What is the gambler's fallacy in gambling?

What is the gambler's fallacy in gambling? [Guildenstern stares at the coin. Heads, again.] Well, there's an even chance… Seventy-eight in a row. A new record, I imagine. Is that what you imagine? A new record? Well — no questions. Not a flicker of doubt. I could be wrong. That was Rosencrantz and Guildenstern Are Dead — heads, again and again, seventy-eight in a row. Every single flip was still an even chance. The feeling that the next one is due is the trap this lesson is about. The false belief that independent results are "due" to even out — that past losses, wins, or streaks change the odds of the next outcome. In plain terms: the coin has no memory, and neither does the game. A losing streak doesn't make the next win more likely — it only makes it feel overdue. “I’ve lost four straight — I’m due.” Nobody is due. Let's use this example. Flip a fair coin four times. Four heads in a row happens one time in sixteen — one half, times one half, times one half, times one half. Now flip it a fifth time. The chance of heads is still one half. Same at the sportsbook: after four straight losses at minus one-ten, your next bet still needs fifty-two point three eight percent to break even — one-ten divided by two-ten — exactly what it needed before the streak. A streak tells you what already happened. It never tells you what happens next. Lines move and books differ. Nothing here is a guarantee or a command to bet — it's how the number works.