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Ages 15–18 · Grades 9–12 · Probability & Statistics

OddsForge

Six heads in a row — luck, or a loaded coin? A p-value answers one precise question: if the honest odds really held, how often would you see a run this extreme by chance? Predict how surprising each case is, then read the answer off the binomial tail — and watch how peeking until it “looks significant” manufactures a false alarm. Evidence, never a verdict.

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Fifty frames a second Expected goals Goals by chance Nested races Missing cards A 1% drop rate Per attack or per shot?

A case · you decide

Reza and the lucky die

Reza, 16 — convinced the die in a friend's board game is loaded toward sixes

The idea in play: a p-value asks how surprising the data would be if the honest odds held — and checking again and again until it "looks significant" makes false alarms.

In 30 rolls the die showed 10 sixes. A fair die would average 5. Reza wants to accuse his friend at the next game night.

Ten sixes in thirty rolls feels like a lot. A fair die gets ten or more sixes in about one game in fifty (p ≈ 0.02).

That is surprising-ish, and it is still one test from one set of rolls.

What is the fairest conclusion from 10 sixes in 30 rolls?

Reza plans to keep rolling and check after every roll, stopping the moment it looks significant. Why is that a problem?

Weigh a streak →

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