Expected value is the single most rigorous framework available for comparing scratch-off tickets. Unlike “overall odds,” which only tells you the probability of any win (including a $1 prize on a $5 ticket), EV accounts for the size of each prize tier alongside its probability — giving you a true dollar-value measure of what each ticket is worth on average.
What Is Expected Value for Scratch-Offs?
Expected value (EV) is the average outcome of a random event calculated over many trials. For a scratch-off ticket, it is the weighted average of all possible prize outcomes:
EV Formula:
EV = ∑ (Prizei × Probabilityi)
Where i represents each prize tier, including $0 (no win)
Let's walk through a concrete example using a hypothetical $5 scratch-off ticket:
| Prize | Odds (1 in X) | Probability | EV Contribution |
|---|---|---|---|
| $100,000 | 576,000 | 0.0000017 | $0.174 |
| $1,000 | 20,000 | 0.000050 | $0.050 |
| $100 | 500 | 0.00200 | $0.200 |
| $50 | 100 | 0.01000 | $0.500 |
| $25 | 50 | 0.02000 | $0.500 |
| $10 | 20 | 0.05000 | $0.500 |
| $5 | 8 | 0.12500 | $0.625 |
| $0 (no win) | — | ~0.787 | $0.000 |
| Total EV per $5 ticket | ~$2.55 | ||
In this example, the $5 ticket has an expected return of ~$2.55 — or about 51 cents per dollar spent. This is a negative expected value of -$2.45 per ticket. Over 100 tickets, your expected total loss is roughly $245. This is typical for scratch-off games — the house retains 25–45% of revenue.
Why Remaining Prizes Are More Important Than Printed Odds
Here is the critical insight most players miss: the printed odds on the ticket are calculated based on the full game run — before any tickets are sold. As the game progresses and prizes are claimed, the actual odds for unsold tickets change — but the printed odds never update.
Consider this example: a game launches with one $100,000 top prize and 576,000 total tickets. The printed odds of winning $100,000 are 1-in-576,000. Now imagine 400,000 tickets have been sold and the $100,000 prize is still unclaimed. With 176,000 tickets remaining, the actual odds of the top prize are now 1-in-176,000 — roughly 3.3x better than the printed odds.
The reverse is equally true and more common: if the $100,000 prize was claimed early in the game's run, every remaining unsold ticket has zero chance of winning the top prize — regardless of what the printed odds say. Yet these tickets continue to be sold at the same price until the game is officially closed.
This is why checking remaining prizes before buying is the single most impactful thing you can do to improve your scratch-off EV — more than any other factor.
How to Calculate Remaining Prize EV
Here is a step-by-step method for calculating the adjusted EV based on remaining prizes:
- Go to your state lottery's website(or LotteryCalc's scratch-off pages) and find the remaining prizes table for the game you're considering.
- Note the total remaining prizes at each tier and the total tickets remaining (estimated from total tickets printed minus sold, if available).
- Recalculate the probability for each prize tier using remaining prizes divided by remaining tickets.
- Apply the EV formula using these updated probabilities instead of the printed odds.
Example: A game originally had 10 top prizes of $50,000 each in 5,760,000 tickets. Today, 5 of the 10 top prizes remain, and approximately 2,880,000 tickets are unsold. The updated probability of the top prize is 5/2,880,000 = 1-in-576,000 — identical to the original printed odds. In this balanced case, EV hasn't changed. But if only 2 top prizes remain in 2,880,000 tickets: 2/2,880,000 = 1-in-1,440,000 — your EV for the top prize has dropped to just 40% of what it was at launch.
Best and Worst Price Points for EV
Price point correlates with expected payout percentage (return-to-player) across the industry. General patterns based on data from multiple state lottery annual reports:
- $1 tickets: Typically the worst RTP (55–65%). Prize pools are small, top prizes cap at $1,000–$5,000, and overall odds are often 1-in-4 or worse. Best treated as pure entertainment at minimal cost.
- $2 tickets: Marginally better than $1 tickets. Top prizes reach $25,000–$50,000 in some games. RTPs of 60–68%.
- $5 tickets: The sweet spot for many players. Better overall odds (often 1-in-3 to 1-in-3.5), more prize tiers, and RTPs of 65–72%.
- $10 tickets: Similar RTP to $5 but with higher absolute prize amounts. Top prizes typically $100,000–$500,000. Good EV relative to price in many states.
- $20–$30 tickets: Highest top prizes ($1M–$5M) and often the best RTPs (70–75%). However, the EV floor is also higher — your expected loss per session is greater in absolute dollars even if the percentage is similar.
If your goal is maximum prize potential per dollar of EV, $5 and $10 tickets typically offer the best balance. If you want the highest absolute prize potential and have a larger budget, premium $20–$30 tickets may be worth considering when top prizes are still available.
Warning Signs a Ticket Has Poor Remaining EV
Before buying any scratch-off, check for these red flags on your state lottery's remaining prizes page:
- Top prize(s) already claimed. Once the top prize is gone, EV drops dramatically regardless of what the ticket cost or what the printed odds say.
- Game launched 6+ months ago.Older games have more tickets sold and more prizes claimed. Without checking remaining data, it's impossible to know the current EV — but time is a proxy for depleted prize pools.
- Low count of second-tier prizes remaining.Second-tier prizes ($5,000–$50,000) contribute significantly to total EV. If both top and second-tier prizes are depleted, the game's EV is mostly in small prizes with very negative net EV overall.
- Game listed as “last day to claim” or closing soon. Lottery commissions typically close games when most high-value prizes have been claimed. A closing game is rarely one with good remaining EV.
Where to Find Remaining Prize Data
Every state lottery that sells scratch-offs is required to publish remaining prize data. You can find it:
- State lottery websites:Search “[state] lottery remaining prizes” or navigate to the scratch-offs section of your state lottery's official site. Data is usually updated daily or weekly.
- LotteryCalc scratch-off pages: We aggregate remaining prize data from state sources and display it alongside odds rankings, price comparisons, and EV estimates. See our Florida scratch-offs page, Texas scratch-offs, and California scratch-offs for examples of this data in action.
For broader strategy beyond EV analysis, see our guide on best scratch-off strategies, which covers budgeting, game selection, and how to interpret official odds data.
Expected value calculations are based on publicly available state lottery data and standard probability math. Negative EV does not mean you cannot win — it means you will lose money on average over many plays. Scratch-offs are games of chance; play responsibly within your entertainment budget. Problem gambling helpline: 1-800-522-4700.