A coin has no memory

Suppose a fair coin comes up heads five times in a row. Many people feel tails is now "due". It isn't. The coin does not know what it did before; each toss is still one half.

This feeling has a name — the gambler's fallacy — and it is ordinary, not foolish. Our sense of pattern expects runs to even out quickly. They do even out, but only by being swamped by many later tosses, never by the coin correcting itself.

The useful habit is to ask: are these events independent? For coins and dice, yes. For things with memory — a deck you are dealing from, a queue that is shrinking — the past really does change the odds.