If a player is in a Blackjack game using only one or two decks of cards in the "shoe," then the fallacy works -- but only because there were only a set number of choices to begin with, and every hand, more of those choices are eliminated.
I have a friend who has played poker professionally, and he says you have to treat it like a job and only bet what you can afford to lose. Consequently, he has had a great deal of success with it. He enjoys it. He's a true poker player, though. He likes the game. If he goes to a casino, he says he will spend maybe $10 on the slots, but nothing else. He told me to stay strictly away from roulette and craps because the house has a huge advantage in both games.