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ELI5 Yahaaa

Objects have no memory

Why Does a Coin Not Owe You Heads?

A coin has no memory, so a run of tails changes nothing about the next throw.

What it feels like?Tails five times —heads is dueWhat is true The next throw is stillfifty-fifty
The coin does not know what it did last time.

  1. Step 1 of 5

    Chance measures how often something happens.

    A coin — two outcomesA die — six outcomes

    A fair coin lands heads about half the time and a die shows a six about one throw in six. That is all a probability is.

  2. Step 2 of 5

    Objects cannot remember their past throws.

    1 Throw a six2 The die isunchanged3 A six is justas likely again

    A coin has no mechanism for recording history. Nothing about it changes between throws, so nothing can make a result overdue.

  3. Step 3 of 5

    Runs are normal, not signs of anything.

    Two in a rowone time in fourThree in a rowone time ineightFive in a rowone time inthirty-two

    Five tails in a row happens about once in every thirty-two attempts, which is often enough that it means nothing at all.

  4. Step 4 of 5

    Long runs even out by dilution, not correction.

    What people expect Later throws correct itWhat happens It just gets diluted

    Nothing pushes the count back towards half. Early imbalances simply matter less as thousands of later throws swamp them.

  5. Step 5 of 5

    This mistake costs people real money.

    A run happensentirely normalIt feels like a patternour brainsinsistThe odds never movedeach throw isfresh

    Betting more because a result is 'due' is the gambler's fallacy. The odds never shift, so the strategy has nothing behind it.

    At a Monte Carlo table in 1913 the ball landed black 26 times running, and gamblers lost fortunes betting that red was overdue.

The short version

A coin or die has no memory, so past results never change the odds of the next throw, however long the run has been.

Try it yourself

Flip a coin fifty times and record it. You will almost certainly see a run of four or five, and it means nothing.

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