The mathematics of odds
Covering every line guarantees the jackpot and still usually loses money. The full-coverage bill for eight major games, the logistics of 292 million slips, and the two famous crews who actually did it.
Every lottery has one unbeatable play: buy all of it. Hold every combination and the jackpot is yours by construction — no luck involved. Operators know this, mathematicians know this, and roughly once a generation somebody with spreadsheets and nerve actually attempts it. Here is what the guaranteed win costs, why the guarantee is weaker than it looks, and how the era of full-coverage raids ended.
Combination counts below are derived in how lottery odds are calculated; prices are standard single-line prices from the operators.
| Game | Combinations | Price per line | Full coverage costs |
|---|---|---|---|
| Saturday Lotto (AU) | 8,145,060 | ~A$0.90 | ~A$7,330,554 |
| Lotto 6/49 (CA) | 13,983,816 | C$3 | C$41,951,448 |
| UK Lotto | 45,057,474 | £2 | £90,114,948 |
| Powerball (AU) | 134,490,400 | ~A$1.35 | ~A$181,562,040 |
| EuroMillions (UK price) | 139,838,160 | £2.50 | £349,595,400 |
| Eurojackpot | 139,838,160 | €2 | €279,676,320 |
| Powerball (US) | 292,201,338 | $2 | $584,402,676 |
| Mega Millions (US) | 290,472,336 | $5 | $1,452,361,680 |
| SuperEnalotto (IT) | 622,614,630 | €1 | €622,614,630 |
Price sources: The Lott, OLG PlaySmart, National Lottery UK, euro-jackpot.net, powerball.com, megamillions.com, Lottomatica.
Against a headline jackpot of, say, $1.5 billion, Powerball's $584 million buy-in looks tantalising. Keep reading.
Money is the easy half. A US Powerball play slip holds 5 lines, so full coverage means:
292,201,338 ÷ 5 = 58,440,268 completed slips
At 30 seconds per slip, that is 58,440,268 × 30 = 1,753,208,040 seconds of marking — about 55.6 years for one person (31,557,600 seconds per year). With 1,000 perfectly coordinated helpers working around the clock:
1,753,208,040 ÷ 1,000 ÷ 86,400 = 20.3 days per draw cycle of roughly 3 days
And that's before the terminals: every slip must be physically processed at retail machines, each taking seconds per transaction, all between draws, without a single missing line — because the one line your operation loses is, by Murphy's law of syndicates, statistically no likelier but emotionally certain to be the winner. Then you must find the winning ticket among 292 million pieces of paper.
1. Sharing. You are guaranteed a jackpot share, not the jackpot. Big jackpots drive huge casual sales, and any other winner halves your prize. A pari-mutuel split turns a guaranteed win into a guaranteed loss with one extra ticket in the world — the same collision arithmetic priced in the number sharing risk tool.
2. The annuity and the tax bill. US headline jackpots are 30-year annuity figures; the cash option is far smaller, and US lottery prizes are taxable. The advertised number is not the number that lands, which is exactly the calculation in the lump sum vs annuity tool and the after-tax prize tool. A "$1.5 billion" jackpot can comfortably fail to cover a $584 million outlay after cash-option discount, tax, and one co-winner.
3. The operator's veto. Modern rules and terminal throughput are designed so that bulk buying at this scale is impractical or refusable — a direct legacy of the crews below.
Dublin, May 1992. The Irish Lotto was then 6 numbers from 36 — C(36,6) = 1,947,792 combinations at 50p per line, so the whole game could be bought for IR£973,896. A syndicate led by accountant Stefan Klincewicz spent months pre-filling slips and, over the bank-holiday rollover weekend, got roughly 80% of the combinations through the terminals (about £820,000 worth) before the operator started shutting their outlets down. The jackpot came in at IR£1.7 million — and was split three ways. What saved the syndicate was the operator's own promotion paying bonuses on match-5 and match-4 tickets, of which the syndicate held thousands, lifting them to a profit of about £310,000 (The Irish Times, RTÉ). The Lotto promptly moved to 6-from-39 (C(39,6) = 3,262,623 — 67% more combinations) and the door closed. Full story: the 1992 Irish syndicate.
Massachusetts, 2005–2011. The MIT-founded and other syndicates who farmed Cash WinFall never bought full coverage — they exploited a "roll-down" rule that pushed an unwon jackpot into the lower tiers, making even partial coverage profitable. Over seven years the syndicates put in roughly $40 million and drew out about $48 million before a Boston Globe investigation and the Inspector General's 2012 report ended the game (The Boston Globe, TIME). Full story: Cash WinFall and the MIT students.
Both stories carry the same moral: the mathematics worked, and the rules were then changed. A lottery is a game whose house edits the rulebook the moment the edge appears.
The conditions are strict and simultaneous: a jackpot (cash, post-tax, assumed-shared) exceeding full-coverage cost; a combination space small enough to physically buy; and an operator that doesn't stop you. Modern flagship games fail on all three at once — that's not an accident, it's the design brief. You can test any claimed opportunity in two minutes with the break-even jackpot tool and the EV calculator; for the merely rich-but-not-institutional version of this fantasy, tickets needed to be favourite prices a 50% chance instead of 100%. Certainty was briefly for sale in Dublin in 1992. It hasn't been restocked.
Last verified: 2026-08-29