Gambler's Fallacy

“A streak feels as if it demands repayment even when the mechanism keeps no memory.”

01 / PLAINLY

What it means, plainly

The gambler's fallacy treats a run of independent outcomes as making the opposite result ‘due.’ If the mechanism has no memory, the streak does not correct the next probability.

02 / CONTEXT

A little more

The fallacy expects independent outcomes to balance in the short run: after many heads, tails seems due. For a fair coin, the next toss remains 50/50.

03 / WHY IT MATTERS

Why it matters

It keeps a desire for balance from becoming a prediction and makes you check whether trials are truly independent first.

04 / EXAMPLE

A familiar example

Five reds in a row on an ideal roulette wheel do not make black more likely on the next spin.

05 / LIMIT

What it does not mean

The warning assumes independence and stability; a streak may still prompt a check for a changed or biased mechanism.

06 / NOTICE

Notice it in your day

Write the probability of heads before and after imagining five tails from a fair coin. Explain what would need to change in the mechanism to update it.

FINAL NOTE

The idea worth keeping

Before calling an outcome overdue, check whether the process has any real memory.

QUESTIONS / 02

Questions people still have

Why does a streak not make the opposite result ‘due’?

If trials are independent and the mechanism is stable, earlier outcomes do not change the next probability.

When might a streak deserve investigation?

When there is reason to suspect the mechanism changed, is biased, or has memory.