Price a Raffle Ticket

Question

A charity raffle sells exactly 1,000 tickets and draws prizes without replacement: one ticket wins 500, two win 100 each, and ten win 10 each. What is the fair value of a single ticket?

Accepted Answer

One ticket's expected payout, by linearity over the prize tiers: mathbbE = frac11000(500) + frac21000(100) + frac101000(10) = frac500 + 200 + 1001000 = 0.80. Equivalently: the raffle pays out 800 of prizes in total, spread over 1,000 equally likely tickets, so each ticket carries frac8001000 = 0.80 of value. No combinatorics about "without replacement" is needed for the mean: every ticket is symmetric, so each owns an equal slice of the prize pool. The trap is reaching for inclusion-exclusion because one ticket could in principle win multiple tiers or none. Expectations add regardless of how the events overlap; that is the entire point of linearity. If the charity charges 2 per ticket, the buyer's expected loss is 1.20, a 60% house edge, which is fine for charity and terrible as a trade. Computing "total payout over total claims" is also exactly how you'd sanity-check the fair value of a lottery-linked note or any pro-rata payout structure on a desk: find the pool, count the claims, divide.

Price a Raffle Ticket

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