Is a lottery ticket worth it?
On average, no: a ticket returns less than it costs, because the lottery pays out only part of what it takes in. The calculator shows by how much for any jackpot, including the effect of taxes and of sharing the jackpot with other winners.
Expected value calculator
How it works
The expected value of a ticket is what it wins on average: each prize times its chance, added up, minus the price. The jackpot part is the jackpot times its odds, reduced by tax and by sharing. If N other tickets are in the draw, each with the same chance, the average share you would keep of a jackpot you win is (1 − (1 − p)N+1) ÷ ((N + 1) × p), where p is the jackpot chance of one ticket.
The break-even jackpot is the jackpot at which the average return equals the price. Big jackpots attract more tickets, so the sharing effect grows exactly when the jackpot does; that is why a "positive" ticket is much rarer than a quick calculation suggests.
Why buy one at all?
A ticket buys a few days of possibility at a known price. As entertainment that can be reasonable; as a plan to make money it is not. Set a small, fixed budget, and if it stops feeling like fun, help is free.
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