About the Ticket Optimizer
This calculator applies the standard expected value (EV) formula from probability theory to raffles, prize drawings, and giveaways. Instead of just telling you "the odds," it converts ticket price, quantity, total tickets sold, and prize value into a single dollar figure: what you'd expect to gain or lose, on average, if the drawing were repeated many times.
The formula
For a single-prize raffle where every ticket has an equal, independent chance of winning:
- Win probability = tickets you buy ÷ total tickets sold
- Expected winnings = win probability × prize value
- Total cost = tickets you buy × ticket price
- Expected value (EV) = expected winnings − total cost
A useful shortcut falls out of this algebra: setting EV to zero and solving for the prize gives break-even prize value = ticket price × total tickets sold. Notice how many tickets you buy cancels out of that equation entirely — the break-even point is a property of the raffle itself (price and pool size), not of your personal ticket count.
How to read a negative expected value
Most charity raffles, promotional giveaways, and lottery-style drawings have a negative expected value by design: ticket sales need to cover the prize plus overhead (and, for charities, a donation). A negative EV does not mean the raffle is unfair — it means that, averaged over everyone who enters, more money goes in than comes back out as prizes. Any individual entrant can still win big; EV describes the average across all entrants, not any one outcome.
Assumptions behind this model
The formula assumes a single prize drawn at random with every ticket equally likely to win, and that you cannot buy more tickets than exist in the pool. It does not model multiple prize tiers, taxes withheld from winnings, or the time value of money for drawings held far in the future — for those, adjust the prize value input to an after-tax, present-value estimate before entering it.