What Is Expected Value?
Expected value (EV) is one of the most fundamental concepts in probability and statistics — and it's especially revealing when applied to lottery tickets. Simply put, EV is the average amount you can expect to win (or lose) per ticket over the long run, accounting for all possible outcomes and their likelihoods.
The formula is straightforward:
EV = (Probability of Winning) × (Prize Amount) − Cost of Ticket
When this number is negative, you are statistically losing money on average every time you play. For the vast majority of lottery tickets, this is exactly the case.
A Simple Example
Suppose a lottery has:
- Jackpot: $10,000,000
- Odds of winning: 1 in 14,000,000
- Ticket price: $2
EV = (1/14,000,000) × $10,000,000 − $2 = $0.71 − $2 = −$1.29
On average, every $2 ticket returns about 71 cents in value — a loss of $1.29 per play. This is a "return to player" of roughly 35%, which is far below most other forms of gambling.
Does EV Ever Turn Positive?
In theory, yes — when a jackpot grows large enough, the EV can approach or exceed the ticket price. However, several factors keep real-world EV negative even during rollover jackpots:
- Taxes: Lottery winnings are taxed heavily in most countries, often reducing the headline prize by 30–50%.
- Lump sum vs. annuity: Advertised jackpots are often annuity values. The lump-sum cash option is typically 50–60% of the headline figure.
- Jackpot splitting: During large rollover periods, more tickets are sold, increasing the probability of multiple winners sharing the prize.
- Secondary prizes: While secondary tiers add EV, they rarely add enough to offset the overall negative expectation.
The Concept of Utility
EV alone doesn't capture the full picture. Economists use the concept of utility to account for the subjective value of outcomes. For many people, the entertainment value of holding a ticket — the anticipation, the daydream — has real personal worth that isn't captured in a pure EV calculation.
Spending $2 on a lottery ticket and $2 on a coffee might have similar "utility" for different reasons. Neither is an investment in the financial sense.
Key Takeaways for Informed Players
| Scenario | Effect on EV |
|---|---|
| Jackpot rollover | EV improves but rarely turns positive after tax |
| More tickets sold | Increases jackpot split risk, reduces EV |
| Tax-free lottery jurisdiction | Significantly improves EV |
| Syndicates | Better odds, but prize is shared proportionally |
Understanding expected value helps you engage with lotteries as an informed participant. It won't make you a winner — but it will help you appreciate exactly what you're buying when you purchase a ticket.