"Last Out" Raffle Probabilities/Stats

Question

I'm part of an online community that raffles away prizes, typically with 30 or 40 spots in a raffle. The numbered chips/balls are placed into some type of hopper, and pulled out one at a time (random/controlled/etc). The rules are pretty simple: you can buy as many spots as you'd like, and the last out wins the prize (so numbers are drawn until there is one chip/ball remaining, and that is the winning spot). Not a math or stats guy, so looking for some help as it's caused some debate...

Let's say it's a 10 spot raffle, and I buy one single spot.

Do I have a 1 in 10 shot of winning? Or do I have a 1 in 10 chance of losing (since you actually want to avoid having your number drawn until the end)? Do my odds reset with every number drawn, or do they carry through the entire raffle?

Do you get where I am going with this?

Thanks for any help/insight!

Answer 1

If you have M chips out of N chips in total, you have a M/N chance of winning. It doesn't matter if the last chip drawn wins, or the first one, or N/2th one - there is exactly one chip that will win, and each of the N chips is equally likely to be it. Every chip has a 1/N chance of being the winning chip, so M chips have an M/N chance of winning overall.

Having the last number drawn be the winner is absolutely no different from having the first number drawn be the winner, it just takes longer.

You odds do "reset" after each number drawn to reflect the remaining N. If there are only two chips left and you hold one of them, your chance of winning at that point is 1/2. But your overall chance of winning at the start before any numbers are drawn is still 1/N (or M/N if you have multiple chips).