Entering a contest

[deception5]

Hi all,

I've been thinking about this for a while and it just occurred to me that someone here would probably be able to figure it out.

My office has a raffle - each time you buy something out of the vending machine you may find a ticket taped on the back of the item. Every month there is a drawing for a free dinner and everyone who submits their tickets is eligible. You can enter as many times as you like and the tickets never expire.

Let's say I have 10 tickets and won't be getting anymore. Assuming all of the prizes are the same and the same # of people enter every month, is it optimal to enter several drawings with a few tickets each, one drawing with all 10 tickets, or 10 drawings with one ticket each? Also does this change depending on the number of people entering each month?

Thanks for your help!

[LetYouDown]

The number of entrants is pretty important here, but my inital guess is that you'd be best off splitting the tickets as evenly as possible between all events...assuming you can theoretically win the prize every single time. I'll try to crunch the numbers out at some point, assuming no one gets to it first.

[Tom1975]

Can you win more than one prize per month?

[PairTheBoard]

I'm finding this hard to believe but it looks to me that you improve your EV by spreading the tickets out.

Suppose there are 10 drawings and 10 other tickets are entered each drawing. Suppose the prize for each drawing is worth $20.

If you enter all 10 of your tickets in one drawing then each ticket has 1/20 chance of winning. Each ticket has $1 EV and you get a total EV of $10.

But if you enter 1 ticket each in 10 different drawings, each ticket has 1/11 chance of winning. Each ticket has about $1.82 in EV and you get a total EV of about $18.

There must be a principle at work here that's worth noting.

PairTheBoard

[PairTheBoard]

I guess by spreading the tickets out you don't have your tickets competing against each other. When entered together, if one of your tickets wins it "causes" your other tickets to lose. This doesn't happen when you spread them out.

PairTheBoard

[pzhon]

[ QUOTE ]
I guess by spreading the tickets out you don't have your tickets competing against each other. When entered together, if one of your tickets wins it "causes" your other tickets to lose.

[/ QUOTE ]
Yes. This is the opposite of what happens in a lottery if you buy different combinations. If everyone else chooses uniformly, then if it is worth it to buy 1 ticket, it is worth it to buy all combinations, since you are winning your own money back, too.

[deception5]

[ QUOTE ]
The number of entrants is pretty important here

[/ QUOTE ]

I figured this would probably be relevant although I'm interested in how this would play out in all scenarios. My estimation is that most people throw them away, so maybe 10 tickets on average go into each contest - although it would also be interesting to see the how it would work with 100 entries.

In response to the other questions there is only one prize per month but if you are lucky you could win every month (so you could win 10 times if you entered 10 different times).

[SumZero]

[ QUOTE ]
I guess by spreading the tickets out you don't have your tickets competing against each other. When entered together, if one of your tickets wins it "causes" your other tickets to lose. This doesn't happen when you spread them out.

[/ QUOTE ]

Exactly, if there are multiple prizes or if the number of tickets from other workers is uniform. And, to use a poker example, this is why a chip race off favors the players with only 1 chip and hurts the players with 4 chips (as long as there are multiple chips being raced off).

[PairTheBoard]

[ QUOTE ]
[ QUOTE ]
I guess by spreading the tickets out you don't have your tickets competing against each other. When entered together, if one of your tickets wins it "causes" your other tickets to lose. This doesn't happen when you spread them out.

[/ QUOTE ]

Exactly, if there are multiple prizes or if the number of tickets from other workers is uniform. And, to use a poker example, this is why a chip race off favors the players with only 1 chip and hurts the players with 4 chips (as long as there are multiple chips being raced off).

[/ QUOTE ]

I'm not so sure about that SumZero. It looks to me like a chip race off would be the same situation as the lottery that Pzhon mentioned - except for the Extra Prize that rounding up would produce.

PairTheBoard

[Chamonyx]

Also, you maximize the probability of winning at least once if you play 10 times (=61.4% versus 50% if you put it all in).