EuroMillions: buying every combination? The Mandel profitability calculator
The economist Stefan Mandel won several jackpots between the 1960s and the 1990s by buying, with investors, almost every combination – the last time in 1992 in Virginia (USA). This calculator replays the thought experiment for EuroMillions: how much does it cost to buy every combination, how much comes back, is it profitable? Pure entertainment – today, cut-off times, stake limits and regulations prevent it in practice.
Assumptions
Result
| Combinations | |
| Total cost | |
| Slips | |
| Working time | |
| Days with helpers | |
| Guaranteed winnings in the lower tiers | |
| Expected jackpot share (split with other winners) | |
| Total expected return | |
| Return on investment (ROI) | |
| Break-even jackpot |
Winnings from buying every combination
| Tier | Matches | Winning lines | Median prize | Total |
|---|---|---|---|---|
| 1 | 5 Matches + 2 Lucky Stars | 1 | Jackpot | |
| 2 | 5 Matches + 1 Lucky Stars | 20 | 259,091.00 € | 5,181,820 € |
| 3 | 5 Matches + 0 Lucky Stars | 45 | 27,721.85 € | 1,247,483 € |
| 4 | 4 Matches + 2 Lucky Stars | 225 | 1,704.40 € | 383,490 € |
| 5 | 4 Matches + 1 Lucky Stars | 4,500 | 139.50 € | 627,750 € |
| 6 | 3 Matches + 2 Lucky Stars | 9,900 | 69.20 € | 685,080 € |
| 7 | 4 Matches + 0 Lucky Stars | 10,125 | 46.40 € | 469,800 € |
| 8 | 2 Matches + 2 Lucky Stars | 141,900 | 15.70 € | 2,227,830 € |
| 9 | 3 Matches + 1 Lucky Stars | 198,000 | 12.40 € | 2,455,200 € |
| 10 | 3 Matches + 0 Lucky Stars | 445,500 | 10.30 € | 4,588,650 € |
| 11 | 1 Matches + 2 Lucky Stars | 744,975 | 7.60 € | 5,661,810 € |
| 12 | 2 Matches + 1 Lucky Stars | 2,838,000 | 6.00 € | 17,028,000 € |
| 13 | 2 Matches + 0 Lucky Stars | 6,385,500 | 4.10 € | 26,180,550 € |
Method: the lower tiers are guaranteed because we hold every combination; they are valued at the tier's median prize. The jackpot is shared: with λ = (other lines) × p₁ expected co-winners, we receive on average jackpot × (1 − e^−λ) / λ. Not taken into account: our own winning lines lower the lower-tier prizes (pari-mutuel), and many lotteries cap the stake per person.
How it works
In the 1980s and 90s Stefan Mandel won several times by buying all combinations when the jackpot exceeded the total cost. The calculator shows cost, logistics (tickets, time, people), lower-tier prizes and the risk of sharing the jackpot.
Example
Eurojackpot example: 139,838,160 combinations at €2 cost around €280 million – more than the jackpot cap of €120 million.
Limitations
With today's lotteries, which have jackpot caps and many players, the sums are practically always negative; bulk buying is also hardly feasible logistically or legally.
Frequently asked questions about this tool
- Why does the Mandel method no longer work today?
- Too many combinations, jackpot caps and rules against bulk buying make it unprofitable and impractical.