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My friends and i are in a football pool where each week you have to pick a loser in a game. At the beginning of the year you purchase how many picks you want - the number of picks you buy determines how many choices you get each week to choose a loser. If you get it right your pick is still alive and you move to the next week. Get it wrong (i.e the team you chose won instead of lost), and your pick is out. We are trying to determine how many picks you would have to buy to garaurantee that you'd win. There are 13 teams in the NFL and there's 17 weeks of play.

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Can you place multiple picks (like 2^16 = 65536) on a single game.

If so, a possible strategy would be to put half you picks on each side of any game.

You will keep (and lose) half of your picks every week.

This will guarantee you have one pick left at the end of the season.

This is probably not an exciting or efficient strategy.

Otherwise, this is a fair and difficult contest.

- Your "pick" is your choice each week. So at the beginning of the year i "buy" a "pick" which means that i now have a choice on a game - i have to choose a loser and if i get it right, i advance to the next week. I can put choose both sides if i want, yes.

- Sorry about the 13 there, not sure what i was thinking. You can choose between the games of all 32 NFL teams.

Let me know if i didn't answer all of the questions there.

If not, you could buy 18 picks. Each week,pick any one game and bet on both sides.

You'll lose one pick each week but remain with one left over at the end.

Apparently this is called a Survivor Pool.

It seems to be a true balance of luck and skill.

It is a fair contest assuming honest management.

The only honest way to assure a win would be to buy a massive number of picks.

If you do that, you would likely wind up splitting you own money with one or more lucky and/or skillful players.

The way to win dishonestly is to pick (or change your pick) after the game is over.

You would lose

That's why I asked "

if you aren't required to use all of your picks every week then your picks go like this...

You use 2 and save the other 16, You lose 1, keep1.

Next week, use 2, save 15, lose 1, keep 1

Next week, use 2, save 14, lose 1, keep 1

etc...

Last week, use 2, save 0, lose 1, finish with 1 pick left for the win.

Again, not very fun - same idea as buying the exponential when you DO have to use them all.

But, if there is a "save" loophole, it's cheaper.

So 2^17= 131072

If you go with 2^16, you'll go into the 17th week with just 1 pick left so you'd have to guess at the last one and maybe not win.

The number of teams playing isn't actually important at all (as long as there is at least one game), you are putting all of your picks on just one game, but split to both sides.

That's not quite true, and it doesn't matter.

There are no byes the first and last few weeks of the season.

You still need to allow for losing half you picks every week, so you need to start with 2^16.

A more important question is:

Just simplifying: let's say I have a season consisting of just one game.

That would mean I would start with 2^0 =1 pick so I can't pick both sides to guarantee a win

I think you need 2^N instead to get the guarantee all the way through

So 2^17 = 131072

"Loss" in what sense?

A loss for the team, meaning a win for you?

Or a loss for the pick, meaning a loss for you?

If a ties mean a loss of the pick, then there are no guarantees.

It's exceedingly unlikely but possible for every game to end in a tie, all picks would be lost - meaning no person could win the pool

However, with the ambiguity around ties, I'm not sure we have an answer yet anyway.

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Start your 7-day free trialMatt M. : 11/17/2008 3:50 pm : link

In most, if not all, survivor pools, you must successfully select one team to win each week. If that team doesn't win you are knocked out. In this scenario,

you lose!

damdevs : 11/17/2008 3:56 pm : link

Math / Science

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What do you mean "your pick is out"

Does that mean the team that I picked is no longer a choice I can make from the pool for the remainder of the season?

Or

Does that mean I have one less choice each week for the remainder of the season?

Or

Does it mean something else?

Also "number of picks you buy determines how many choices" - I assume one pick=one choice?

Also, 13 teams? Since that's not all of them. Do you only pick between teams in the subset of games that are between those 13, or between all games or between games where they don't play each other?

If you can pick from games they play each other, are you allowed to pick both sides (assuming you have 2 picks left?)