Is it really irrational to play the lottery?

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Is it really irrational to play the lottery?

Post by Jaeger »

Everybody knows that the lottery has a slightly negative expected value. But expected value doesn't always determine the rationality of something.

Say you are offered 1 billion dollars with 100% chance, or 2 billion dollars with 70% chance. I would take the first offer anyday, even though the second has a higher expected value.

Playing the lottery also has some intangible benefits such as being exciting, etc.
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Re: Is it really irrational to play the lottery?

Post by Runtius »

It reminds me on the St. Petersburg Paradox (https://en.wikipedia.org/wiki/St._Petersburg_paradox). A better way to decide wether a decision is irrational or not is to use the expected utility (https://en.wikipedia.org/wiki/Expected_utility_hypothesis)
I dont think lottery must be irrational in theory, because there could be a utility function that the expected utility is positive, but its very unlikely.
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Re: Is it really irrational to play the lottery?

Post by momuuu »

No, but its unwise.
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Re: Is it really irrational to play the lottery?

Post by Gendarme »

ovi12 wrote:Say you are offered 1 billion dollars with 100% chance, or 2 billion dollars with 70% chance. I would take the first offer anyday, even though the second has a higher expected value.

Because every dollar is not equally important. If you are poor, money is worth more. The second billion dollars is not worth as much as the first billion.

ovi12 wrote:Playing the lottery also has some intangible benefits such as being exciting

I am not sure about this, but I think it is exciting mostly due to the fact that people don't understand the concept of expected value. I don't find lottery exciting at all.
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Re: Is it really irrational to play the lottery?

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Post by Goodspeed »

I would say no, it's not actually irrational (or unwise). Yes, participating costs money, but not enough that it lowers your standard of living unless you are very poor. Yet the potential profit would greatly improve your standard of living. It could therefore be argued that there is a lot of potential gain for no cost.
Ask yourself: would losing $1 per month change your life in any way? Would winning $10m?

It's not only about the numbers. It's about the (potential) effect on quality of life.
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Re: Is it really irrational to play the lottery?

Post by Jaeger »

Gendarme wrote:
ovi12 wrote:
ovi12 wrote:Playing the lottery also has some intangible benefits such as being exciting

I am not sure about this, but I think it is exciting mostly due to the fact that people don't understand the concept of expected value. I don't find lottery exciting at all.

I thought so too but I recieved a free lottery ticket once and I got the first three numbers right, I was super excited for the 4th and 5th numbers :D
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Re: Is it really irrational to play the lottery?

Post by Jaeger »

Goodspeed wrote:I would say no, it's not actually irrational (or unwise). Yes, participating costs money, but not enough that it lowers your standard of living unless you are very poor. Yet the potential profit would greatly improve your standard of living. It could therefore be argued that there is a lot of potential gain for no cost.
Ask yourself: would losing €1 per month change your life in any way?

It's not only about the numbers. It's about the (potential) effect on quality of life.

+1 yeah this is exactly what I had in the back of my mind but never expressed it explicitly as you did here.

I guess the next step would be, would $2 a month change your life in any way? or $3? I guess that should be about the maximum though, not because $3 a month has a huge impact on your life, but for some reason it feels like a waste to spend more than that.
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Re: Is it really irrational to play the lottery?

Post by Gendarme »

Goodspeed wrote:I would say no, it's not actually irrational. Yes, participating costs money, but not enough that it lowers your standard of living. Yet the potential profit would greatly improve your standard of living. It could therefore be argued that there is a lot of potential gain for no cost.
It is a good point you're making. Most people do not have an "investor-mentality" for the lack of a better word. If you give them more money, they will spend more that month, and if you take money from them, they will spend less that month - at the end of the month, they are just as wealthy as they would have been without your interference.

With that said, I think you overlook the first part of that. If the average person wins even a huge sum like $100,000, it won't greatly improve their standard of living - at least not for long.

Of course, if it's $1/month, it is negligible, and you will never win $10,000,000 - it is essentially nothing but procrastination. However, a more accurate example would be $20/month in which case I wouldn't call it negligible. Sure, as previously discussed in the end you'll be equally wealthy, but you could have enjoyed a night out at a restaurant once a month with friends instead of buying a ticket once a week for $4.50.
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Re: Is it really irrational to play the lottery?

Post by Goodspeed »

Gendarme wrote:
Goodspeed wrote:I would say no, it's not actually irrational. Yes, participating costs money, but not enough that it lowers your standard of living. Yet the potential profit would greatly improve your standard of living. It could therefore be argued that there is a lot of potential gain for no cost.
Of course, if it's $1/month, it is negligible, and you will never win $10,000,000 - it is essentially nothing but procrastination. However, a more accurate example would be $20/month in which case I wouldn't call it negligible. Sure, as previously discussed in the end you'll be equally wealthy, but you could have enjoyed a night out at a restaurant once a month with friends instead of buying a ticket once a week for $4.50.
Or you would do both and not save as much. If you're consistently making $1000 more than you are spending each month, even $20 changes nothing. Over 8 years, instead of saving $100000 you are saving $98000. Won't change anything.
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Re: Is it really irrational to play the lottery?

Post by Gendarme »

Yeah, it doesn't. That's why I said you'll be equally wealthy nonetheless. However, instead of spending the $20 on lottery, you could spend it on something much more enjoyable. Going to a restaurant with friends one additional time per month is not insignificant, especially if you almost never do it.
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Re: Is it really irrational to play the lottery?

Post by deleted_user0 »

Goodspeed wrote:
Gendarme wrote:
Goodspeed wrote:I would say no, it's not actually irrational. Yes, participating costs money, but not enough that it lowers your standard of living. Yet the potential profit would greatly improve your standard of living. It could therefore be argued that there is a lot of potential gain for no cost.
Of course, if it's $1/month, it is negligible, and you will never win $10,000,000 - it is essentially nothing but procrastination. However, a more accurate example would be $20/month in which case I wouldn't call it negligible. Sure, as previously discussed in the end you'll be equally wealthy, but you could have enjoyed a night out at a restaurant once a month with friends instead of buying a ticket once a week for $4.50.
Or you would do both and not save as much. If you're consistently making $1000 more than you are spending each month, even $20 changes nothing. Over 8 years, instead of saving $100000 you are saving $98000. Won't change anything.


the vast majority of people aren't making that much money honestly. And for example, in the netherlands it costs like 30 euros for the national lottery which runs once a month. Many people play their entire adult life, and the vast majority never wins anything significant. So that's 360 euro's a year, for 50 years. That's 18k euro's which is a significant sum, specially considering you couldve spent that money elsewhere. However, 50 years is a long time, and its not like you have that 18k right off the bat to do something with. If you think of your grandchildren for example, instead of just of yourself, then suddenly the rationality of the picture changes. 18k which would be more after the interest on it for 50 years, specially if you wouldve invested it in something with low but steady returns, is enough to help a grandkid go to college, atleast in NL. The irrational part of it is though that people actually believe that becoming rich over night is always a dream, instead of the nightmare it might very well become if you're not capable of dealing with it. http://theweek.com/articles/493775/7-lo ... ll-updated
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Re: Is it really irrational to play the lottery?

Post by Goodspeed »

Gendarme wrote:Yeah, it doesn't. That's why I said you'll be equally wealthy nonetheless. However, instead of spending the $20 on lottery, you could spend it on something much more enjoyable. Going to a restaurant with friends one additional time per month is not insignificant, especially if you almost never do it.
Well you are saving $1000 a month so if you wanted to spend that $20 on something else, you would. You can easily afford it. Why not go out with friends ánd participate in the lottery?
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Re: Is it really irrational to play the lottery?

Post by Goodspeed »

umeu wrote:
Goodspeed wrote:
Gendarme wrote:Of course, if it's $1/month, it is negligible, and you will never win $10,000,000 - it is essentially nothing but procrastination. However, a more accurate example would be $20/month in which case I wouldn't call it negligible. Sure, as previously discussed in the end you'll be equally wealthy, but you could have enjoyed a night out at a restaurant once a month with friends instead of buying a ticket once a week for $4.50.
Or you would do both and not save as much. If you're consistently making $1000 more than you are spending each month, even $20 changes nothing. Over 8 years, instead of saving $100000 you are saving $98000. Won't change anything.
the vast majority of people aren't making that much money honestly.
I think many are, they are just not good at saving. People live in much bigger spaces than they need, spend money on shit they never use, etcetera. It's not the lack of income that's the problem. But yeah, you are correct, most people don't save $1000 a month. It's a hypothetical.

And for example, in the netherlands it costs like 30 euros for the national lottery which runs once a month. Many people play their entire adult life, and the vast majority never wins anything significant. So that's 360 euro's a year, for 50 years. That's 18k euro's which is a significant sum, specially considering you couldve spent that money elsewhere. However, 50 years is a long time, and its not like you have that 18k right off the bat to do something with.
That, and 18k is not at all a significant sum if you are saving $1000 a month. Over 50 years that's 600k. Does 18k matter then?

The irrational part of it is though that people actually believe that becoming rich over night is always a dream, instead of the nightmare it might very well become if you're not capable of dealing with it. http://theweek.com/articles/493775/7-lo ... ll-updated
Yes, if you are stupid it's going to be a nightmare rather than a dream. But why would we assume that? Obviously we are going to land on it being irrational if we assume that more money is worse. The way I see it, winning the lottery means never working another day in my life. That's a positive thing.
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Re: Is it really irrational to play the lottery?

Post by britishmusketeer »

I would say that the chances are winning are so low they can be considered negligible. Rather than wasting £104 per year on buying a lottery ticket each week I would much rather spend that on something I actually want. Also I don't think that having more money increases quality of life unless you are too poor to afford things you need in which case you probably shouldn't be buying lottery tickets. That being said if you would feel you will get entertainment value out of it then it can be worth it.
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Re: Is it really irrational to play the lottery?

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it's true that many people aren't good at saving, and are very good at wasting money, yet even a hypothetical 1000 is alot, specially considering people maybe have children or i dont know what. i wasn't even making 1k a month in NL, and not for lack of trying. so there's no way i couldve saved 1k a month :P and the same goes for many people who don't have decent jobs or get the hours they need. and if you have to support a family or what not, then there won't be alot left.

sure vs 600k, 18k is significant, but not crucial. however, 1k a month saving is just a figure you pulled out of your ass, and its not realistic for the vast majority of the people, and i'm not sure on the numbers, but i wouldnt be surprised that the demographics for lottery players are unequally distributed amongst the poorer people
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Re: Is it really irrational to play the lottery?

Post by Goodspeed »

i wasn't even making 1k a month in NL, and not for lack of trying.
1k after tax is less than minimum wage (€1200) so you either must have been making more or not working full time. Or are you talking about jobs you had as a teenager?
1k a month saving is just a figure you pulled out of your ass, and its not realistic for the vast majority of the people, and i'm not sure on the numbers, but i wouldnt be surprised that the demographics for lottery players are unequally distributed amongst the poorer people
Sure, but it's a hypothetical which shows that participating in the lottery is not inherently irrational. Of course, it is irrational to participate if you can't really afford it, which to your point I'm sure most participants can't.
Anyway I don't think it's unrealistic to have $1000 of savings each month for a household of medium to highly educated people.
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Re: Is it really irrational to play the lottery?

Post by Durokan »

ovi12 wrote:Everybody knows that the lottery has a slightly negative expected value. But expected value doesn't always determine the rationality of something.

Say you are offered 1 billion dollars with 100% chance, or 2 billion dollars with 70% chance. I would take the first offer anyday, even though the second has a higher expected value.

Playing the lottery also has some intangible benefits such as being exciting, etc.

In your example, let's change the place value quite a bit. I would imagine for people of a modest/average income, somewhere on the order of 10 to 20 dollars is a relatively small amount of money. I would also conjecture that those same people would be willing to play those same 70% odds if given the chance at winning $20 versus the 100% chance at getting $10, as the expected outcome is $14 (0.70 *20) for one and $10 (1.00 * 10) for the other.

For that same group of people, $1,000,000,000 is perceived as an infinite amount of cash because it is so insanely large that it is hard to comprehend. $2,000,000,000 is also perceived as an infinite amount of cash in this situation so the math comes out as 1.00 * infinity versus 0.70 * 2 * infinity, which are comparable infinities so it makes more sense to pick the one with the higher chance of receiving infinity dollars

I'm fairly certain there is some interval of cash that you might be willing to take up that 70% chance on, whether it be in the single dollar denomination or up into the millions. This is likely shaped by your tendency for risk aversion and income levels.
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Re: Is it really irrational to play the lottery?

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Goodspeed wrote:
i wasn't even making 1k a month in NL, and not for lack of trying.
1k after tax is less than minimum wage (€1200) so you either must have been making more or not working full time. Or are you talking about jobs you had as a teenager?
1k a month saving is just a figure you pulled out of your ass, and its not realistic for the vast majority of the people, and i'm not sure on the numbers, but i wouldnt be surprised that the demographics for lottery players are unequally distributed amongst the poorer people
Sure, but it's a hypothetical which shows that participating in the lottery is not inherently irrational. Of course, it is irrational to participate if you can't really afford it, which to your point I'm sure most participants can't.
Anyway I don't think it's unrealistic to have $1000 of savings each month for a household of medium to highly educated people.


no it wasnt full time, because no full time hours were to be had, even with 3 jobs. i agree its not inherently irrational by the way you present it, and imo it's quite a good way to think about it. I also don't think most people can't afford it, just that the fee for participation is not as insignificant for them as in your example of 1k, simply because most people are not in that position. i think 200 to 300 is a much more realistic estimation, and 10 to 15 % of your monthly surplus is not insignificant, considering that there is no certain return on the investment.
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Re: Is it really irrational to play the lottery?

Post by Goodspeed »

3?? Sounds like story time.
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Re: Is it really irrational to play the lottery?

Post by deleted_user0 »

Goodspeed wrote:3?? Sounds like story time.


it's not really interesting, it's just what happens in an economy where 1k people apply to work in the snackbar at the local zoo.
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Re: Is it really irrational to play the lottery?

Post by Jaeger »

30 euros is quite a lot for lottery though, I would never spend that much. Maybe $5 at most.
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Re: Is it really irrational to play the lottery?

Post by deleted_user »

In moderation, no. For a small fee you gain an escapist fantasy to day dream about. My calc 3 professor would play the lotto every week and he is more acquainted with the slim probabilities of it more than any of us. He called it a vice that gave him pleasure much like drinking or smoking would do.
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Re: Is it really irrational to play the lottery?

Post by Goodspeed »

umeu wrote:
Goodspeed wrote:3?? Sounds like story time.


it's not really interesting, it's just what happens in an economy where 1k people apply to work in the snackbar at the local zoo.
I see. Should've just dealt drugs.
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Re: Is it really irrational to play the lottery?

Post by deleted_user »

Should've just been born with rich parents ya dork.
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Re: Is it really irrational to play the lottery?

Post by deleted_user0 »

Goodspeed wrote:
umeu wrote:
Goodspeed wrote:3?? Sounds like story time.


it's not really interesting, it's just what happens in an economy where 1k people apply to work in the snackbar at the local zoo.
I see. Should've just dealt drugs.


ye, much better odds then playing the lottery

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