Reviewed by CalcMulti Editorial Team·Last updated: ·← Probability Hub
Lottery odds are pure combinatorics. To win the jackpot, your ticket must match r numbers drawn from a pool of n, with order not mattering. The total number of possible combinations is C(n, r) = n! / (r! × (n−r)!).
Powerball (as of 2024): draw 5 from 69 white balls + 1 from 26 Powerballs. Jackpot odds = C(69,5) × 26 = 11,238,513 × 26 = 292,201,338. That's roughly 1 in 292 million.
Mega Millions: draw 5 from 70 + 1 from 25. Jackpot odds = C(70,5) × 25 = 17,259,390 × 25 = 302,575,350. Slightly longer odds than Powerball.
The expected value of a $2 Powerball ticket is almost always negative. Even at a $1 billion jackpot, after federal taxes (~37%) and the lump sum discount (~60% of advertised jackpot), the after-tax jackpot is roughly $372 million. Expected value ≈ $372M / 292M − $2 ≈ −$0.73 per ticket.
Jackpot Odds = 1 / (C(n,r) × B)
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.