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Law of Large Numbers
“Stability emerges in the average of many repetitions, not as a debt the next trial must repay.”
01 / SUMMARY
In short
Under suitable conditions, the sample average approaches the expected value as observations increase. The law describes convergence of averages, not immediate correction of streaks.
03 / SCENE
In the wild
The proportion of heads from a fair coin tends toward 0.5 over very many tosses, even though short runs are uneven.
04 / LIMIT
The limit
It does not say that after ten heads the next toss must be tails.
FINAL NOTE
What remains
Separate the cumulative behavior of many trials from the next outcome.