Expected value (EV) is the average profit you'd make per ticket if
you played the same drawing infinitely many times. It's the sum of
every possible payout, weighted by how likely it is, minus what
the ticket costs. The formula:
EV = jackpot × P(jackpot)
+ Σ ( prizetier × P(tier) ) — over every non-jackpot prize tier
− ticket price
The jackpot term grows with the prize, the middle term is a fixed
contribution from all the smaller prizes, and the last term is what
you always pay. EV turns positive only when the jackpot gets large
enough to outweigh the ticket cost.
The fixed pieces
Every drawing uses the same odds and the same non-jackpot prize
amounts, so the middle term is a constant per game. Computed from
the official prize tables:
Powerball ($2 ticket)
Jackpot odds: 1 in 292,201,338
Mega Millions ($5 ticket)
Jackpot odds: 1 in 290,472,336
Every ticket gets a random multiplier (2X, 3X, 4X, 5X, or 10X)
that scales every non-jackpot prize. Expected multiplier ≈ 3.00,
already baked into the prizes below.
Putting it together
Plug the current jackpot in. For Powerball, EV = jackpot ÷ 292,201,338
+ $0.32 − $2. For Mega Millions, EV = jackpot ÷ 290,472,336
+ $1.12 − $5. The break-even jackpot — where EV crosses zero
before any other adjustments — is roughly $491M for Powerball and
$1.13B for Mega Millions.
What this number doesn't include
- Taxes. Federal withholding alone is ~37% on large prizes, plus state tax in most places. Real after-tax EV is materially lower.
- Lump sum vs. annuity. Advertised jackpots are the 30-year annuity. The cash option is typically about half.
- Splitting the jackpot. When jackpots get huge, more tickets get sold, which raises the chance of multiple winners splitting the pot.
Each of these pushes the true EV down. Treat the number on this page
as a generous upper bound.
