Gambler's Fallacy/Monte Carlo Fallacy

This is almost the entire reason Las Vegas is Las Vegas. The Gambler’s Fallacy (also known as the Monte Carlo Fallacy) is the idea that just because one outcome from a random event has come up over and over again, that outcome is either less or more likely to happen again.

More simply, you’re in Vegas for a weekend. You hit the slots and lose on 34 straight tugs on the old one-armed bandit. Because you’ve lost so often, you feel like you’re “due” a win. Not so fast, Chief. The odds of winning the next game don’t change just because you stunk out loud on the previous 34 tries. Similarly, you might be on the winning streak of all winning streaks. You’re not “due” a loss just because you’ve been winning. The odds of losing on that machine are the same every time you play, no matter how many times you’ve won in a row.