GenerateRandomSearch

Jackpot Break-Even Calculator

Every so often a rollover gets big enough that someone points out the expected value has gone positive. Usually they have left out the part that matters most: a bigger jackpot sells more tickets, and more tickets mean more chance of splitting it. This computes the expected value with that sharing included, using the distribution of how many other winners there would be, and reports the jackpot at which a ticket would genuinely break even.

What this generator does

Multiplies the chance of winning by what a winning share is actually worth once other winners are accounted for, adds the smaller prizes, subtracts the ticket price, and then inverts the whole thing to find the jackpot at which it would come to nothing.

How to use this tool

  1. Enter the advertised jackpot and what a ticket costs.
  2. Enter the odds and how many tickets are in the draw.
  3. Set what the smaller prize tiers return on average.
  4. Read the expected value, the sharing discount, and the break-even jackpot.

Understanding the controls

Advertised jackpot
The headline figure. Use the same currency units throughout — the arithmetic does not care which, only that they match.
Ticket price
What one entry costs, in the same units as the jackpot.
Odds are one in
How many combinations there are. A six-from-forty-nine draw is one in 13,983,816.
Tickets sold
How many entries are in this draw. This is the number that decides how many people you would be splitting a jackpot with, and it is the input most people leave out.
Smaller prizes
What the lesser tiers return on average as a share of the ticket price. Around ten per cent is typical for a national draw.

Common use cases

  • Checking whether a rollover has really made a ticket worth buying
  • Seeing how much a shared jackpot cuts a winning share
  • Understanding why the break-even jackpot is higher than price times odds
  • Comparing two draws with different odds and ticket sales
  • Explaining expected value with a familiar and honest example

How this generator works

If tickets are bought independently, the number of other jackpot winners follows a Poisson distribution whose mean is the tickets sold divided by the odds. What matters is not that count but the expected value of one over one plus it — the share you would actually receive — which works out to a simple closed form. Multiplying the jackpot by that gives the honest value of a winning ticket, and the rest is arithmetic. Before display the sharing factor is re-derived by summing the distribution term by term rather than trusting the formula, and the break-even jackpot is put back through the whole calculation to confirm it comes to exactly nothing.

Randomness and fairness

Nothing here is random, and nothing here picks numbers. This is the arithmetic of a ticket's value — the lottery number generators are the ones that produce a line to play.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

  • Tickets are assumed to be bought independently and uniformly, and they are not: people pick birthdays and patterns, so popular combinations are shared far more often than this implies.
  • A positive expected value is not a good bet in any ordinary sense. The near-certain outcome is losing the ticket price, and the arithmetic only comes good over more draws than a lifetime holds.
  • Tax, annuity payments and the option to take a reduced lump sum all reduce a real jackpot, and none of them is modelled.
  • The smaller-prize figure is an average across tiers rather than a full prize table.

Privacy and your data

The calculation runs in your browser and the figures you enter are never transmitted, stored or included in analytics.

This works out what a ticket is worth, and the answer is almost always less than it costs. It is not a system, and it does not improve anyone's chance of winning — every combination has the same probability however the arithmetic comes out.

Related generators