Raffle odds. 10 bought, 400 available. What is 1/x

[Scruff]

Just buy OneCoin instead...

[BrilloPad]

I might have over thought this by browsing the web as most of the calcs deal with a raffle with multiple prizes so your odds change every draw but lets say..

Raffle has 400 tickets. You buy 1 ticket. You've a 1 in 400 chance of winning.
If you buy 10 do you have a 10 in 400 or 1 in 40 chance of winning or is it more complex than that?

Have I over thought it and it is as simple as the explaination above?

If someone buys 10 of the 420 tickets, they will have a 10 in 420 chance of winning. Which is better than 1 in 420, but is MASSIVELY different to 1 in 42. Having 10 tickets give you just 2.38% of the overall tickets available, it does not mean the odds change as dramatically as you are claiming.

To actually have a 1 in 42 chance of winning, you would need to buy 379 tickets. That would mean either one of your 379 tickets or one of the remaining 41 tickets has to be the winner (giving you 1 in 42 chance) because either you OR one of the remaining 41 tickets has to win.

If the odds you claim were correct and that was how it worked, you'd only need to buy 70 Lottery tickets to guarantee the first prize!

My degree is partially in statistics. LM is right it is complex and counter intuitive.

It is as simple as post 1. Post 2 assumes that each person submits only one ticket.

Where it gets more tricky is non-independent events, where there is a 2nd prize, or where you compare each of the "winners". To name a few.

If there are 5,000 primary schools in the UK, and you pick 82 people at random who attended those schools, there is a 50% chance two went to the same school.

If you toss 20 coins, there is a 25% chance you get a run of 5 heads or tails.

EDIT: a more complex case. You are on a game show. Prize is behind one door of 3. You pick a door. Another door is opened and prize is not there. Should you swap your choice? In theory they are independent. But you have more information. Imagine there were a million doors. You pick one. Then 999,998 are opened. Should you swap? Well the odds you picked it first time where 1 in a million. Now its 1 in 2. So you swap.

22 random people will have a 50% chance of same birthday. Lets try it at the next CUK meet up. Oh wait. WE already know that NAT and cojak where born on the same day. 25th December. They clearly both think they are Jesus Christ.

[NotAllThere]

It seems to be a variation of "you either win or you don't, so the odds are 50/50". The poster seems to think that the 379 tickets you buy have equal chance of being the winner as any of the 41 you didn't buy.

It's complete twaddle. With one prize, ten tickets is 10/420 = 1/42.

[SimonMac]

So this is from the chatroom but I've read it so many times I've gone word blind.



It just looks like gobbledgook to me. You need to buy 379 tickets to have a 1 in 42 chance of winning in a 420 ticket draw.. That's gotta be wrong? Just second guessing myself now. That's all bollox yes?

I'm not an expert but I think its to do with the 1st ticket has a 1/420, the second has a 1/419, the third has a 1/418 etc so overall 10/420 is not quite 1/42

[BrilloPad]

I'm not an expert but I think its to do with the 1st ticket has a 1/420, the second has a 1/419, the third has a 1/418 etc so overall 10/420 is not quite 1/42

All 10 have 1/420.

[eek]

I'm not an expert but I think its to do with the 1st ticket has a 1/420, the second has a 1/419, the third has a 1/418 etc so overall 10/420 is not quite 1/42

That's if there are multiple prizes:

the first ticket is picked from 420,
the second ticket from 419 and so on.

With 1 prize the odds are 1 in 420 that a particular ticket wins so with 10 tickets NLUK has a 10 in 420 chance or 1 in 42 chance of winning.

Worryingly NLUK plays poker so I would expect him to be better at odds than that but I can see he's ended up going number blind.

[BrilloPad]

That's if there are multiple prizes:

the first ticket is picked from 420,
the second ticket from 419 and so on.

With 1 prize the odds are 1 in 420 that a particular ticket wins so with 10 tickets NLUK has a 10 in 420 chance or 1 in 42 chance of winning.

Worryingly NLUK plays poker so I would expect him to be better at odds than that but I can see he's ended up going number blind.

Thats a bit like saying darts players(who are good at subtracting) should be good at maths.

[ladymuck]

I'm not an expert but I think its to do with the 1st ticket has a 1/420, the second has a 1/419, the third has a 1/418 etc so overall 10/420 is not quite 1/42

That's for multiple prizes, where a drawn ticket is not returned to the pool.

All 10 have 1/420.

That's for any one ticket. So assuming only one prize is available.

[eek]

Thats a bit like saying darts players(who are good at subtracting) should be good at maths.

Card games are all to do with probability.

[northernladuk]

Card games are all to do with probability.

Not just probability as there is a cash value as well which brings implied odds and other factors. You are right what you said earlier about those types of odds playing poker and they are a bit ridiculous but if there is value there it makes it worth a bet. If it's 1 in 420 and you have to put £10 in win £300 then that's terrible. If the pot is £20k then you bet every day of the week.

So it's probability and expected value.