After eight heads in a row, tails can feel overdue. For a fair coin, the next toss still has a 50–50 chance.
That belief is the gambler’s fallacy: treating earlier independent outcomes as if they push the next one toward balance. Each toss is a fresh physical event; the coin has no memory. Eight heads in a row is unlikely before the sequence begins, but once those tosses have happened, they do not change the odds of the next toss.
A particular sequence of ten tosses—say, heads, tails, heads, then seven more outcomes—is just as likely as ten heads: each has probability 1 in 1,024 for a fair coin. A shuffled-looking sequence seems more typical because many different sequences look mixed, not because any one exact order is favored.