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

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

The story behind it

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