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Lesson
Lesson 1. The gambler's fallacy and randomness
Understand why we have a poor feel for randomness: the gambler's fallacy, belief in “the law of streaks”, and the idea that random things should “look random”.
A coin has no memory
Gambler's fallacy
The gambler's fallacy is the belief that past random outcomes affect future ones. If a coin has come up heads five times in a row, it feels like “now it's bound to come up tails, to even things out”. That's false: a coin has no memory. The chance of tails on the sixth toss is the same 50% as always.
It's also called the Monte Carlo fallacy: in 1913, at the Monte Carlo casino, the roulette ball landed on black 26 times in a row. Gamblers bet heavily on red, sure it was “bound to come up any minute now” — and lost entire fortunes. Every spin is independent: a long run of black doesn't make red any more “due”.
Don't confuse this with a different fact: over the long run, heads and tails really do come up about equally often (the law of large numbers). But that's not because the coin “makes up for” past tosses; it's because individual imbalances simply drown in a huge number of tosses. The future doesn't “correct” the past — it dilutes it.
The same fallacy shows up in lotteries (“this number hasn't come up in ages, time to bet on it”) and in gambling in general.
Lesson notes
Gambler's fallacy
The gambler's fallacy is the belief that past random outcomes affect future ones. If a coin has come up heads five times in a row, it feels like “now it's bound to come up tails, to even things out”. That's false: a coin has no memory. The chance of tails on the sixth toss is the same 50% as always.
It's also called the Monte Carlo fallacy: in 1913, at the Monte Carlo casino, the roulette ball landed on black 26 times in a row. Gamblers bet heavily on red, sure it was “bound to come up any minute now” — and lost entire fortunes. Every spin is independent: a long run of black doesn't make red any more “due”.
Don't confuse this with a different fact: over the long run, heads and tails really do come up about equally often (the law of large numbers). But that's not because the coin “makes up for” past tosses; it's because individual imbalances simply drown in a huge number of tosses. The future doesn't “correct” the past — it dilutes it.
The same fallacy shows up in lotteries (“this number hasn't come up in ages, time to bet on it”) and in gambling in general.
Why streaks fool us
True randomness looks suspiciously “non-random” to us. If you actually toss a coin 20 times, streaks like HHHH or TTTTT will almost certainly appear — and that's normal. But to people such streaks seem “wrong”, as if there were a pattern.
Because of this:
— When a playlist is on “shuffle”, we feel that one artist plays “too often” and suspect the shuffle is broken. In fact, true chance produces exactly such clusters. (Some services deliberately make shuffle LESS random so that it will SEEM more random.)
— We see a “lucky streak” or “the law of streaks” where there are only random coincidences.
— A player who scores several times in a row is credited with the “hot hand”, although it's often within the range of ordinary chance.
The takeaway: the brain is a poor generator and a poor judge of randomness. It looks for patterns everywhere, even where there are none. This is called apophenia — the tendency to see meaningful patterns in random noise.