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Reading the draws and working out what chance predicts.

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LotteryOracle

LotteryOracle reports what happened; it does not predict what is next. Every draw is independent — no number is ever "due".

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Take 5: Arithmetic Progression Garden — LotteryOracle

LotteryOracle · F-48

Arithmetic Progression Garden

Find equal steps and mirror pairs in history, then grow a fair comparison.

Choose a ball game with established pool rules: 1–8 numbers drawn, with labels from 1 to 100. An observed maximum alone is insufficient.

∑The maths, in plain language

✦The story behind it

Up to 240 recent valid draws from one game, era and slot. Every motif counts, including overlaps. Exact expectations use inclusion probabilities; equal-gap pairs use 8,000 fair simulations with a standard error. The fair archive has the same draw count. Expected motif count is not the probability of finding any motif; browsing these four families is descriptive.

E[APℓ] = Σd [N−(ℓ−1)d] × C(k,ℓ) / C(N,ℓ)

NIST · Hypergeometric distribution

Equal spacing is easy to notice. In a 6/49 draw, the expected number of three-term arithmetic progressions is about 0.625. Several can occur in the same draw; the garden makes these overlaps visible.

NIST · Hypergeometric distribution