Independent site. CasinoCalcs is not affiliated with or endorsed by any lottery operator, including the National Lottery, Allwyn and Ireland’s National Lottery. Game names are used only to describe the rules the maths is based on.
- Maths reviewed by Josh Miller
- Tested by Diana Westfield
A lottery expected value calculator for anyone who’s wondered whether a big rollover finally makes a ticket worth it. EuroMillions at £100 million, £2.50 a line, 60 million lines sold. The jackpot part of each line is worth about 58p after allowing for sharing. The smaller prizes add roughly 50p. Total: about £1.08 back for £2.50, an expected value of −£1.42. The CasinoCalcs calculator is free and works for any game and any jackpot.
The lottery expected value formula
EV = (jackpot ÷ odds) × average share + smaller prizes − ticket price Average share = (1 − e−λ) ÷ λ, λ = lines sold ÷ odds
The first part is simple: £100 million at 1 in 139,838,160 is 72p a line. The share is the part people miss. With 60 million lines sold, you’d expect 0.43 other winning lines, so on average you’d keep 81% of the jackpot. That’s 58p.
Smaller prizes are a percentage of the ticket that the lower tiers pay back on average. 20% is a fair rule of thumb, but games differ, so check the prize table.
Break-even jackpots
| Game | Line price | Odds, 1 in | Break-even jackpot (no sharing) |
|---|---|---|---|
| UK Lotto | £2 | 22,528,737 | about £36 million |
| EuroMillions | £2.50 | 139,838,160 | about £280 million |
| Irish Lotto | €2 | 10,737,573 | about €17 million |
| Lotto 6/49 | C$3 | 13,983,816 | about C$34 million |
That assumes 20% back from the smaller prizes and nobody to share with. In real life, the draws that reach those numbers are the ones everybody plays, so the share drops and the break-even point moves further away. EuroMillions also caps its jackpot, so it may never get there at all.
Positive EV still loses
Suppose a draw did tip positive. You’d still lose virtually every ticket. All of the value sits in an outcome that happens once in tens of millions of lines. Expected value tells you the price is fair, not that playing makes sense. The lottery reality check turns the odds into years of play, and the lottery odds calculator works out the odds for any format.
Comparing games? Which lottery has the best odds lines them up. And if you play in a group, the lottery syndicate calculator splits the cost and the winnings.
Dreaming about the win itself? The lottery win interest calculator shows what a jackpot earns and how long it lasts.
A lottery ticket is entertainment, not a plan. BeGambleAware.org is free if spending on draws is getting out of hand.