clarkacal
clarkacal
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November 1st, 2010 at 1:04:44 PM permalink
I made a bet with a friend who used to book that I could beat the spread on 50% or more of every regular season game this upcoming nfl year. If I win I get $1000, if he wins I pay $500. There is no vig, just pick winners, ties don't count. It seems to me this is a very good bet and he is on tilt...what do you think? With no vig it seems there is no mathematical disadvantage. The only argument i'm hearing seems to be psycholigical biases when picking being a common downfall. Is this legitimate? I plan on making completely random picks to offset this possibility. Isn't this like getting 2:1 on a coin flip?

Through Sunday 10/31 I am +19 and he is talking about a deal. What would be a good offer to take here? $800? $700? I'm in real good shape now but it's so volatile that 2 bad weeks I could be back close to even...or should I just hold out for the whole amount to teach him a lesson?
SOOPOO
SOOPOO
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November 1st, 2010 at 1:41:11 PM permalink
The better math guys will easily be able to calculate the present expected value of your bet. What they cannot calculate is the 'value' to you of 'teaching him a lesson'. +19 on a 50/50 proposition with about 150 games left is probably worth about $850, but I would guess mathextremist or the Wiz will give you the exact value.
FinsRule
FinsRule
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November 1st, 2010 at 2:04:41 PM permalink
Depends on how reliable your friend is on paying. I'd take $800 from him right now.
mkl654321
mkl654321
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November 1st, 2010 at 2:14:42 PM permalink
Quote: clarkacal

I made a bet with a friend who used to book that I could beat the spread on 50% or more of every regular season game this upcoming nfl year. If I win I get $1000, if he wins I pay $500. There is no vig, just pick winners, ties don't count. It seems to me this is a very good bet and he is on tilt...what do you think? With no vig it seems there is no mathematical disadvantage. The only argument i'm hearing seems to be psycholigical biases when picking being a common downfall. Is this legitimate? I plan on making completely random picks to offset this possibility. Isn't this like getting 2:1 on a coin flip?

Through Sunday 10/31 I am +19 and he is talking about a deal. What would be a good offer to take here? $800? $700? I'm in real good shape now but it's so volatile that 2 bad weeks I could be back close to even...or should I just hold out for the whole amount to teach him a lesson?



For him to catch up, he'd have to be more than two games better than you per week for the rest of the season, or there would have to be two weeks where he was a genius and your picks were a disaster, or some combination of the two. I would peg your chances at something like a 4:1 favorite, and for that reason, I would think you should settle for $700. Here's why. If he refused the offer, he would be risking an additonal $300 (by having to ultimately pay you $1000, not $700) to try to win $1200 (not paying you $700, and winning $500 from you, to boot). Mathematically, this would be fair, given your 80% chance of winning.

The above is why I don't think an offer of $800 is fair. If he refused, he would be getting 6 1/2 to 1 on his bet (risking having to pay you $200 more). I don't think his chances are that bad (i.e., he isn't a 13:2 underdog).
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
MathExtremist
MathExtremist
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November 1st, 2010 at 2:35:58 PM permalink
Quote: clarkacal

I made a bet with a friend who used to book that I could beat the spread on 50% or more of every regular season game this upcoming nfl year. If I win I get $1000, if he wins I pay $500. There is no vig, just pick winners, ties don't count. It seems to me this is a very good bet and he is on tilt...what do you think? With no vig it seems there is no mathematical disadvantage. The only argument i'm hearing seems to be psycholigical biases when picking being a common downfall. Is this legitimate? I plan on making completely random picks to offset this possibility. Isn't this like getting 2:1 on a coin flip?

Through Sunday 10/31 I am +19 and he is talking about a deal. What would be a good offer to take here? $800? $700? I'm in real good shape now but it's so volatile that 2 bad weeks I could be back close to even...or should I just hold out for the whole amount to teach him a lesson?



That mostly depends on how good of a friend he is, and how badly you want to teach him a lesson vs. just letting him admit he screwed up and forfeit. Surrender in blackjack is 1/2, and letting him pay you $500 now would be very generous.

I'm not sure exactly how many more regular season games there are this year, but someone posted about 150, so I'll use that and compute that the probabilities of you coming out on top. You need to get less than 131/2 games right in order for your friend to win, otherwise you do. In other words, if you go 65-85 or worse, you lose. The chance of going 65-85 or worse in 150 games, assuming each pick is 50/50 (which it would be if you were flipping coins), is:

C(150,N)/(2^150)
summed over N = 0 .. 65

That's about 6%, or more than a 15-1 dog, so you're way ahead at this point. With a 94% chance of winning, your bet has a present value of about $910 (not accounting for investment returns or inflation, etc), so to me it's unlikely that $90 would get him to do a deal now. Again, the question is how much of a lesson you want to teach him.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
thecesspit
thecesspit
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November 1st, 2010 at 2:36:07 PM permalink
Quote: mkl654321

For him to catch up, he'd have to be more than two games better than you per week for the rest of the season, or there would have to be two weeks where he was a genius and your picks were a disaster, or some combination of the two. I would peg your chances at something like a 4:1 favorite, and for that reason, I would think you should settle for $700. Here's why. If he refused the offer, he would be risking an additonal $300 (by having to ultimately pay you $1000, not $700) to try to win $1200 (not paying you $700, and winning $500 from you, to boot). Mathematically, this would be fair, given your 80% chance of winning.

The above is why I don't think an offer of $800 is fair. If he refused, he would be getting 6 1/2 to 1 on his bet (risking having to pay you $200 more). I don't think his chances are that bad (i.e., he isn't a 13:2 underdog).



His friend is not making bets as well. It's clarkacal versus the bank.

To lose he'd have to go 2 under par each week (on average). I assume pushes are no action?
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
mkl654321
mkl654321
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November 1st, 2010 at 2:43:23 PM permalink
Quote: thecesspit

His friend is not making bets as well. It's clarkacal versus the bank.

To lose he'd have to go 2 under par each week (on average). I assume pushes are no action?



The bet is hypothetical. If the offer is made to let him settle the bet for less than $1000, then by refusing, and continuing, he is betting the difference between the settlement and the $1000 that he will be able to come from behind and win. His payoff is the settlement that he will not pay, plus the $500 that he will win.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
Wizard
Administrator
Wizard
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November 1st, 2010 at 2:46:46 PM permalink
Outstanding bet, like taking candy from a baby. Agreed, like getting 2 to 1 on a coin flip. Even better, since you would win on a tie.

By my count, 190 games have been played at the time of your question, about of 512 in the regular season. Using the binomial distribution I show your probability of winning is 99.87%. A fair settlement price would be $998.02.

Note: Answer corrected 11/12/10.
It's not whether you win or lose; it's whether or not you had a good bet.
clarkacal
clarkacal
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November 1st, 2010 at 3:19:28 PM permalink
Thanks wizard for your input. He offered me $600 and I told him when he wanted to make a serious offer let me know. He works for my dad btw so collecting shouldn't be a problem ;-)
Wizard
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Wizard
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November 1st, 2010 at 5:17:15 PM permalink
Quote: clarkacal

Thanks wizard for your input. He offered me $600 and I told him when he wanted to make a serious offer let me know. He works for my dad btw so collecting shouldn't be a problem ;-)



You're welcome. Yup, $600 is way too low.
It's not whether you win or lose; it's whether or not you had a good bet.

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