Why real randomness looks streaky
· 5 min read
People expect too much evenness
Ask people to invent a random coin sequence and they alternate too often. Real fair flips produce runs: in 100 flips a run of six or more identical results is more likely than not.
No outcome is ever 'due'
Independent events have no memory. A sequence that has favoured one side so far does not push the next result the other way. Believing otherwise is called the gambler's fallacy, a well-studied reasoning error that this site only uses as a teaching topic.
What a fair shuffle looks like
The Fisher–Yates shuffle walks down the deck, swapping each card with a random card at or before it. Every one of the 52! ≈ 8 × 10⁶⁷ orderings is equally likely. A naive “swap with any random position” version is subtly biased because its number of equally likely swap sequences cannot divide evenly into 52!.
for i from n − 1 down to 1: swap(deck[i], deck[random 0..i])Seeds make randomness testable
Software uses pseudo-random numbers. Starting from the same seed produces the same sequence, so any experiment on this site can be repeated exactly.