Interesting Situation in my NFL Picks League
 

I play in a 20-25 person per week NFL picks league. Each person attempts to pick all the winners for each game, no spread involved. It has come to my attention that one player is actually registered three times. He still pays for three "players", so I can not figure out if this creates an advantage for him or not.

Has anyone run into this before? Should I be concerned?

Re: Interesting Situation in my NFL Picks League
 

Yes. Take his money and boot him.

Re: Interesting Situation in my NFL Picks League
 

After speaking with the person running the league, he says that he is not concerned with the person playing multiple pick teams. How exactly could playing multiple teams help? It seems shady to me but I can not put my finger exactly how paying for extra teams could help. Please advise.

Re: Interesting Situation in my NFL Picks League
 

seems to me to be the same thing as buying multiple bingo cards. it doesn't really put anyone at a disadvantage like at a poker table.

Re: Interesting Situation in my NFL Picks League
 

If he's paid for three and it isn't against the rules, there's nothing wrong with it.

Re: Interesting Situation in my NFL Picks League
 

it definitely creates an advantage in a winner take all system. i am pretty sure it creates an advantage in any system but not 100%. if you want to ill type up some math to prove it but yes, it does create an advantage.

Re: Interesting Situation in my NFL Picks League
 

It is winner take all. If you could show me the math, that would be greatly appreciated.

If I can show it creates an advantage, this will not be allowed in the league.

Re: Interesting Situation in my NFL Picks League
 

If it is winner take all then he definitely gets a big edge here and if this was not something that was known to people in the league either as an option for themselves or that it was going on, the guy should get his money back for two teams and stick to one.

Think about it, if I had 5 teams, I could stick same on the huge favorites since its simple win not spread, and then on the PK type games I could have a few different groupings.

For example:

1 v. 2 1 is 10 pt. favorite
3 v. 4 3 is a 2.5 pt. favorite
5 v. 6 5 is a 9 pt. favorite
7 v. 8 PK

He can basically have all/most his teams pick the big favorites, then on 3/4 and 7/8 game have different combos to assure one will be correct.

Simply not fair.

Re: Interesting Situation in my NFL Picks League
 

it's interesting that you should say that, because i was just thinking the opposite.

Whether you're sticking to the oddsmakers' favorites or not, each person is making what they believe is the optimum choice on every game.

Obviously this guy isn't going to duplicate his picks on all of his accounts, so he's then deviating from what he thinks are the best picks, and therefore gambooling.

So i'm interested in what makes it an advantage.

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
If it is winner take all then he definitely gets a big edge here and if this was not something that was known to people in the league either as an option for themselves or that it was going on, the guy should get his money back for two teams and stick to one.

Think about it, if I had 5 teams, I could stick same on the huge favorites since its simple win not spread, and then on the PK type games I could have a few different groupings.

For example:

1 v. 2 1 is 10 pt. favorite
3 v. 4 3 is a 2.5 pt. favorite
5 v. 6 5 is a 9 pt. favorite
7 v. 8 PK

He can basically have all/most his teams pick the big favorites, then on 3/4 and 7/8 game have different combos to assure one will be correct.

Simply not fair.

[/ QUOTE ]

But if everyone else is also using the same method, basically on the same ground as him; it's not as though he gets to take his best result from each week and build from there-- each team stays separate.

If you just assume it comes down to 16 coinflips (one each week), all people have an equal possibility of getting the most heads, so his 3 entries would have bought him 3 times the chance.

Re: Interesting Situation in my NFL Picks League
 

If he has an advantage by having three teams, then the other twenty players should get together and play as one unit and have an incredible super advantage. [img]/images/graemlins/tongue.gif[/img]

Lori

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
He can basically have all/most his teams pick the big favorites, then on 3/4 and 7/8 game have different combos to assure one will be correct.

[/ QUOTE ]

Except there's no reason the same account will win every week, so none of his accounts will be obviously stronger than yours. Besides that, he's paid for three entries, so he needs to have three times the winning probability in order for it to be +EV.


It's not an advantage for him.


If you believe it is, I'd like to see some kind of non-handwaving explanation.

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]

It's not an advantage for him.
If you believe it is, I'd like to see some kind of non-handwaving explanation.

[/ QUOTE ]

I agree with the above that it is probably not an advantage. I would also like to see some sort of rigorous proof that he has an advantage from anyone that believes that it is the case.

I really doubt there is an advantage, but I admit I don't have a rigorous proof that shows that he has no advantage...my mental handwaving just leads to the conclusion that there is no advantage.

I may take a crack at it (i.e. proof), if I get anything good I'll post it.

Re: Interesting Situation in my NFL Picks League
 

Each opportunity at choosing an extra team is counterbalanced by the fact that he had to pay extra money to play multiple times.

This sort of thing is just like the lottery. Say I buy one ticket and Joe buys 40. Each ticket has the same chance of winning, but he's got more chances - that he paid more money for. Of course, my ONE chance is just as likely to win as any one of his chances.

Yes, I'm aware of the differences between an outcome that is unpredictable (lottery) and one that has some potential of being predicted. IMO, it doesn't matter here because just like the lottery, regardless of the amount of tickets we have, the winner gets the same prize. We're talking about advantages, but none exists when each "ticket" costs the same as every other ticket and the payout amount doesn't correspond to the number of chances, regardless of the predictability of the outcome.

Re: Interesting Situation in my NFL Picks League
 

There is an advantage but the reason its hard to figure it out is because it most likely hasn't came into play much yet. Imagine this scenerio:

1.) He picks virtually identical in all 3 for 12 weeks. He could be ahead but lets say in this time he is behind 3 games to the leader. He goes and looks at the picks made by the leader to get a good idea what he will do. Now he makes his picks. He finds that his are off by one of what he thinks with almost certainty what the leader will do . He picks in two what he believes what to be correct, and picks the other the same as the leader. If his pick is correct he can pick up a game in two and fall behind another in only 1. The next week he can do the split the two he is only two behind and pick more upsets with the one that is now 4 behind. Continue the process to give himself an advantage to catch up without having to tank his only team with upsets.
2.) He finds himself ahead in week 14 with his 3 teams ahead of one opponent by 1 game. He simply picks with 2 what he believes is best and alters one game in one trying to match his opponent. Week 15 he may be two ahead in two and tied in one or the opposite but not behind or tied.

Re: Interesting Situation in my NFL Picks League
 

If he had (16^2)^17 teams he could lock in a win hmm...

I can't imagine him playing all 3 teams patiently until week 12, but apparently this was all done hush hush so who knows what nefarious purposes he had.

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
There is an advantage but the reason its hard to figure it out is because it most likely hasn't came into play much yet. Imagine this scenerio:

1.) He picks virtually identical in all 3 for 12 weeks. He could be ahead but lets say in this time he is behind 3 games to the leader. He goes and looks at the picks made by the leader to get a good idea what he will do. Now he makes his picks. He finds that his are off by one of what he thinks with almost certainty what the leader will do . He picks in two what he believes what to be correct, and picks the other the same as the leader. If his pick is correct he can pick up a game in two and fall behind another in only 1. The next week he can do the split the two he is only two behind and pick more upsets with the one that is now 4 behind. Continue the process to give himself an advantage to catch up without having to tank his only team with upsets.
2.) He finds himself ahead in week 14 with his 3 teams ahead of one opponent by 1 game. He simply picks with 2 what he believes is best and alters one game in one trying to match his opponent. Week 15 he may be two ahead in two and tied in one or the opposite but not behind or tied.

[/ QUOTE ]

These scenarios do not prove anything.

1. He could be three games behind. He could also be 15 games behind, in which case he pretty much just loses 3x the money. Furthermore many pools do not allow you to look at others picks until after the submission deadline. Even if they did, leader could diffuse this strategy by just submitting late, or making "fake" picks and then changing them later.

2. Once again, he could just as easily be 15 games behind. You are not calculating the downside risk. Sure he will be in great shape if he has 3 teams out in front, but he has to get to this point and if he does not, then he loses three times the entry fee.

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
[ QUOTE ]
There is an advantage but the reason its hard to figure it out is because it most likely hasn't came into play much yet. Imagine this scenerio:

1.) He picks virtually identical in all 3 for 12 weeks. He could be ahead but lets say in this time he is behind 3 games to the leader. He goes and looks at the picks made by the leader to get a good idea what he will do. Now he makes his picks. He finds that his are off by one of what he thinks with almost certainty what the leader will do . He picks in two what he believes what to be correct, and picks the other the same as the leader. If his pick is correct he can pick up a game in two and fall behind another in only 1. The next week he can do the split the two he is only two behind and pick more upsets with the one that is now 4 behind. Continue the process to give himself an advantage to catch up without having to tank his only team with upsets.
2.) He finds himself ahead in week 14 with his 3 teams ahead of one opponent by 1 game. He simply picks with 2 what he believes is best and alters one game in one trying to match his opponent. Week 15 he may be two ahead in two and tied in one or the opposite but not behind or tied.

[/ QUOTE ]

These scenarios do not prove anything.

1. He could be three games behind. He could also be 15 games behind, in which case he pretty much just loses 3x the money. Furthermore many pools do not allow you to look at others picks until after the submission deadline. Even if they did, leader could diffuse this strategy by just submitting late, or making "fake" picks and then changing them later.

2. Once again, he could just as easily be 15 games behind. You are not calculating the downside risk. Sure he will be in great shape if he has 3 teams out in front, but he has to get to this point and if he does not, then he loses three times the entry fee.

[/ QUOTE ]

Well put.

Cliff's Notes: FreerollinIsRight

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
If he had (16^2)^17 teams he could lock in a win hmm...


[/ QUOTE ]

I am assuming you meant 2^16 instead of 16^2 (of course, even this is not correct since most week do not have 16 games, but I understand what you are getting at). Even so, this does not lock in a win. If he ties with one person, then he loses half of the massive amount he paid to enter. If he ties with two people he loses even more, etc.

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]

Cliff's Notes: FreerollinIsRight

[/ QUOTE ]

I agree with your conclusion, but I am not sure what the precise reasoning is. I am not satisfied with my justification. I am not convinced by yours either. Specifically,

[ QUOTE ]
This sort of thing is just like the lottery. Say I buy one ticket and Joe buys 40. Each ticket has the same chance of winning, but he's got more chances - that he paid more money for. Of course, my ONE chance is just as likely to win as any one of his chances.

Yes, I'm aware of the differences between an outcome that is unpredictable (lottery) and one that has some potential of being predicted. IMO, it doesn't matter here because just like the lottery, regardless of the amount of tickets we have, the winner gets the same prize. We're talking about advantages, but none exists when each "ticket" costs the same as every other ticket and the payout amount doesn't correspond to the number of chances, regardless of the predictability of the outcome.

[/ QUOTE ]

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).

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]

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).

[/ QUOTE ]

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.

Re: Interesting Situation in my NFL Picks League
 

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.

Re: Interesting Situation in my NFL Picks League
 

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.

Re: Interesting Situation in my NFL Picks League
 

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.

Re: Interesting Situation in my NFL Picks League
 

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?

Re: Interesting Situation in my NFL Picks League
 

[ 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?

[/ QUOTE ]

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

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
[ 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?

[/ QUOTE ]



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

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

Re: Interesting Situation in my NFL Picks League
 

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.

Re: Interesting Situation in my NFL Picks League
 

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.

Re: Interesting Situation in my NFL Picks League
 

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.

Re: Interesting Situation in my NFL Picks League
 

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

[/ QUOTE ]

He isn't picking against the spread which means there are no "coin-flips" in a typical week.

Thus after he calculates the optimals picks, he is forced to pick suboptimal picks for his other 2 entires since they have to be different. If his optimal picks are breakeven, then he is losing money on his suboptimal picks.

If 20 people play the pool and he has three entries, He breaks even at a 15% chance to win. If the game were complete luck, each of his $10 entries would have an EV of $10 and his total EV would be $30.

~PBNC

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
He isn't picking against the spread which means there are no "coin-flips" in a typical week.

[/ QUOTE ]

Dunno why I didn't take that into account.

Essentially eliminating coinflip situations effectively negates any advantage multi-teaming would have...so basically anyone multi-teaming is just pumping the pool, right?

OP: Suggest to whomever runs the league to make it clear that running multiple teams IS allowed, then use my pseudoanalysis a few posts up to convince everyone else that they'd have an advantage running multiple teams, then just run one team yourself [img]/images/graemlins/wink.gif[/img]

Re: Interesting Situation in my NFL Picks League
 

If the lines were 100% accurate this forum probably would not exist. For the sake of this, lets say that there are two games each week that are essentially coinflips (spread being 1-2 points). There is one +-1 pt game this week and there were multiple games last week.

It is looking like there is no advantage, but the person doing this sports bets often and has done well at the picks league in the past. I see the argument for having multiple teams creating teams with suboptimal picks, but if the game is a true coinflip, wouldn't this create an advantage?

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
[ QUOTE ]

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).

[/ QUOTE ]

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.

[/ QUOTE ]
I just didn't want to type it all out, unless someone really cared or if you figured it out. Anyway, here it is.

Let's say you have a lottery with one number (1-10). You can buy a ticket with any number from 1-10 printed on it and each week one number from 1-10 will be pulled out of a hat. Each ticket costs $1 and you can buy as many tickets as you want (and for each ticket you can choose whatever number you want). The prize pool is the total receipts collected from ticket sales. Any player who has a ticket with the winning number is entitled to a share of the prize pool (i.e., if there is only one winning ticket, that person gets all of the prize money, if there are two winning tickets then each person gets 1/2 of the prize pool, etc).

Now let's say three players decide to play this lottery. Player A decides to buy 10 tickets with so that he has one ticket with each number. Player B and Player C decided that they will just buy one ticket and they randomly choose which number to play (it really doesn't matter what they choose, all that is important is that they just pick one number).

In this scenario, total prize pool = $12 ($10 from Player A, $1 from Player B, and $1 from Player C)

According to your reasoning, Player A should have no advantage, because even though he has 10x the chance of winning, he paid 10 times as much, so it should even out. Let's see if this is the case with some simple EV calculations.

EV for Player A

*81% of the time Player A will have the only winning ticket and win 100% of the prize pool for a net win of $2 (i.e., no tie)
*18% of the time Player A and only one of player B or player C will have the same winning ticket so Player A will win 50% of the prize pool for a net loss of $4 (i.e., two way tie)
*1% of the time Player A, B, an C will have a winning ticket and each get 1/3 (i.e., three way tie), so player A will have a net loss of $6

So, therefore the EV equals

0.81*2 + 0.18*(-4) + 0.01*(-6) = 0.84,

So Player A has a EV of $0.84. Similar calculations will yield an EV of -$0.42 for the other players.

So in this instance, by buying multiple entries, player A has managed to gain an advantage in the lottery.

However, for this same lottery game, it is easy to also come up with examples where it is -EV to buy multiple tickets. So, in the end, we can show that buying multiple tickets can be either +EV or -EV, depending on the strategy employed.

I may have made a mistake, somewhere. If so, let me know. Furthermore, as I said previously, I am not sure how to apply this to the football pool case.

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
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.

[/ QUOTE ]

I believe that you made a mistake here and it has nothing to do with whether there are coinflip games or not (which is an entirely different issue). If we simply use the assumptions that you have put forth, I believe that this analysis is incorrect.

Let's go through each scenario.

*Mr. Q has one 1 pick
25% of the time he will share a prize pool with 25% of the participants (5 people). So his share of the pot will be $200/5, which is $40. When this happens he will have a $30 profit.

75% of the time he will be wrong and lose $10.

EV = 0.25*(+30) + 0.75*(-10) = 0

*Mr. Q has two picks.
Now here is where the mistake is made.
With two picks Mr. Q will have a 50% chance of winning the the prize pool and sharing it with 25% of the contestants (5.25 people). IT IS NOT 5 people as you presented. It is 25% of the contestants. If we ran this a million times, sometimes there would be 3 winners, sometimes 4, sometimes 5, sometimes 6, etc. and the average number of winners would be 5.25. So, when he wins, his share of the pot will be $210/5.25 = $40, which will give him a net profit of $20.

50% of the time Mr Q will lose $20.

Therefore

EV = 0.5*(+20) + 0.5*(-20)= 0

*Mr. Q has three picks
75% of the time he will share the pot with 25% of the participants (5.5 people). If he wins, his share will be $220/5.5 = $40, giving him a profit of $10.

25% of the time he will lose $30.

Therefore,

EV = 0.75*(+10) + 0.25*(-30) = 0


So, in your example, one, two, or three picks gives no advantage. EV is zero for all scenarios.

I too admit that I could be wrong and graciously accept any flames/corrections.

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]
If he has an advantage by having three teams, then the other twenty players should get together and play as one unit and have an incredible super advantage. [img]/images/graemlins/tongue.gif[/img]

Lori

[/ QUOTE ]

I can't believe I failed to end the thread with this [img]/images/graemlins/mad.gif[/img]

Of course, if the guy is a winning capper, then his +EV is multiplied ZeeJustin style and that would be a good reason to not allow multiple entries in the future.

Lori

Re: Interesting Situation in my NFL Picks League
 

[ QUOTE ]

So, in your example, one, two, or three picks gives no advantage. EV is zero for all scenarios.

[/ QUOTE ]

Thanks, rsk111. Makes sense to me...I tried to think deeper on it but my brain started to hurt. All I know is it's -EV for me to devote any more time on this one [img]/images/graemlins/wink.gif[/img]

Re: Interesting Situation in my NFL Picks League
 

Many years ago, I was in a pick 'em pool and someone purchased two entries each week. One with his picks and one with the exact opposite picks.

I guess he was buying insurance. He won more often than anyone else that year.