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LotteryOracle · F-46

Thirty Years of Saturdays

One hypothetical routine, thousands of lives, and the full spread of outcomes.

A fictional 6/49 game: each play costs 2 credits. Match 3, 4, 5 or 6 for fixed prizes of 10, 100, 2,000 or 1,000,000 credits. No sharing, tax, inflation or rollovers; every play is independent.

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∑The maths, in plain language

Match probabilities are exact hypergeometric probabilities for one fixed line in a fictional 6/49 game. A categorical draw selects one mutually exclusive prize on each independent play. Spending and realised payouts are counted in integer cents. The lifetime jackpot probability is calculated analytically, independently of the number of simulated people. The shaded 10th–90th percentiles describe simulated outcomes, not a confidence interval for a parameter.

P(M=m) = C(6,m)C(43,6−m)/C(49,6); P(≥1 jackpot in T plays) = 1 − (1 − 1/C(49,6))^T

NIST · Binomial · NIST · Bonferroni

✦The story behind it

A fictional 6/49 game: each play costs 2 credits. Match 3, 4, 5 or 6 for fixed prizes of 10, 100, 2,000 or 1,000,000 credits. No sharing, tax, inflation or rollovers; every play is independent.

The mean includes the rare jackpot even when this simulation has none. Changing the routine changes both cost and exposure; it does not improve any individual play’s odds.