To think this is not how raffles work?

[PopcornAndPizza]

Hotly contested discussion at work and although light-hearted I now think I'm either losing the plot or almost all my work colleagues are all weird.

A colleague was pleased yesterday that she had won a coffee voucher at her grandsons school raffle. She mentioned her prize was the 8th top prize and that unfortunately her ticket didn't win any more prizes after that including the top prize which was a tablet.

I was only half paying attention until the other colleague (that I think is right) then said well surely they announced that one first? To which she replied well no they did that one last to build suspense.

To help the other colleague I tried to point out that's not how it works because then your ticket isn't actually in with the chance of winning the top prize but only me and this one other lady had this viewpoint, everyone else couldn't see the issue.

It's not us is it, that's not how raffles work? Surely the top prize should be drawn first so everyone has an equal chance at winning?

@BusWankers I see you edited so you might have realised what I meant.
You - the person entering the raffle - buying 20 tickets for 20 prizes not only 20 tickets sold in total.
Some people buy 100s of tickets.

I’ve never entered a raffle that’s done it that way.
The star prize is generally drawn last, so people pay more attention as everyone wants that one.
I’m in my 50’s so maybe the top prize first is a new way of doing it?

Yes I did. I'm ab idiot and can't read 🤣

Love your user name though 😂

Best prize last would be fairer if the earlier winning tickets were put back in the pot, ie, like say 6 separate raffles.

True story, someone I knew was brought in to fundraise for something like a new village hall, they wanted to raise a lot so the prize was substantial.

Afterwards there was a fuss about just this issue and they got back to the man to solve it. He just said ..."we've raised the money, what more do you want"

And here lies the confusion…

The overall odds of winning as the second ticket have to account for not winning as the first ticket. In your example, it’s 999 in 1,000 to not win first, and 1 in 999 to win second having not won first. The odds of winning second overall are 999/1,000 x 1/999, which is 1 in 1,000

And so on…

Its seems like its actually a question of psychology not statistics. It feels like an injustice, but at the end of the draw the probability of having the winning was always the same.

But surely ..my brain is broken?

You have ticket number 9 or of 10 tickets sold.

After prize 1 and ticket no. 1 are removed.
,
There are 9 tickets now to choose from

The ticket will be selected..that 1 in 9

You have a 1 in 9 chance of winning Prize 2.

The chances of winning Prize 1 AND Prize 2 is 1/10 x 1/9 , surely?

But you're saying the chances of winning the second prize is 9/10 x 1/9? ie 1/10.

The odds of you winning Prize 2 is 1/10 at the beginning of the draw, but how come it's not 1/9 at the point the first ticket is removed?

In my PTA days we had a list of the prizes and numbered them 1 to however many there were. When a number was pulled if the person was there they chose themselves and if they weren’t they got the whatever was at the top of the list. But it was definitely the ‘best’ prize snaffled first!

The only odds that matter are the odds at the start of the draw. Once it gets going the odds of certain outcomes might get more (or less) likely, but since those outcome can’t be influenced (that is, no more tickets can be bought) then fairness isn’t an issue.

You’re correct that once you haven’t won Prize 1, your odds of winning Prize 2 become 1 in 9. However, that’s of no real value to you (unless you were to sell your ticket for a profit, but that’s probably taking raffles too seriously!)

It makes no difference.

start with 500, end with 1
doesnt matter if you remove 50, 100, or 499 then chose the winner. Same odds

This is the problem, though - charity or not.

If you're using an incentive to get people to spend a lot more of their money - such as a raffle or other competition - rather than just asking for donations, you have to scrupulously honour it.

The Omaze competition adverts always say "And the best part of it is that you're helping to raise money for [name of charity]" - but they know very well that nobody entering truly thinks that that is the best part of the competition. People would be furious if they were to not be 100% scrupulously fair in giving the house away, or indeed just decided not to give it away after all; and if they just said "Well, X charity made £Xmillion out of it, so that's all that matters".

It does matter because taking out a ticket when you win an alternate prize changes the odds. Would you be happy if at the start of the draw the organisers removed 50% of the tickets? According to you that would be absolutely fine because it doesn't change your chance of winning, you were in at the start. In reality there would be a riot.

I agree with your logic. Not sure why they’d do it like that, you almost don’t want your ticket to be drawn in the earlier prizes. Very odd.

Once again (see my post above), people are talking at cross purposes. The odds of each TICKET winning a prize are different from the odds of each PERSON.

Perfectly fair, sorry

Yes, the final two tickets each have a 1 in 2 chance of winning the car. But as every entrant has the same chance of being in the final two, that's irrelevant.

In fact, every ticket has the same chance of being drawn in each of the 500 positions.

To answer your final paragraph, yes, if the tickets are removed at random, then the odds of you winning haven't changed. Everyone has the same random chance of being drawn first or last, or being taken out of the draw. It's just a random distribution of 500 tickets

@2thumbs explains it pretty clearly, I think.

Again, “Would you be happy if at the start of the draw the organisers removed 50% of the tickets?”

Yes.

As long as it’s done at random, it makes no difference. Only one of the tickets can ultimately win. It might be yours. It might not. Every ticket has the same chance of being discarded or being the winner.

I didn't know that! Never bothered to wonder, to be fair, but I thank you for today's lesson 😀

Yes because it literally makes no difference

take out 250 then pick a winner
take out 499 then pick a winner

it doesnt matter what happens

This
yes the last 2 tickets have a 50% chance of being drawn but they also have 2/500 chance of being in the last 2. You multiply those and you get 1/500

Just re-posting this solution as it seems the same arguments are being repeated (understandably, as I was sure one was correct then this changed my mind!)

I have been at raffles where you pick your own prize. I won a massive hamper this way. I was the 5th ticket picked. No one wanted it before me, which was odd.

Or they say what the prize is for that particular drawing of a number, and that number wins it. Sometimes it is the top prize first, sometimes the smallest. It really does not matter what order it is done in.

In both cases, your ticket is then binned so you can't win again with that particular number.

I was originally team OP but now I’m sort of swaying towards the viewpoint of you have an equal chance. But aren’t the people who don’t win getting the chance after chance? Oh I don’t know.

Ive definitely noticed strip raffles (sounds fun!) are more common these days or am I just paying more attention now I’m older? When I was younger it seemed like it was more individual tickets. Maybe that’s because people aren’t likely to only want to ‘donate’ 50p these days?

Also don’t think I’ve ever been to a raffle where you’ve picked your own prize! I’d hate that cos I’m that awkward person who wouldn’t want to look greedy picking the best one.

Raffles local to me do the big prize last.