Powerball's '4 + Powerball' Tier Is 1 in 913,129 — and Most Napkin Calculations Are Off by 64×

Powerball.com's Prize Chart lists the '4 white + Powerball' tier at 1 / 913,129.18. The hypergeometric derivation is C(5,4)·C(64,1) / C(69,5) × 1/26 = 320 / 292,201,338. Drop the C(64,1) factor — the way an 'I just need 4 out of 5 plus the red ball' intuition does — and you get 1 / 58,440,267, exactly 64× too rare. The bug is a single combinatorial factor, and it shows up in every consumer lottery calculator that treats partial-match tiers as constraints rather than hypergeometric counts.