1Two things to know about a fair coin
Every flip is its own 50/50
Before we test anything, here are the only two ideas you need. Watch them wiggle:
It's 50/50
One flip = two outcomes. Heads is just as likely as tails — half and half, every single time.
It has no memory
The coin can't remember. It has no way to know what it did last time — so the past can't change the next flip.
2Two rules people believe
After 5 heads, what's next?
Here are the two ways people guess the next flip. Same streak of heads — two different beliefs about what comes after.
Tails is due
Bets the next flip is mostly tails
The coin has to "balance out," so after a heads streak it's leaning toward tails.
Still 50/50
Bets the next flip is plain 50/50
The coin forgot the streak. The next flip is heads-or-tails, same as always.
3Your turn — flip the coin
Tap the coin and build a streak
Flip it yourself. Watch each result land, and watch your streak of heads grow. Can you feel "due for tails" creeping in?
4The real test
Flip hundreds of times after a streak
One coin won't settle the argument. So: every time the coin hits 5 heads in a row, we record the very next flip — hundreds of times. Which rule will be right more often?
Guess before you find out
We'll catch hundreds of "next flips," each one right after a 5-heads streak. If "tails is due" is real, tails should show up more than half. If the coin has no memory, it should be exactly half. Which rule wins?
5So is "due" totally wrong?
The average DOES even out — but not the way it feels
Over thousands of flips, the percentage of heads gets very close to 50%. So part of the feeling is true: things even out.
Those 5 extra heads stay in the count forever. Nothing erases them or owes you tails to match.
A fair coin has no memory — it's 50/50 every single time, so nothing is ever "due." The average evens out because new flips bury the old streak, not because tails ever catches up.
Psst, grown-ups: this is the gambler's fallacy. Coin flips are independent trials, so P(tails) stays 1/2 no matter the history. The law of large numbers says the relative frequency converges to 1/2 — but it makes no promise about the absolute difference between head and tail counts, which is not driven toward zero and often grows. Convergence happens by averaging over many trials (dilution), not by a compensating force.