I’ll take a piece of 400 million.
If he was a regular player, I believe he should be included. In our office (where I run the pool) if a person is consistent I would have just thrown the money in for him.
On the rare occassions at work when we throw in for lotto (sometimes we do it with left over money from lunch if everyone overpays), I always encourage someone to not go in so that we will win and have a court case. In truth no-one is ever left out - even if you were away on holidays and didn’t go to lunch you would get a share. There are 10 of us that work together and there are 10 shares in any good luck.
I think your math is off here. Imagine a very simple lottery, in which 100 tickets are sold for $1 each, and the only prize is a $30 jackpot.
In this case, each ticket you purchase has an expected return of $0.30, or a net expected loss of $0.70. (Note that in most cases, you won’t hit the expected return: for example, if you purchase 1 ticket, you’ll either exceed expectations by $29.70, or you’ll fail them by $0.30). You’ve got a 1% chance of getting $30, and a 99% chance of getting zilch.
Join an office pool with nine other people, and those chances change: now, your group has a 90% chance of getting nothing, and a 10% chance of getting $30. If y’all get the $30, you split it ten ways, so personally you’ve now got a 90% chance of getting nothing and a 10% chance of getting $3.
So your odds change–but the expected return remains the same. 10% of $3 is $0.30, so your expected return is exactly what it was for a larger ticket. The only difference is that now, instead of having a miniscule chance of getting a big winning, you’ve got a much larger chance of getting a small winning.
There’s nothing stupid about it. It’s a way people have of massaging their winning chances, without changing the underlying expected returns. As long as folks are comfortable with the fact that the lottery is not a good investment strategy–as long as they’re playing for the pleasure of gambling, not for the need for cash–then an office pool is one of the few meaningful strategies out there.
Daniel
Lots of businesses ban pools of any kind- especially sports, which could be seen as illegal wagering.
Eh. Sounds like the guy is jealous and pissed off. I would be too, but I wouldn’t be suing.
The above is posted with the disclaimer that we don’t have all the facts, we’re just guessing, blah blah blah… :rolleyes:
If he actually contributed all the time (rather than, say, half the time), I think his coworkers should have shared the prize. That’s what I would have proposed in this situation, anyway. There’s really no need for creating bad feelings between coworkers, nor to have leave a buddy upset because he missed the one bet that won (that must be very irritating) just to keep a slightly larger share of money.
If this is true and he wins, I’m suing for my share! Who’s with me? We’ll file a class action!
I think that’s what the poster you’re responding to meant. It wasn’t the maths, but the psychological aspect of it. If you made a pool with 1 000 000 persons, the expected return would still remain the same. But if you got the winning ticket, you’d win only some dollars, which would be pointless.
I think the idea of the poster was : anyway, with 1 or 100 tickets, the chance of winning is close to nil. And I’d rather dream about winning 1 million than 1/100th of a million. That’s the point of lottery, I think. Not the odds, not the expected return (or else nobody would play), but the hope of winning big.
Different Math for you:
What is your chance of winning on 1 ticket. It approaches 0
What is your chance of winning with 300 tickets, It approaches 0
I think that is what Revtim meant.
Jim
Exactly. When the chances of winning one ticket is nearly zero, that means your chances are still nearly zero when you buy ten tickets. 10 times a number very close to zero is still very close to zero.
It’s not usefully comparable to a hypothetical lottery situation where the chance of buying a winning ticket is 1/100.
The point, though, is that your expected winnings in either case approach zero, too. Doing a group ticket buy is no stupider than doing an individual ticket buy. As long as a person is buying a ticket for entertainment and not for a financial investment, I don’t see it as stupid at all.
Daniel
I’m not arguing that an individual ticket isn’t stupid too. I’m arguing that it’s even stupider to reduce the prize by a large practical amount for no practical increase in probability of winning, not to mention the added hassle of situations similar to the one in the OP and the one Duke of Rat mentions.
Example: The Florida lottery is 6 numbers, each of range 1-53. If I remember probability, the chances of a ticket winning are 1/(53^6), or 4.511e-11, or about .000000000045 (where 1.0 = 100 percent probability). This is very close to zero.
If you’re part of a 10 ticket group, your chances increase to ten times that, or to .00000000045. In real world terms, your chances of winning are still damn close to zero. There was no real practical gain here, even though it’s technically ten times greater.
But if the jackpot was say, a million bucks, that gets reduced to $100,000. Still nice, but you paid $900,000 for pretty much no practical increase in your odds of winning.
You’re definitely missing an important part of the math: you’re reducing the prize by exactly the same amount that you’re increasing your chance of winning. The two are exactly inversely proportional to one another. If you don’t see the increase in odds of winning as a practical increase, then you shouldn’t see the decrease in actual winnings as a practical decrease.
In your example, while the difference between .00000000045 and .0000000045 may not look like much to you, it’s a tenfold difference, exactly mirroring the difference in earnings. You’re ten times as likely to win in the latter case, the case in which you win a tenth as much. There’s no practical difference between the two: in both cases, for all practical purposes your winnings will total $0.
Daniel
To put it a different way: let’s say I’m running a lottery with a $250,000 jackpot, for which I’ll sell one million tickets for one dollar each. Then I’m going to skip town and go to Jamaica. The chances of winning my lotter ARE zero.
Bob buys a ticket by himself, spends a dollar, hoping to get the $250,000 prize for himself. Mary buys a ticket as part of a ten-person office pool, hoping to get $25,000 for herself. Which one of them has made the worse investment?
Answer: neither, since they’ve got exactly the same chance of winning, i.e., zero. If we say that the office pool has the same practical chance of success as the individual ticket, we only say that because we think the chance equals zero; and in such a case, the amount of the prize money is irrelevant.
The amount of the prize money only becomes relevant if the chance of winning is not zero; and in such a case, the chance of winning with an office pool increases in exact inverse proportion to the size of each person’s prize money. The individual ticket purchase is precisely as stupid as the office pool purchase.
Daniel
RevTim
The actual number of ways of choosing ‘k’ objects from a group of ‘n’ objects is:
n! ÷ (k! • (n-k)!) with the exclamation point meaning ‘factorial’
In the Florida lottery k = 6 and n = 53 and so we have:
53! ÷ (6! • 47!) which reduces to:
53 • 52 • 51 • 50 • 49 • 48 ÷ 6 • 5 • 4 • 3 • 2
which equals 16,529,385,600 ÷ 720 which equals:
22,957,480
So the odds of hitting the “jackpot” are 1 in 22,957,480
The probability of this would be 0.000000043558788
or about 4.36 × 10[sup]-8[/sup]
Just thought I’d help out. 
I disagree, because there’s a difference between “zero” and “extremely close to zero” or “practically zero”. If it were actually zero, I agree the prize size is irrelevent. But because the chances of winning are non-zero, the amount of the prize is relevent.
My point is that the difference of one probability over the other that is “purchased” by a significant prize reduction, is itself non-significant (but not zero).
Dangit, I forgot you cannot pick the same number more than once. Thanks for the correction.
Again, the significance of prize reduction is exactly equivalent to the significance of the increased chance of winning. If the chance of winning is insignificant, then the amount of the potential winnings is insignificant, so it’s not stupid to reduce the amount of the potential winnings–it’s insignificant. If the chance of winning is significant, then you need to recognize that this significant chance is multiplied by exactly the same number by which the potential earnings are divided.
Daniel
From a mathematical point of view, I completely agree with Left Hand of Dorkness.
If the chances are exactly zero, then the prize money is insignificant (and obviously by definition the chances of winning are too).
However, if one is going to argue that the prize money is significant because the chances of winning are not exactly zero then I cannot see how one could ignore the slight increase in the chances of winning. By even acknowledging the significance of the prize money, you are acknowledging the significance of an actual chance of winning, in which case I fail to see why one wouldn’t acknowledge the tenfold increase in this chance.
In conclusion, I believe the lottery pool idea does not affect your rate of return.
From a psychological point of view, I completely agree with Revtim.
I imagine many people who purchase lottery tickets are really purchasing the idea of winning a huge sum of money. It’s pretty cool to think about all that loot and the additional spice of having the theoretical possibility of winning is essentially what you are purchasing. From this point of view, since dreaming of $10,000,000 is probably more valuable than dreaming of $1,000,000, lottery pools do not make much sense.
Since lottery tickets are fundamentally a terrible investment, I tend to give more weight to the physiological point of view which is why I would never do the lottery pool thing myself. Actually, I’d never do the lottery ticket thing myself either, but I’m even less likely to do the lottery pool thing.
Excellent! 
Hmm. If someone enters a ten-person pool for a $10 million jackpot, and they’re dreaming of winning $10 million, AND they actually win the jackpot, I’ll agree that psychologically, they’re being dumb.
However:
- I’m figuring that most folks entering these pools know that they won’t get the full prize. As such, they’re the best judge of whether they’re getting the most psychological bang for their buck, not me; if the increased chance of winning is more fun for them, then that’s their monkey.
- Of the ones who DON’T understand that their prize is decreased, then sure, they’re math idiots. HOWEVER, the overwhelming, overwhelming majority of this group isn’t going to win anyway. So for them, they get the psychological advantage of the pool (increased chance of winning) WITHOUT the psychological disadvantage of the pool (decreased winnings). It seems to me that this group of idiots are psychologically the happiest lotto players of all.
So in the end, I’m not convinced that even from a psychological perspective Revtim is right–unless his judgment of the psychology is purely personal, and doesn’t apply to anyone besides himself.
Daniel