Lottery Odds Calculator

By combinations: n choose k, since the order of the numbers does not matter. Picking 6 from 59 gives 45,057,474 possible tickets.

Proportionally and from a very low base. Buying ten tickets multiplies a one-in-45-million chance by ten, which is still one in four and a half million.

Not the chance of winning, which is identical for every combination. It does reduce the chance of sharing a jackpot, since many players pick birthdays and patterns — so avoiding 1 to 31 slightly raises the expected payout.

Almost always negative, and this calculates it. Even when a rolled-over jackpot pushes the headline expected value positive, tax and the possibility of sharing usually pull it back down.

It has been attempted, most famously in Virginia in 1992. It requires an enormous rollover, the logistics of printing millions of tickets in days, and the acceptance that a shared jackpot ruins the arithmetic.

Better odds of a small prize and generally a worse expected return per pound. The overall payout percentage is what matters, and it is usually published in the game rules.

Because the odds are set so that most draws produce no jackpot winner. Rollovers build the jackpot and drive ticket sales, which is a deliberate design rather than a coincidence.

It improves the expected value up to a point and also attracts more players, which raises the chance of sharing. The two effects partly cancel, and a very large jackpot is frequently shared.

It varies by lottery and is usually published — commonly around half, with the rest split between good causes, retailers, operating costs and tax. That payout ratio is why the expected value is negative.

Mechanical draw machines with numbered balls are extensively tested and audited. Any detectable bias would be exploited immediately, which is why the testing regime is as heavy as it is.

Believing that a number is due because it has not appeared recently. Draws are independent, so past results carry no information about future ones — the balls have no memory.

It depends on the discount applied to the lump sum, your tax position and your confidence in managing a large sum. The annuity is worth more nominally and less in present value.