xkcd

by **faranim** » Wed Mar 28, 2012 7:00 pm UTC

http://www.cbsnews.com/8301-201_162-57405833/mega-millions-jackpot-largest-ever-at-$500m/
http://www.latimes.com/news/nation/nationnow/la-na-nn-mega-millions-jackpot-476-million-20120328,0,5783964.story?track=rss

Spoiler:

I tried to search the fora for an existing thread about the Lottery / Mega Millions, but didn't see anything worth bumping. I find the psychology behind the lottery quite interesting - even though the odds of winning are always the same, more people buy tickets when the jackpot is larger. I was even tempted to buy one when I was at the gas station and saw the payout was up to $476M.

by **Роберт** » Wed Mar 28, 2012 7:06 pm UTC

faranim wrote: I find the psychology behind the lottery quite interesting - even though the odds of winning are always the same, more people buy tickets when the jackpot is larger.

Ummm... yes?

In fact, if the odds of winning (and not having to split your winnings) is 1 in 175,711,536 and the payout (after tax) is 300000000, than it would be worth to spend slightly more than $1.50 fro a ticket (assuming you don't care about the publicity you'd get from winning). Basic math.

by **LaserGuy** » Wed Mar 28, 2012 7:29 pm UTC

faranim wrote:I tried to search the fora for an existing thread about the Lottery / Mega Millions, but didn't see anything worth bumping. I find the psychology behind the lottery quite interesting - even though the odds of winning are always the same, more people buy tickets when the jackpot is larger. I was even tempted to buy one when I was at the gas station and saw the payout was up to $476M.

As the size of the payout increases, the per-ticket expectation values increases. The larger the size of the pot, the more worthwhile it is to buy a ticket.

by **yoni45** » Wed Mar 28, 2012 7:37 pm UTC

LaserGuy wrote:As the size of the payout increases, the per-ticket expectation values increases. The larger the size of the pot, the more worthwhile it is to buy a ticket.

I feel like when it comes to the lottery though, while the chances of winning are still equally "not happening", the size of the payout, even if it increases in terms of the hard numbers, is still simply "holy fuck I'm rich". Unless you're buying these tickets in quantities that will give you any kind of "real" chance of winning, the increased payout really shouldn't be a factor.

(if I let you buy 1 ticket for $100 000, with a 0.1% chance of winning $1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, it's still probably not a good idea.)

by **sourmìlk** » Wed Mar 28, 2012 7:40 pm UTC

That's not so much from a mathematical standpoint as it is a practical standpoint: if it's $100,000, you can't afford to lose.

by **Arrian** » Wed Mar 28, 2012 7:52 pm UTC

sourmìlk wrote:That's not so much from a mathematical standpoint as it is a practical standpoint: if it's $100,000, you can't afford to lose.

Mmmm, loss aversion.

by **Iulus Cofield** » Wed Mar 28, 2012 8:16 pm UTC

I'm gonna buy a ticket. The risk/payout is faurly solid and the extremely probable loss is negligible. Plus, that's nearly twenty million dollars a year until I'm near retirement age. That's enough to build a castle, which is my long standing and otherwise impossible dream.

by **Dauric** » Wed Mar 28, 2012 8:19 pm UTC

Should build an evil mastermind fortress. And buy a volcanic island to build it on.

Sure a suave British secret agent will come along, steal your incredibly beautiful and loyal lead henchwoman, kill you and destroy your base of operations, but on the upside you've got more money per year to spend before being forcibly retired, and you will have had an incredibly beautiful supermodel as a loyal lead henchwoman to serve your every whim.

by **sourmìlk** » Wed Mar 28, 2012 8:21 pm UTC

I forget the exact rules of each lottery. What's the probability of winning the US Mega Millions Lottery Jackpot?

by **yoni45** » Wed Mar 28, 2012 8:25 pm UTC

sourmìlk wrote:That's not so much from a mathematical standpoint as it is a practical standpoint: if it's $100,000, you can't afford to lose.

It doesn't matter if you can afford to lose it or not. It's a bad investment in practical terms, since in practical terms you're throwing that money away.

And that's the point -- whether the jackpot is 400 million, 500 million, or "only" 50 million, it doesn't matter. All will effectively give you the same practical result: being rich.

by **Dauric** » Wed Mar 28, 2012 8:35 pm UTC

yoni45 wrote:
sourmìlk wrote:That's not so much from a mathematical standpoint as it is a practical standpoint: if it's $100,000, you can't afford to lose.

It doesn't matter if you can afford to lose it or not. It's a bad investment in practical terms, since in practical terms you're throwing that money away.

It's not a financial investment though.

It is, to paraphrase the webcomic Cat and Girl: The price of hope.

It's the modern fairy godmother. It's about the same part of the brain that makes it seem reasonable to toss coins in fountains or leave notes for forest spirits, or make any sacrifice to deities of any shape.

The difference is there's actually a known mechanism organized by mortal agents that takes those sacrifices and makes miracles happen. In that regard the Lottery is a vastly better form of wishful thinking than draining chickens of blood and making a mess.

by **CorruptUser** » Wed Mar 28, 2012 8:43 pm UTC

yoni45 wrote:
LaserGuy wrote:As the size of the payout increases, the per-ticket expectation values increases. The larger the size of the pot, the more worthwhile it is to buy a ticket.

I feel like when it comes to the lottery though, while the chances of winning are still equally "not happening", the size of the payout, even if it increases in terms of the hard numbers, is still simply "holy fuck I'm rich". Unless you're buying these tickets in quantities that will give you any kind of "real" chance of winning, the increased payout really shouldn't be a factor.

(if I let you buy 1 ticket for $100 000, with a 0.1% chance of winning $1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, it's still probably not a good idea.)

Buy 1000 tickets for $100,000,000 (I assume you can get Warren Buffet to help you out or something), and when you win and your money is completely worthless...

But yes, utility theory would state that $100,000 is worth far more than a 1 in 1000 chance of a google.

by **induction** » Wed Mar 28, 2012 8:46 pm UTC

sourmìlk wrote:I forget the exact rules of each lottery. What's the probability of winning the US Mega Millions Lottery Jackpot?

In this case it's choose 5 numbers from 1-56, plus 1 'mega-ball' number from 1-46. So (56 choose 5)*46 = 175,711,536, like Po6ept said.

by **yoni45** » Wed Mar 28, 2012 8:52 pm UTC

Dauric wrote:It's not a financial investment though.

It is, to paraphrase the webcomic Cat and Girl: The price of hope.

It's the modern fairy godmother. It's about the same part of the brain that makes it seem reasonable to toss coins in fountains or leave notes for forest spirits, or make any sacrifice to deities of any shape.

The difference is there's actually a known mechanism organized by mortal agents that takes those sacrifices and makes miracles happen. In that regard the Lottery is a vastly better form of wishful thinking than draining chickens of blood and making a mess.

Sure, but my point is you'll get that hope and your chance for a miracle regardless of whether the winnings are $100million or $500million.

CorruptUser wrote:Buy 1000 tickets for $100,000,000 (I assume you can get Warren Buffet to help you out or something), and when you win and your money is completely worthless...

But yes, utility theory would state that $100,000 is worth far more than a 1 in 1000 chance of a google.

Right, which is why I qualified my statement with "unless you're buying these tickets in quantities that will give you any kind of "real" chance of winning". If you're using the numbers to buy up lottery tickets in significant numbers so the the chances of winning are realistic, that's a different story. But if all you're doing is saying "I'm buying this one lottery ticket this time, because this time it's worth it" -- it really isn't. The chances of winning are the same, and the payout is still, for practical purposes, simply "rich".

by **Роберт** » Wed Mar 28, 2012 8:54 pm UTC

yoni45 wrote:
LaserGuy wrote:(if I let you buy 1 ticket for $100 000, with a 0.1% chance of winning
Spoiler:
$1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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, it's still probably not a good idea.)

It'd totally be worth it, if true and not on a scale that your money would actually cause deflation, to get 99,999 friends to go in with you at 5 bucks each, and if any of those tickets wins, you split the money evenly.

Not realistic.

yoni45 wrote:The chances of winning are the same, and the payout is still, for practical purposes, simply "rich".

I'm not sure I agree.

If I won 50 billion dollars, I could build a space elevator. If I won 50 million dollars, I couldn't.

Simple math.

by **CorruptUser** » Wed Mar 28, 2012 8:58 pm UTC

Plus, there are many people who would jump at even the 1 in 1000 chance to have enough money to buy continents. Do you know how many people fought tooth and nail just for a chance to be Emperor of Rome even when the Emperor had a lifespan of months?

by **Dauric** » Wed Mar 28, 2012 9:00 pm UTC

yoni45 wrote:
Dauric wrote:It's not a financial investment though.

It is, to paraphrase the webcomic Cat and Girl: The price of hope.

It's the modern fairy godmother. It's about the same part of the brain that makes it seem reasonable to toss coins in fountains or leave notes for forest spirits, or make any sacrifice to deities of any shape.

The difference is there's actually a known mechanism organized by mortal agents that takes those sacrifices and makes miracles happen. In that regard the Lottery is a vastly better form of wishful thinking than draining chickens of blood and making a mess.

Sure, but my point is you'll get that hope and your chance for a miracle regardless of whether the winnings are $100million or $500million.

Except that you don't get the same hope. The thing about lotteries is that you may have to share that fairy wish with others. The more money in the jackpot the more hope you have that if you have to share that money that it won't be rendered irrelevant by division.

The other thing to keep in mind is that we're talking about astronomical numbers. The kinds of numbers that scientists use scientific notation to reduce their size so they can get their heads wrapped around them.

Average Joe/Jane Doe goes in to the 7-11 to grab a 1-liter of Dr-Pepsi's Coke Dew and sees that the number is close to half a thousand (_E6) it's clearly better than when it was only 100(_E6) or 200(_E6).

by **yoni45** » Wed Mar 28, 2012 9:01 pm UTC

Роберт wrote:It'd totally be worth it, if true and not on a scale that your money would actually cause deflation, to get 99,999 friends to go in with you at 5 bucks each, and if any of those tickets wins, you split the money evenly...

"if I let you buy 1 ticket for $100 000, with a..."

Роберт wrote:
yoni45 wrote:The chances of winning are the same, and the payout is still, for practical purposes, simply "rich".

I'm not sure I agree.

If I won 50 billion dollars, I could build a space elevator. If I won 50 million dollars, I couldn't.

A motivation that affects few people playing the lottery.

by **Dauric** » Wed Mar 28, 2012 9:05 pm UTC

yoni45 wrote:
Роберт wrote:
yoni45 wrote:The chances of winning are the same, and the payout is still, for practical purposes, simply "rich".

I'm not sure I agree.

If I won 50 billion dollars, I could build a space elevator. If I won 50 million dollars, I couldn't.

A motivation that affects few people playing the lottery.

The underlying "More == Better" motivation often does though. The thing to remember is that the brain is really bad with the concept of "enough". People earning millions a year have a tendency to think of themselves as "Middle Class" if there's someone earning more than they do. Our brains are numerically jealous little blobs by nature and it takes extraordinary effort to override that natural process.

by **yoni45** » Wed Mar 28, 2012 9:07 pm UTC

Dauric wrote:Except that you don't get the same hope. The thing about lotteries is that you may have to share that fairy wish with others. The more money in the jackpot the more hope you have that if you have to share that money that it won't be rendered irrelevant by division.

The other thing to keep in mind is that we're talking about astronomical numbers. The kinds of numbers that scientists use scientific notation to reduce their size so they can get their heads wrapped around them.

Average Joe/Jane Doe goes in to the 7-11 to grab a 1-liter of Dr-Pepsi's Coke Dew and sees that the number is close to half a thousand (_E6) it's clearly better than when it was only 100(_E6) or 200(_E6).

I doubt $200 million won't provide more than enough even if you share it with others for most people. It's not in question whether Joe or Jane see the number as bigger and thus might be more inclined to buy a ticket. My point is the practical value of that ticket really doesn't increase with the jackpot past a certain point.

by **yoni45** » Wed Mar 28, 2012 9:12 pm UTC

Dauric wrote:The underlying "More == Better" motivation often does though. The thing to remember is that the brain is really bad with the concept of "enough". People earning millions a year have a tendency to think of themselves as "Middle Class" if there's someone earning more than they do. Our brains are numerically jealous little blobs by nature and it takes extraordinary effort to override that natural process.

Of course it does -- my point is that it shouldn't. For your average Joe making $30k a year, the substantive difference between "winning enough money to never have to work another day while having pretty much anything I want" and "winning enough money to never have to work while having pretty much anything I want... AND MORE" is negligible.

by **Dauric** » Wed Mar 28, 2012 9:17 pm UTC

yoni45 wrote:I doubt $200 million won't provide more than enough even if you share it with others for most people. It's not in question whether Joe or Jane see the number as bigger and thus might be more inclined to buy a ticket. My point is the practical value of that ticket really doesn't increase with the jackpot past a certain point.

Again, it's not a practical thing, buying lottery tickets doesn't appeal to the logical/practical parts of the brain. You're saying "it shouldn't" as though the decision was a purely practical one.

Hope doesn't give a shit about practicality. It's "magical thinking" in the first place, the expectation of a miracle. It has to override the part of the brain that is practical and saying "You know, we could just flush dollar bills down the toilet for fun if you're really in to that." In that regard higher jackpots, regardless of the practicality threshold, exploit the brain's basic response that more is better. If the hopeful part of the brain that's looking for miracles can exert enough force with a bigger "More is better" lever it can override the practical, logical thoughts.

by **Роберт** » Wed Mar 28, 2012 9:20 pm UTC

yoni45 wrote:
Роберт wrote:It'd totally be worth it, if true and not on a scale that your money would actually cause deflation, to get 99,999 friends to go in with you at 5 bucks each, and if any of those tickets wins, you split the money evenly...

"if I let you buy 1 ticket for $100 000, with a..."

Even if it was only 1 ticket, it would still be worth it if I could go in with 99,999 friends.

by **yoni45** » Wed Mar 28, 2012 9:32 pm UTC

Dauric wrote:Again, it's not a practical thing, buying lottery tickets doesn't appeal to the logical/practical parts of the brain. You're saying "it shouldn't" as though the decision was a purely practical one.

Hope doesn't give a shit about practicality. It's "magical thinking" in the first place, the expectation of a miracle. It has to override the part of the brain that is practical and saying "You know, we could just flush dollar bills down the toilet for fun if you're really in to that." In that regard higher jackpots, regardless of the practicality threshold, exploit the brain's basic response that more is better. If the hopeful part of the brain that's looking for miracles can exert enough force with a bigger "More is better" lever it can override the practical, logical thoughts.

Sure, except I also don't see much of a difference between hope for "winning enough money to never have to work another day while having pretty much anything I want" and hope for "winning enough money to never have to work while having pretty much anything I want... AND MORE!".

In fact, I'd say that "hope" is even less of a factor than the actual numbers are, since the hope is generally simply for getting rich. I doubt many people will say "yeah, but you know, I was actually hoping for $500million, not $200million...".

Роберт wrote:Even if it was only 1 ticket, it would still be worth it if I could go in with 99,999 friends.

Then it should be equally worth it to go it alone.

Would you really still think it's worth it, under either scenario, if we made your chances 10000 times lower, but made the jackpot 10000 times bigger?

by **Роберт** » Wed Mar 28, 2012 9:34 pm UTC

yoni45 wrote:Then it should be equally worth it to go it alone.

If it's worth it to buy a single candy bar, than surely it's worth it to go into significant debt buying thousands of candy bars.

by **faranim** » Wed Mar 28, 2012 9:39 pm UTC

I was thinking more along the lines that yoni is saying. Yes, I understand that mathematically the expected value of the ticket increases as the Jackpot increases. But for most people, winning the Jackpot is basically "I'm Super Rich" so the fact that it's worth $500M or $200M or even $20M shouldn't affect my desire to buy a ticket. But somehow it does.

PS, the Wikipedia page has a chart showing the various amounts you can win with the odds. You have a 2.5% chance of winning at least $2 with your ticket
http://en.wikipedia.org/wiki/Mega_Milli ... g_and_odds

by **yoni45** » Wed Mar 28, 2012 9:40 pm UTC

Роберт wrote:If it's worth it to buy a single candy bar, than surely it's worth it to go into significant debt buying thousands of candy bars.

Interestingly enough, I feel like in a different way, this actually supports my point: whether it's candy or money, there's a point at which "more" is just meaningless. Regardless, for the purposes of my question though, I assumed you can afford the $100 000 so 'going into significant debt' isn't an issue.

And you didn't answer the far more interesting followup question.

by **Dauric** » Wed Mar 28, 2012 9:45 pm UTC

yoni45 wrote:Sure, except I also don't see much of a difference...

Congratulations -you- don't see the difference and can behave with greater rationality towards the lottery.

-You- are not the bulk of the population who, on aggregate, are significantly affected by the parts of their brains shouting "More = better" because at the dawn of our current species food and resources were incredibly scarce, and he who could hoard and protect more frequently had the ability to hold on to it.

by **Роберт** » Wed Mar 28, 2012 9:47 pm UTC

yoni45 wrote:
Роберт wrote:If it's worth it to buy a single candy bar, than surely it's worth it to go into significant debt buying thousands of candy bars.

Interestingly enough, I feel like in a different way, this actually supports my point: whether it's candy or money, there's a point at which "more" is just meaningless.

You do realize what my quote was in response to, right? It was in response to your point

Then it should be equally worth it to go it alone.

... which is the opposite of what you're saying here. You don't really have a consistent stance.

Let me ask you something: is it worth it to buy insurance?

Another question: is it worth it to spend $1 to ride a carnival ride?

by **Isaac Hill** » Wed Mar 28, 2012 10:02 pm UTC

Iulus Cofield wrote:I'm gonna buy a ticket. The risk/payout is faurly solid and the extremely probable loss is negligible. Plus, that's nearly twenty million dollars a year until I'm near retirement age. That's enough to build a castle, which is my long standing and otherwise impossible dream.

That's not so impossible. A farmer in England built a castle for 50,000 pounds about 10 years ago (another article with interior pic). That doesn't include the price of the land, which he already owned. However, he tried to get around the planning board by building it within a pile of hay bales to take advantage of a rule that says if nobody complains about a structure for 4 years after it's built, it can stay up. After 4 years, he took the hay down and revealed his castle, but the local officials rejected that reasoning. I haven't found any recent articles about whether or not he was able to appeal. To be on the safe side, you'd better budget an extra few grand to bribe the proper officials when you start.

As for people being more likely to buy lottery tickets for a bigger jackpot, that may be related to stories of broke lottery winners. Enough people have won a few million dollars and ended up broke, some people who doubt their ability to handle money might figure that'd happen to them. But, if the prize hits hundreds of millions, those people might figure, "I won't blow that much money" and buy a ticket.

by **yoni45** » Wed Mar 28, 2012 10:07 pm UTC

Роберт wrote:
yoni45 wrote:
Роберт wrote:If it's worth it to buy a single candy bar, than surely it's worth it to go into significant debt buying thousands of candy bars.

Interestingly enough, I feel like in a different way, this actually supports my point: whether it's candy or money, there's a point at which "more" is just meaningless.
You do realize what my quote was in response to, right? It was in response to your point
Then it should be equally worth it to go it alone.
... which is the opposite of what you're saying here. You don't really have a consistent stance.

Er? Not sure where that inconsistency is?

Роберт wrote:Let me ask you something: is it worth it to buy insurance?

Another question: is it worth it to spend $1 to ride a carnival ride?

To both: possibly.

by **Роберт** » Wed Mar 28, 2012 10:14 pm UTC

yoni45 wrote:
Роберт wrote:
yoni45 wrote:
Роберт wrote:If it's worth it to buy a single candy bar, than surely it's worth it to go into significant debt buying thousands of candy bars.

Interestingly enough, I feel like in a different way, this actually supports my point: whether it's candy or money, there's a point at which "more" is just meaningless.
You do realize what my quote was in response to, right? It was in response to your point
Then it should be equally worth it to go it alone.
... which is the opposite of what you're saying here. You don't really have a consistent stance.

Er? Not sure where that inconsistency is?

...If you can't figure it out, I'm at a loss.

Say I want some chocolate. There's a chocolate bar that's 1 kg and costs $20 bucks. I decide I only want to buy it if I can buy it with friends. You say if I'm willing to buy it with some friends

Then it should be equally worth it to go it alone.

by **yoni45** » Wed Mar 28, 2012 10:19 pm UTC

Роберт wrote:Say I want some chocolate. There's a chocolate bar that's 1 kg and costs $20 bucks. I decide I only want to buy it if I can buy it with friends. You say if I'm willing to buy it with some friends
Then it should be equally worth it to go it alone.

Why would you only want to buy it with friends if you can afford the full thing on your own? Is there an analogous equivalent with money for your reason?

by **thc** » Wed Mar 28, 2012 10:37 pm UTC

Роберт wrote:
yoni45 wrote:
Роберт wrote:It'd totally be worth it, if true and not on a scale that your money would actually cause deflation, to get 99,999 friends to go in with you at 5 bucks each, and if any of those tickets wins, you split the money evenly...

"if I let you buy 1 ticket for $100 000, with a..."

Even if it was only 1 ticket, it would still be worth it if I could go in with 99,999 friends.

This is incorrect, it wouldn't be worth it.

This should be easy to see by the fact that utility has diminishing returns and in all likelihood is asymptotic. $1 is worth far more than a 1 in 10^1000 chance of winning $10^100000000000000000000000000.

by **++$_** » Wed Mar 28, 2012 11:15 pm UTC

thc wrote:
Роберт wrote:
yoni45 wrote:
Роберт wrote:It'd totally be worth it, if true and not on a scale that your money would actually cause deflation, to get 99,999 friends to go in with you at 5 bucks each, and if any of those tickets wins, you split the money evenly...

"if I let you buy 1 ticket for $100 000, with a..."

Even if it was only 1 ticket, it would still be worth it if I could go in with 99,999 friends.

This is incorrect, it wouldn't be worth it.

This should be easy to see by the fact that utility has diminishing returns and in all likelihood is asymptotic. $1 is worth far more than a 1 in 10^1000 chance of winning $10^100000000000000000000000000.

As stated, if you and your friends pitch in to split the ticket, you each have a 1/1000 chance of winning a googol dollars, at the cost of $1 each. Now, is $1 worth more than a 1/1000 chance of winning a googol dollars?

See, asymptotic utility functions cut both ways. It means it isn't worth spending 1 dollar for a 1/N chance of winning N dollars, but it might be worth spending 1/2 dollars for a 1/N chance of winning N/2 dollars, because N/2 dollars has approximately the same utility as N dollars for sufficiently large N.

by **Iulus Cofield** » Wed Mar 28, 2012 11:20 pm UTC

Isaac Hill wrote:
Iulus Cofield wrote:I'm gonna buy a ticket. The risk/payout is faurly solid and the extremely probable loss is negligible. Plus, that's nearly twenty million dollars a year until I'm near retirement age. That's enough to build a castle, which is my long standing and otherwise impossible dream.
That's not so impossible. A farmer in England built a castle for 50,000 pounds about 10 years ago (another article with interior pic). That doesn't include the price of the land, which he already owned. However, he tried to get around the planning board by building it within a pile of hay bales to take advantage of a rule that says if nobody complains about a structure for 4 years after it's built, it can stay up. After 4 years, he took the hay down and revealed his castle, but the local officials rejected that reasoning. I haven't found any recent articles about whether or not he was able to appeal. To be on the safe side, you'd better budget an extra few grand to bribe the proper officials when you start.

Not big enough. It needs to be on a large hillside and surrounded by walls twenty feet high and ten feet thick enclosing a total area of at least 100,000 sq. ft. It will also need to be surrounded by at least 10,000 acres of arable land and preferably within 20 miles of a source of iron or copper and tin.

by **Adacore** » Wed Mar 28, 2012 11:45 pm UTC

Most of my plans for hundred million plus lottery wins (not that I ever buy tickets) would involve setting up long-term foundations to do things forever (or at least for decades/centuries, in a similar fashion to the Nobel Prizes, for example). It's hard to get a high enough annual return on your capital to do anything significant/worthwhile in that area with less than a hundred million or so.

I do think yoni has a point, though, the value of a resource to someone is not normally constant as the quantity of that resource in their possession increases. As an extreme example, if my salary were reduced by 90% my quality of life would be terrible, whereas if it were doubled the improvement would be far less important. If someone offered a coinflip to either double my pay or reduce it by 90% then the expected value argument would dictate I should go for it, but that's clearly (for most people) a terrible idea.

Similarly, with lotteries, if I had more than ten million or so I could not work and live with a better lifestyle than I currently do for the rest of my life; having a hundred million wouldn't change that, and in fact if I went much over 20 million I'd start looking for other things to 'waste' the excess on, such as setting up the foundation I mentioned above, or donating to charity, because the marginal value of the extra money would be so low for my personal use. Maybe if I was actually a multi-millionaire already, I'd want to move up to a several-million-a-year lifestyle and would require hundreds of millions to finance it, but from where I am now I can't see I'd have a significantly increased qualtiy of life over living on a few hundred thousand a year.

by **lutzj** » Wed Mar 28, 2012 11:45 pm UTC

yoni45 wrote:
Роберт wrote:Say I want some chocolate. There's a chocolate bar that's 1 kg and costs $20 bucks. I decide I only want to buy it if I can buy it with friends. You say if I'm willing to buy it with some friends
Then it should be equally worth it to go it alone.

Why would you only want to buy it with friends if you can afford the full thing on your own? Is there an analogous equivalent with money for your reason?

Because nobody needs an entire kilogram of chocolate, the same way nobody needs a 1/1000 chance at an entire 10^100 dollars. If I can pay $1 for a 1/1000 chance at 10^95 dollars, that's well worth it because $1 is worth less than a pack of gum anyway, so the guaranteed loss isn't significantly bad, and 10^95 dollars is just as good for all realistic purposes as 10^100 dollars (ignoring inflation of course, since that would make either amount essentially useless).

by **yoni45** » Thu Mar 29, 2012 3:35 am UTC

lutzj wrote:Because nobody needs an entire kilogram of chocolate, the same way nobody needs a 1/1000 chance at an entire 10^100 dollars. If I can pay $1 for a 1/1000 chance at 10^95 dollars, that's well worth it because $1 is worth less than a pack of gum anyway, so the guaranteed loss isn't significantly bad, and 10^95 dollars is just as good for all realistic purposes as 10^100 dollars (ignoring inflation of course, since that would make either amount essentially useless).

Well, according to Роберт's reasoning that's silly, because the entire $10^100 would allow you to build that many more space elevators. "Basic math", as he calls it.

If you accept the idea that at a certain point, "more" money really doesn't mean all that much, then you're coming towards my point: for all intents and purposes, people generally don't need $500 million much more than they need $200 million. The idea that the increased jackpot makes your lottery ticket "worth more" in any practical sense is silly at best.

by **buddy431** » Thu Mar 29, 2012 4:01 am UTC

yoni45 wrote:
lutzj wrote:Because nobody needs an entire kilogram of chocolate, the same way nobody needs a 1/1000 chance at an entire 10^100 dollars. If I can pay $1 for a 1/1000 chance at 10^95 dollars, that's well worth it because $1 is worth less than a pack of gum anyway, so the guaranteed loss isn't significantly bad, and 10^95 dollars is just as good for all realistic purposes as 10^100 dollars (ignoring inflation of course, since that would make either amount essentially useless).

Well, according to Роберт's reasoning that's silly, because the entire $10^100 would allow you to build that many more space elevators. "Basic math", as he calls it.

If you accept the idea that at a certain point, "more" money really doesn't mean all that much, then you're coming towards my point: for all intents and purposes, people generally don't need $500 million much more than they need $200 million. The idea that the increased jackpot makes your lottery ticket "worth more" in any practical sense is silly at best.

But you don't get $500 million. You get maybe $250 million for taking the money as a lump sum, and Uncle Sam takes half of that - you're looking at $100-150 million. And that's for the largest jackpot in history. To me, that is a fair difference than the $50 million you'd get on a $200 million jackpot, and especially the $15 million you'd get on a $50 million jackpot. $50 million buys you a trip into space and a nice house, $15 million you're just stuck with a house (and not even any house. You want to live in Jordan's pad? Be ready to lay down $30 million). You want a luxury yacht? Be ready to lay down $10 million plus just to get it, and then you still need to crew it. There are lots of things to spend money on, even at the high end.

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