Interesting Situation in my NFL Picks League

[Freerollin`]

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I thought about it in exactly this way and I don't think it is right. Instead of the classic "do you see why?" I'll say that upon request I think I can provide a specific counterexample to refute the lottery example. While my counterexample can refute the lottery example I am *not* sure that it generalizes to apply to the football pool example (I am still thinking about how to do that).

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Noobie:

After hanging around here for a while, you'll realize that I'm wrong most of the time. Therefore, do not wait for me to request a counterexample to prove me wrong, just do it like everyone else does.

[sp3ctr3]

I may have confused some. There is only one first place at the end of the season.

But there is a weekly pot ie

The buy in per week is $12

2 goes to season pot

10 to weekly

So it is not exactly winner take all. Sorry about that.

[sp3ctr3]

I worked some things out but I have based it only on winning a perfect 14 games. There are many other possibilities and and I don't know if there is an edge in those.

Below is a list of 14 possible games and the how often the picker is correct. Two games are 50-50 those are given more detail.

A 50% Team X - Team Z
B 90%
C 80%
D 85%
E 95%
F 90%
G 95%
H 85%
I 95%
J 90%
K 50% Team W - Team Y
L 70%
M 80%
N 75%

One Picks Team all 14 wins = ~3.79%

Possible outcomes – XW, XY, ZW, ZY

Picks Team 1 – AC
Picks Team 2 – AD
Picks Team 3 – BD

One out of three teams getting 14 wins = ~11.38%

~3.79 x 3 = ~ 11.38

no gained equity

I think the actual benefits could come in the other possibilties, but so far it looks like 3 teams do not have an advantage. Someone else give a run at the numbers. I was messing around with another model but it would take time I do not have on my lunch break to figure out.

[WaimanaloSlim]

It's not unfair.

Just imagine what you'd be thinking if you did the same: I just tripled my chances of winning! But if I lose, I lose 3 times as much.

His increased chances of winning is offset by the fact that he's paid for and submitted at least 2 guaranteed losers. And the other entries benefit from the money he's added to the prize pool from these picks.

It's not unfair, especially if no one else is restricted from doing the same.

[sp3ctr3]

So what is the optimal way to play three teams? You get to pick the winners so there should be a "best" way to play.

Is having three teams a bad thing? Obviously submitting three teams with the same picks would be -ev. But is there a way to play optimally?

[paperboyNC]

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So what is the optimal way to play three teams? You get to pick the winners so there should be a "best" way to play.

Is having three teams a bad thing? Obviously submitting three teams with the same picks would be -ev. But is there a way to play optimally?

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Playing 3 teams is -EV period. So the guy is at a disadvantage playing them.

[Freerollin`]

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[ QUOTE ]
So what is the optimal way to play three teams? You get to pick the winners so there should be a "best" way to play.

Is having three teams a bad thing? Obviously submitting three teams with the same picks would be -ev. But is there a way to play optimally?

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Playing 3 teams is -EV period. So the guy is at a disadvantage playing them.

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Please explain. I can't see how it is anything other than the same EV as one team.

[WaimanaloSlim]

There are 2^14=16,384 possible entries, so 3 picks isn't gonna make much of a dent into this.

But they're not coin flips. Look at the lines, flip-flop on the closest games.

I think you could gain an edge if the game is supposed to be close, but most everyone seems to be picking one team. Here you'd pick the other team to separate yourself from the pack. You're just as likely to separate yourself backwards, but you're trying to win the thing. The game is effectively meaningless if everyone is picking the same team. Getting 1 game ahead over most of the field is a big deal.

[BiPolar_Nut]

I know there are more qualified people here than I to do the math, as I've never had any formal stats/probabillity classes other than sections/blurbs in my math studies almost 2 decades ago (that never went beyond diff eq)...but this is how I see it:

This pseudoanalysys is based on only the weekly results at $10 (OP said $10 went to the weekly pool and $2 to the season) to win $200 (20 teams w/ "Mr Questionable" only having one team in the first example.
Also assuming there are 2 coinflip games in the week.
Also assuming everyone has the same chance at winning the coinflip games.

So w/ Mr Questionable having one team, he is betting $10 to win $200 with the same 25% chance of winning as everyone else...and it would be expected that 5 teams would correctly pick the 2 coinflips (25% of the 20 teams). Net result, a 25% chance that Mr Q's $10 will win $40 ($200 split between 5 winners) from a $10 bet. That's a PK as expected since I assumed everyone had an equal chance of guessing the coinflips.

Now if Mr Q has 2 teams, and picks 2 different coinflip outcomes, he'd have a 50% chance of winning $42 (25% of $210 since there are 21 teams now) from a $20 bet. +104?

If Mr Q has 3 teams, he now has a 75% chance of winning $44 from a $30 bet. +110?

Looks like an advantage to me but perhaps my assumptions were too much.

Corrections/flames graciously accepted.

[BiPolar_Nut]

Further thoughts:

My pseudoanalysis above obviously ONLY gives an advantage on the coinflip games...which could be substantial since every week here people put up picks and another replies w/ "I just don't know which way to go on this one". Since all the games must be picked in the league, coinflips will occurr.

More importantly, however, is how good is Mr Q at handicapping? If 2 of 16 games are coinflips, his slight advantage is only good on 12.5% of the picks.

If Mr Q is a poor capper, by all means encourage him to have even more teams since the small advantage on coinflips won't offset overall poor capping skills [img]/images/graemlins/smile.gif[/img]

If he's actually good tho...I'd want him back at 1 team.