes to teach people that they can't base there salary on gambling or even see it as a work, because in the long run they are guaranteed to lose.