The Math of Scratchers: Odds vs. EV vs. ROI Explained — With Real 2026 Data
Most scratch-off players look at one number: the odds of winning. But odds alone don't tell you whether a game is actually worth playing. This guide breaks down the three metrics that matter — Odds, Expected Value (EV), and Return on Investment (ROI) — using real data from games we track across 43 states. By the end, you'll understand why a game with "1 in 3" odds can be a worse buy than one with "1 in 4.5" odds.
Last updated: May 2026 · Data refreshed daily from official state lottery websites
What Are "Odds" on a Scratch-Off Ticket?
When a state lottery prints "Overall Odds: 1 in 4.00" on a scratch-off ticket, they're telling you the probability of winning any prize — including prizes equal to or less than the ticket price (like winning $1 on a $5 ticket).
How Odds Are Calculated
Overall Odds = Total Tickets Printed ÷ Total Prizes Available
For example, if a game prints 3,000,000 tickets and includes 750,000 total prizes:
3,000,000 ÷ 750,000 = 4.00"1 in 4.00"What Odds DON'T Tell You
- They don't distinguish prize values. A $1 win and a $1,000,000 win both count equally toward "overall odds."
- They're based on total tickets printed — not what's currently available. If 60% of tickets are sold but only 40% of prizes are claimed, the current odds are actually better than stated.
- They don't account for ticket price. A $30 ticket with 1 in 3 odds isn't necessarily better than a $1 ticket with 1 in 5 odds.
What Is Expected Value (EV)?
Expected Value is the average dollar amount you'd receive per ticket if you could buy every remaining ticket in a game. It accounts for both the probability of winning AND the value of each prize.
The Formula
EV = Σ (prize_amount × remaining_prizes ÷ estimated_tickets_remaining)
In plain English: for each prize tier, multiply the prize amount by the number of remaining prizes, divide by the estimated tickets still in circulation, then add up all the tiers.
Worked Example: A $10 Ticket
Consider a $10 scratch-off with these remaining prizes and an estimated 800,000 tickets remaining:
| Prize Tier | Remaining | EV Contribution |
|---|---|---|
| $250,000 | 2 | $250,000 × 2 ÷ 800,000 = $0.625 |
| $10,000 | 5 | $10,000 × 5 ÷ 800,000 = $0.063 |
| $1,000 | 40 | $1,000 × 40 ÷ 800,000 = $0.050 |
| $500 | 120 | $500 × 120 ÷ 800,000 = $0.075 |
| $100 | 2,400 | $100 × 2,400 ÷ 800,000 = $0.300 |
| $50 | 8,000 | $50 × 8,000 ÷ 800,000 = $0.500 |
| $20 | 24,000 | $20 × 24,000 ÷ 800,000 = $0.600 |
| $10 | 80,000 | $10 × 80,000 ÷ 800,000 = $1.000 |
| Total EV | $3.213 | |
This $10 ticket has an EV of $3.21. On average, each remaining ticket returns $3.21 in prize value. Since you paid $10, you're losing $6.79 per ticket on average.
Why EV Matters More Than Odds
Two games can have identical odds but wildly different EVs. A game loaded with $1 "break-even" prizes will have great odds but terrible EV. A game with fewer but larger prizes might have worse odds but much higher EV per ticket.
What Is ROI — and Why It's the Only Number That Matters
Return on Investment (ROI) converts EV into a percentage that's easy to compare across any ticket price. It answers the simplest question: "For every dollar I spend, how much do I get back?"
The Formula
ROI = (EV ÷ Ticket Price − 1) × 100%
Interpreting ROI
| ROI | What It Means | Example |
|---|---|---|
| +6.9% | Positive EV — you statistically profit | Spend $10, expect $10.69 back |
| 0% | Break-even — EV equals ticket price | Spend $10, expect $10.00 back |
| -25% | Typical scratch-off — expected loss | Spend $10, expect $7.50 back |
| -60% | Poor value — heavy expected loss | Spend $10, expect $4.00 back |
Using Our $10 Ticket Example
ROI = ($3.21 ÷ $10.00 − 1) × 100%ROI = (0.321 − 1) × 100%ROI = -67.9%An ROI of -67.9% means you lose about 68 cents of every dollar spent. This is below average for scratch-offs (typical range is -20% to -50%).
Why ROI Is the Best Comparison Tool
ROI normalizes everything to a per-dollar basis. This lets you directly compare:
- A $1 ticket vs. a $50 ticket
- Games from different states
- The same game at different points in its lifecycle
- Alternative spending strategies (like buying two cheaper tickets instead of one expensive one)
Real 2026 Examples: Good ROI vs. Bad ROI
Let's look at actual games from our database to see how dramatically ROI varies — even among games at the same price point.
🟢 Games With Positive ROI (Statistically Profitable)
These games currently have an expected value higher than their ticket price. They're rare, and they don't last forever — as prizes are claimed, ROI drops.
| Game | State | Price | ROI | EV |
|---|---|---|---|---|
| $50, $100 & $500 BLOWOUT | FL | $10 | +51.4% | $15.14 |
| Cash is King | IL | $30 | +6.9% | $32.08 |
| Scorching Hot 7s | FL | $10 | +2.5% | $10.25 |
| Florida 300X the Cash | FL | $30 | +1.7% | $30.50 |
🔴 Games With Poor ROI (High Expected Loss)
These games have significantly negative ROI — you're expected to lose a large portion of your ticket price. Often these are games where top prizes have already been claimed.
| Game | State | Price | ROI | EV |
|---|---|---|---|---|
| $500 A Week For Life | FL | $1 | -49.6% | $0.50 |
| Millionaire Maker | FL | $5 | -49.1% | $2.54 |
| 7-11-21® | IL | $1 | -48.2% | $0.52 |
| $10,000 HOLIDAY CA$H | FL | $1 | -46.1% | $0.54 |
| $50,000 HOLIDAY CA$H | FL | $2 | -43.7% | $1.13 |
Why ROI > Odds: Side-by-Side Proof
Here's the core argument: odds measure frequency of winning; ROI measures the financial outcome. They often point in opposite directions.
Scenario: Two $5 Games, Same State
| Metric | Game A: "Lucky 7s" | Game B: "Cash Vault" |
|---|---|---|
| Overall Odds | 1 in 3.50 (better) | 1 in 4.80 |
| EV per Ticket | $2.85 | $4.15 (better) |
| ROI | -43.0% | -17.0% (better) |
| Top Prize Remaining? | No (all claimed) | Yes (2 of 3 left) |
Game A has better odds but Game B is the better buy. Game A wins more often, but mostly $1 and $2 prizes (below ticket price). Game B wins less often, but when it does, the prizes are larger — and the top prizes are still available.
Why This Happens
- Odds count all prizes equally. A game stuffed with $1 "free ticket" prizes has great odds but terrible value.
- Top prize depletion crushes EV without changing odds much. When a $500,000 prize is claimed from a game with 2,000,000 tickets, odds barely move (one fewer prize out of 500,000+). But EV drops by $0.25 per ticket instantly.
- Price matters. A $30 ticket with 1 in 3 odds and $18 EV has -40% ROI. A $2 ticket with 1 in 5 odds and $1.80 EV has -10% ROI. The "worse odds" ticket is the better financial play.
The Decision Framework
| If You Care About... | Look At... | Why |
|---|---|---|
| Winning something (any amount) | Overall Odds | Higher frequency of any prize |
| Getting the most money back per dollar | ROI | Best financial return regardless of win frequency |
| Chasing a big jackpot | Top Prize Remaining + Odds for that tier | No point chasing if it's already claimed |
| Entertainment value (longest play time) | Odds + Ticket Price | More wins = more fun, even if small |
How ROI Changes Over a Game's Lifetime
A scratch-off game's ROI isn't static. It shifts daily as prizes are claimed. Understanding this lifecycle helps you time your purchases.
The Typical Lifecycle
| Phase | Timeframe | ROI Trend | What's Happening |
|---|---|---|---|
| Launch | Week 1-4 | Baseline (usually -20% to -40%) | All prizes intact. ROI reflects the game's designed payout percentage. |
| Mid-Life | Months 2-8 | Fluctuates ±5% | Small prizes claimed proportionally. ROI stays relatively stable. |
| Top Prize Claimed | Any time | Sharp drop (−5% to −25%) | Each top prize claim removes significant EV. This is the biggest single-event ROI change. |
| Late Life | Final months | Can improve OR worsen | If small prizes deplete faster than large ones, ROI can actually improve. If top prizes are gone, it worsens. |
| End of Game | Final weeks | Often very negative | Most valuable prizes claimed. Remaining pool is mostly small prizes. |
When to Buy (and When to Avoid)
- Best time: Early in a game's life (all prizes intact) OR when our data shows ROI trending upward (small prizes depleting faster than large ones).
- Worst time: After all top prizes are claimed. We flag these games with a "Top Prizes Gone" indicator on every state hub page.
- Check the trend: On each game's detail page, the History & Trends tab shows ROI over time. Look for games where ROI is stable or improving.
Quick EV/ROI Calculator
Use this calculator to estimate the EV and ROI of any scratch-off ticket. Enter the ticket price and prize information to see the math in action.
Key Takeaways
- Odds ≠ Value. A game with 1 in 3 odds can be a worse buy than one with 1 in 5 odds. Odds measure win frequency, not financial return.
- EV tells you the dollar value. It's the average amount you'd receive per ticket based on remaining prizes. Higher EV = more money back.
- ROI is the ultimate comparison tool. It normalizes EV to a per-dollar basis so you can compare any ticket at any price point.
- Positive ROI games exist — but they're rare and temporary. When we find them, they appear in the "Best Value" tab on each state's page.
- Top prize depletion is the #1 ROI killer. Always check if top prizes are still available before buying. We flag "Top Prizes Gone" games automatically.
- Data changes daily. A game that's a great buy today might not be tomorrow. Check back regularly or browse current data.
Ready to find the best games in your state? Visit your state's hub page to see every active scratch-off ranked by ROI, with daily updates.
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Related Guides
- Our Full Methodology — Detailed formulas for EV, ROI, Daily Value Claimed, and Top Prize Depletion Events
- Why Buying 2× $5 Tickets Often Beats One $10 Ticket — Data-backed proof using our alternative strategy analysis
Disclaimer: This information is provided for educational purposes only. All data is sourced from official state lottery websites and is updated regularly, but we cannot guarantee 100% accuracy. Lottery games are games of chance, and past performance does not guarantee future results. Please play responsibly and never spend more than you can afford to lose. If you or someone you know has a gambling problem, call 1-800-GAMBLER.