Probability of winning a small sweepstakes?

johnd192 · #1 09-12-2005, 04:45 PM

I was asked about this one.
If you can enter as many times as you like for each drawing and there are multiple drawings. Is it better to pool your entries into one drawing or to enter one time for multiple drawings. I.E. If I have 20 entry tickets is it better to enter 20 times into 1 drawing with about 1000 other entries or is it better to enter 20 different drawings once with each drawing have 1000 other entries. I thought it would be better to enter one time with 20 tickets to give you a 2 percent chance. I thought the other way would give you 1/1000 chance each time independently. This is in relation to the xbox360 giveaway. Thanks in advance.

Mr. Curious · #2 09-12-2005, 04:55 PM

How much is each drawing worth, how many entries are there, and what are the prize payouts?

Once you know those three variables you can calculate your EV and figure your strategy from there.

johnd192 · #3 09-12-2005, 05:02 PM

There is only one prize for each sweepstake. An Xbox360 which is a 400 dollar value.
Each entry costs approximately 1 dollar.

LetYouDown · #4 09-12-2005, 05:05 PM

Same Topic, essentially

johnd192 · #5 09-12-2005, 05:22 PM

It is but I guess it doesn't make common sense to me.
If you have only 1 prize to win per drawing it still seems better to place all your lots into one basket. If you have 10 tickets and only 10 other entrants then it seems you would have 10/20 chances to win and not 1/20 chances to win with each ticket as the other poster pointed out. Am I way off base here? It's been 12 years since I did anything with math so if I am thinking wrong someone please point it out.
Thanks in advance.

KJL · #6 09-12-2005, 05:40 PM

You have to look at the value of each induvual ticket. If there are 10 other entrants in every other time. If you enter 10 tickets, granted have a 50% chance to win that time, but each ticket has only a 1/20 chance to win. As opposed to a 1/11 chance if you enterted 1 ticket each drawing. I think that someone said the exact same thing in the linked thread.

KramerTM · #7 09-12-2005, 05:52 PM

[ QUOTE ]
It is but I guess it doesn't make common sense to me.
If you have only 1 prize to win per drawing it still seems better to place all your lots into one basket. If you have 10 tickets and only 10 other entrants then it seems you would have 10/20 chances to win and not 1/20 chances to win with each ticket as the other poster pointed out. Am I way off base here? It's been 12 years since I did anything with math so if I am thinking wrong someone please point it out.
Thanks in advance.

[/ QUOTE ]

Don't forget that by doing 20 separate ones, you are allowing yourself to win up to 20 Xboxes.

BigBiceps · #8 09-12-2005, 09:56 PM

here is the basic theoretical answer.

if you want to win once, put all the tickets in one drawing.

if you want to maximize your expected value by giving you a chance to win multiple times, spread your tickets out over all the drawings.

The basic theory is that, by putting all in one drawing you are essentially wasting tickets if you win.

The second method, you can win more than once, but you are more likely to come up empty handed.

johnd192 · #9 09-13-2005, 09:52 AM

Thanks.
I found out you can only win once so I guess the correct strategy would be to load up on one drawing

LetYouDown · #10 09-13-2005, 09:55 AM

[ QUOTE ]
Thanks.
I found out you can only win once so I guess the correct strategy would be to load up on one drawing

[/ QUOTE ]
If that's the case, you absolutely should load up on one. Otherwise, I spread them out every time.