The idea of guaranteeing a lottery jackpot by purchasing every single possible number combination is one of the most enduringly popular thought experiments in gambling mathematics, and the question of whether it is possible to buy every lottery combination is one that raises fascinating issues of cost, logistics, taxation, and legal practicality.
In short, the answer is yes in theory and almost certainly no in practice, for reasons that extend well beyond simply having enough money to fund the exercise.
Is It Possible To Buy Every Lottery Combination: What The Numbers Say
The UK National Lottery Lotto game requires players to choose six numbers from 1 to 59, producing exactly 45,057,474 possible unique combinations, and since each line currently costs £2, the theoretical cost of purchasing every single combination would be approximately £90 million.
The United States presents an even starker picture, with Powerball offering 292,201,338 possible combinations at $2 per ticket, meaning a complete coverage of every entry would require an investment of approximately $584 million before taxes, administration, or logistics are factored into the equation.
Lottery Combination Costs By Game
| Lottery | Total Combinations | Ticket Price | Cost to Buy All |
|---|---|---|---|
| UK Lotto | 45,057,474 | £2 | ~£90 million |
| EuroMillions | 139,838,160 | £2.50 | ~£350 million |
| US Powerball | 292,201,338 | $2 | ~$584 million |
| US Mega Millions | 302,575,350 | $2 | ~$605 million |
| Irish Lotto | 8,145,060 | €2 | ~€16 million |
Why The Maths Rarely Works In The Buyer’s Favour
| Factor | Impact |
|---|---|
| Lump sum reduction | US winners receive roughly 50–60% of advertised jackpot |
| Federal tax (US) | 24–37% withheld immediately |
| Jackpot sharing | Any other winner splits the prize equally |
| Smaller prize offsets | Minor prizes partially offset cost but rarely significantly |
| Logistics failure | Time and transaction limits make full purchase near-impossible |
The Stefan Mandel Method: When Someone Actually Tried It
The most famous real-world attempt to purchase every lottery combination was executed by Romanian-Australian economist Stefan Mandel, who successfully exploited a Virginia state lottery in the early 1990s when the game had just under 7 million possible combinations and the jackpot had grown to a level that made comprehensive coverage theoretically profitable.
Mandel’s syndicate, working with printed ticket sheets and a vast network of buyers, managed to purchase approximately 5 million of the 7 million available combinations before the sales window closed, and while they failed to achieve complete coverage, they had secured the winning combination and claimed the jackpot, though the legal proceedings that followed lasted several years.
Modern lottery systems have introduced extensive safeguards specifically to prevent any repetition of such exercises, including transaction monitoring, purchase limits, fraud prevention algorithms, and digital oversight that would make mass purchases immediately visible to operators.
The taxation problem alone disqualifies the strategy for most major lotteries today, since the US Powerball jackpot is paid out over 30 annual instalments by default, and choosing the lump-sum cash option reduces the headline prize by approximately 40 to 50 percent before federal and state taxes are deducted, leaving a net receipt that frequently falls short of the investment required to buy all combinations.
Even in a scenario where the jackpot was large enough to make pre-tax mathematics work on paper, the physical or digital logistics of purchasing hundreds of millions of unique tickets within the narrow window before a single draw closes represents an organisational challenge that no individual or syndicate has ever successfully solved in a regulated modern lottery environment.
