Start with the draw rules
Count every ticket in the final pool, including your own. Suppose N tickets exist, K are yours and d winning tickets are drawn fairly without replacement. Each ticket can win once; one person may hold several winning tickets.
Use the chance of no wins
There are C(N,d) possible sets of winners and C(N − K,d) sets with none of your tickets. So your chance of at least one prize is 1 − C(N − K,d)/C(N,d). The tool evaluates the ratio with logarithms to reduce numerical overflow.
For 5 tickets out of 500 and 3 prizes, the no-win probability is (495/500) × (494/499) × (493/498). The win probability is about 2.98%.
Expected prizes are not win probability
d × K/N is the average prize count. It can exceed one. A probability cannot exceed one, and someone may win multiple prizes, so the two measures are not interchangeable. Removing a winner’s remaining tickets changes the rules and is not included in this model.
A larger pool changes your odds
If entries are still open, results are conditional on the total you enter. A current entry count is not a final promise. Use the final total when it is available.
Put the idea to work
Pull odds · Raffle odds · Custom pity · Tries for a target chance