Lottery Expected Value Calculator
The Number That Explains Why the House Always Wins
Expected value is the probability-weighted average outcome of a bet, and for a lottery ticket it's almost always negative — the tiny probability of a huge jackpot doesn't compensate for the ticket's cost once you weight it by how unlikely that jackpot actually is. This calculator computes exactly that figure per ticket, combining jackpot odds, jackpot size, any smaller-prize expected value, and ticket cost into one signed number that tells you precisely how unfavorable (or, rarely, favorable) a given ticket is.
The Formula
P(jackpot) is 1 divided by the odds denominator (the X in "1 in X"). The jackpot's contribution to expected value is almost always a fraction of a cent per dollar of jackpot, since the odds denominator is typically in the hundreds of millions.
Where This Matters
- Understanding why EV is (almost) always negative — even a $500 million jackpot at 1-in-292,201,338 odds only contributes roughly $1.71 of expected value per ticket — less than a typical $2 ticket price, before even counting smaller prizes.
- Spotting the rare positive-EV moment — on very rare occasions, an unusually large rolled-over jackpot can push expected value (before taxes) into positive territory, which is the mathematical explanation for surging ticket sales during record jackpots.
- Comparing games on a like-for-like basis — two lotteries with different ticket prices, odds, and jackpots can be ranked directly by which has the least negative expected value.
| Component | Value |
|---|---|
| P(jackpot) | 0.00000000342 |
| Jackpot contribution | $1.71 |
| Smaller-prize contribution | $0.32 |
| Ticket cost | −$2.00 |
| Expected value | $0.03 |
This worked example lands close to break-even only because of an unusually large jackpot; typical jackpots produce a clearly negative expected value per ticket.
How to Use This Calculator
- Enter the ticket cost.
- Enter the jackpot amount.
- Enter the jackpot odds as the X in "1 in X" (from the lottery's published odds).
- Enter the expected value of smaller prizes, if known (optional).
- Select Calculate for the total expected value per ticket.
Related Calculations
Check the odds behind this calculation with the Lottery Odds Calculator, or see what taxes do to a jackpot with the Lottery Tax Calculator.