Arithmetic Progression Garden

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