Raffle Odds & Expected Value Calculator

How it works

P(no win) = Π (T − m − i) ÷ (T − i) for i = 0 … P−1 (without replacement) or (1 − m/T)^P (with replacement) · P(exactly k) = C(m, k) × C(T − m, P − k) ÷ C(T, P) · P(≥ 1 win) = 1 − P(no win) · expected wins = m × P ÷ T · EV = expected wins × prize − tickets × price · net proceeds = T × price − prizes − costs

In a raffle every ticket has the same chance, so the probability that a particular prize goes to one of yours is simply your share of the tickets — and with several prizes the expected number of wins is that share times the prize count. The chance of winning at least once is easiest to reach through its opposite, the chance every prize misses you, which is a product of shrinking fractions as winning tickets leave the drum. The full spread — exactly 0, 1, 2 or more wins — follows the hypergeometric distribution (or the binomial if winning tickets go back in). Expected value compares what you paid with what the average ticket returns and, since charity raffles keep most of the pot, it is nearly always negative. Under More options you can enter how many similar raffles you play to see the combined chance. Switch to Organiser to see ticket revenue, net proceeds after prizes and costs, break-even sales and the tickets needed to reach a fundraising goal.

Worked example

Five tickets out of 500 with three prizes: the chance of at least one win is 1 − (495/500 × 494/499 × 493/498) ≈ 2.98%, about 1 in 34, and the expected number of wins is 0.03. At $2 a ticket you paid $10 for an expected $3 of prize value; 103 tickets would be needed for a 50% chance. As the organiser, selling all 500 tickets raises $1,000; after $300 of prizes you keep $700, and you break even at 150 tickets.

Frequently asked questions