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Mathematics

The Law of Large Numbers and the Gambler's Fallacy

Quick fact

In a fair coin toss, the probability of heads is always 50%, regardless of previous outcomes; after a run of five heads, the next toss still has a 50% chance of heads. The law of large numbers only guarantees that the overall average will approach 50% over many tosses—it does not predict a 'correction' in the short run.

Why this is interesting

After flipping a coin and getting heads five times in a row, do you feel a tail is 'due'? That feeling is one of the most common statistical illusions—and it has a name.