Expected Value of Lotteries: What Do You Get Back for €100?
Have you ever wondered how much money you actually get back from different lotteries? We've calculated the mathematical expected value for 11 of the world's largest lotteries – from 6aus49 to Powerball. The result: You lose between €47 and €65 for every €100 invested.
What is Expected Value (EV)?
Expected value is a mathematical concept that tells you how much money you can expect to get back on average from a bet. The formula is simple:
Formula
EV = Σ (Wahrscheinlichkeit × Gewinn)
Summed across all possible prize tiers
An EV of 50% means: For every euro invested, you get 50 cents back on average. Under normal conditions, lottery EV typically ranges from 35-50% – this is the "house edge" that funds the lottery operators. (With very high jackpots, EV can theoretically exceed 100%, but more on that later.)
Expected Value Comparison: €100 Investment
What happens when you invest €100 in different lotteries? Lotteries are ranked by: 1) Total EV, 2) Jackpot odds (easier odds = better rank when EV is equal).
BonoLoto
Spain
Jackpot Odds
1:13,983,816
Jackpot EV%
5.7%
Total EV%
50%
Return/€100
Jackpot Odds
1:19,068,840
Jackpot EV%
4.8%
Total EV%
50%
Return/€100
El Gordo
Spain
Jackpot Odds
1:31,625,100
Jackpot EV%
10.5%
Total EV%
50%
Return/€100
UK Lotto
United Kingdom
Jackpot Odds
1:45,057,474
Jackpot EV%
2.2%
Total EV%
50%
Return/€100
Jackpot Odds
1:139,838,160
Jackpot EV%
0.6%
Total EV%
50%
Return/€100
Eurojackpot
Europe
Jackpot Odds
1:139,838,160
Jackpot EV%
3.6%
Total EV%
50%
Return/€100
EuroMillions
Europe (9 countries)
Jackpot Odds
1:139,838,160
Jackpot EV%
4.9%
Total EV%
50%
Return/€100
La Primitiva
Spain
Jackpot Odds
1:139,838,160
Jackpot EV%
2.1%
Total EV%
50%
Return/€100
Jackpot Odds
1:292,201,338
Jackpot EV%
3.4%
Total EV%
45%
Return/€100
Jackpot Odds
1:302,575,350
Jackpot EV%
3.3%
Total EV%
45%
Return/€100
SuperEnalotto
Italy
Jackpot Odds
1:622,614,630
Jackpot EV%
0.3%
Total EV%
35%
Return/€100
Summary: Your Expected Loss
-€50
European Lotteries
-€55
US Lotteries (pre-tax)
-€65
SuperEnalotto
Based on official payout ratios from lottery operators
What is Jackpot EV%?
Jackpot EV% shows what percentage of your total EV% depends solely on the jackpot. The formula:
Jackpot EV% = (1 / Jackpot-Odds) × Start-Jackpot / Ticketpreis × 100
A high Jackpot EV% means a larger portion of your "expected return" depends on the nearly impossible jackpot. A low Jackpot EV% means more value comes from smaller, more achievable prizes.
Low Jackpot EV%
6aus49 (0.6%), SuperEnalotto (0.3%): 99% of EV% comes from smaller prizes → more "action", frequent small wins
✓ Flatter payout structure
High Jackpot EV%
El Gordo (10.5%), BonoLoto (5.7%): More of EV% is in the jackpot → fewer small wins, but "bigger dreams"
✓ Top-heavy structure
Detailed Calculation: Eurojackpot
Let's look at how the expected value is calculated for Eurojackpot. Each prize tier contributes differently to the total value:
| Tier | Odds | Avg. Prize | EV/Ticket |
|---|---|---|---|
| 5+2 | 1:139,838,160 | €10,000,000 | €0.072 |
| 5+1 | 1:6,991,908 | €500,000 | €0.072 |
| 5+0 | 1:3,107,515 | €100,000 | €0.032 |
| 4+2 | 1:621,503 | €5,000 | €0.008 |
| 4+1 | 1:31,075 | €200 | €0.006 |
| 4+0 | 1:13,811 | €100 | €0.007 |
| 3+2 | 1:10,344 | €50 | €0.005 |
| 2+2 | 1:672 | €20 | €0.030 |
| 3+1 | 1:517 | €18 | €0.035 |
| 3+0 | 1:230 | €15 | €0.065 |
| 1+2 | 1:128 | €10 | €0.078 |
| 2+1 | 1:42 | €8 | €0.190 |
| Total EV per €2 Ticket | ~€1.00 | ||
This means: From every €2 ticket, you get €1 back on average – a 50% loss. With 50 tickets for €100, you expect a return of about €50.
Why SuperEnalotto Has the Worst EV
SuperEnalotto has the hardest jackpot odds of any major lottery at 1:622,614,630. This means:
- You'd need to buy about 600 million tickets to statistically hit the jackpot once
- Most of the money flows into the extremely hard-to-reach jackpot
- Fewer prize tiers mean less return from small wins
Fun Fact: If you buy one SuperEnalotto ticket every week, you would statistically win the jackpot in about 12 million years. That's longer than all of human history!
UK Lotto: Favorable Mechanics
UK Lotto has some interesting mechanics that set it apart from other lotteries:
- "Easier" jackpot odds of 1:45 million (vs. 139-622 million for others)
- "Must Be Won" draw after 5 consecutive rollovers without a jackpot winner – money then flows to lower tiers
- Free Lucky Dip (worth £2) for matching 2 numbers – this increases the effective return
According to official statements, on average about 50% of Lotto sales are paid out as prizes – similar to most European lotteries.
When Does Expected Value Become Positive?
Theoretically, EV can exceed 100% with very high jackpots. However, the exact thresholds are difficult to determine and depend on many factors:
⚠️ Factors Affecting the "Break-Even" Point
- •Cash vs. Annuity (US): Jackpots are advertised as annuities, cash value is only ~60%
- •Taxes: US winnings are heavily taxed (up to 37% federal + state taxes)
- •Jackpot sharing: With high jackpots, more people buy tickets → higher probability of sharing
- •Caps & Rolldowns: EuroMillions has a €250M cap with rolldown mechanics
Rough estimates for theoretically positive EV (pre-tax, without sharing):
Eurojackpot / EuroMillions
Above €140-180M*
Powerball / Mega Millions
Above $800M+ (Cash)*
*These values are rough estimates, not precise calculations. Actual thresholds vary significantly.
Key Takeaways
Expect to Lose
For €100 invested, you lose €50-65 on average. That's the entertainment cost.
~50% Payout in Europe
Most European lotteries officially pay out about 50% of stakes as prizes.
SuperEnalotto: Outlier
With ~35% return and 1:622M jackpot odds, SuperEnalotto is the most expensive dream.
Play Responsibly
Lottery is entertainment, not investment. Only spend money you can afford to lose.
🤯Mathematical Curiosity
You may have noticed that 6aus49, Eurojackpot, EuroMillions, and La Primitiva all have the same jackpot odds: 1:139,838,160. This is a fascinating mathematical coincidence!
C(49,6) × 10 = 13,983,816 × 10 = 139,838,160
C(50,5) × C(12,2) = 2,118,760 × 66 = 139,838,160
Despite completely different game formats, they yield exactly the same probability!
Check Your Numbers at LottoROI
Curious how your numbers would have performed historically? Check them against decades of draw data and find your best match!
Check Numbers NowData Sources: EV values are based on official payout ratios from lottery operators (e.g., lotto.de: 50%, UK National Lottery: ~50%). Actual returns may vary depending on jackpot levels and number of winners.
Disclaimer: The "positive EV" thresholds are rough estimates and don't account for all factors (taxes, jackpot sharing, cash vs. annuity). Lottery is a game of chance – play responsibly and only with money you can afford to lose. LottoROI is not affiliated with official lottery operators.