Hey guys, this is my first post so don't flame me too bad

Now we all know any form of gambling (excluding possibly sports?) is -EV, including playing the lottery. However, a friend and I are of the opinion that lotto is in fact a +EV game (like to call it 'life EV'). This is because IF we hit at our age (20) we still have our youth to be ballin'. Sorry to any 80 yr olds reading this post, but we also think old people playing lotto has the reverse effect - while they'll be balling for a little while, they can't spend on the same stuff as us.
Generally, the younger you are when you start playing lotto, the better.
Are we correct or just trying to justify our obscene gambling habits?
Thoughts?

Your point of view is based on the idea that being able to spend the money is somehow important. To an 80 year old, it might be more important to have the money to leave for his kids and grandkids.

Sherman

You are probably wrong.

Utility functions are concave downwards, or at worst, flat, barring some totally ludicrous scenario like a hitman will kill you unless you pay him exactly one million dollars next week.

This assumes utility functions exist, which may not be the case.

You have the choice between an instant $100k award or a (one shot) lottery which gives you $2M one time out of ten. Which one do you chose ?

I don't understand how a utility function could not exist. Perhaps the OP hasn't explicitly calculated what his looks like, but regardless it will exist for him, and ignoring really absurd scenarios, it will be concave downwards.

I take the lottery in your example. Others may take the cash. This example is not similar to what the OP is asking about though, as the lottery is more +EV than the fixed cash alternative. More like the OPs would be to say you have the choice between an instant $5, or a lottery which will give you $1m one time out of a million.

I still have to make my point. You would take the lottery ? Fine, I wouldn't. Neither would a lot of people who will better take the sure money than the unsure one, whatever EV it is. Especially since $100k is quite a few for a lot of us. People maximize utility, not EV (as you can witness in the bubble of expensive tournaments).

Utility functions are assumed to be well behaved. But utility functions are functions of what parameters ? Let's assume for a moment that it be a function of the expected value and standard deviation of the proposal (as in the lottery example). A poker player will routinely order the proposals as follows :
- A is better than B when EV(A) > EV(B)
- if EV(A) = EV(B) then A is better than B when SD(A) < SD(B)
(- if EV(A) = EV(B) and SD(A) = SD(B) then A is better than B if I have more fun playing A than B)*

Exercise : Show that any utility function associated with this ordering is not continuous (and therefore cannot be concave or quasiconcave).

And, by the way, in this case you can build a utility function (function of EV and SD), although mathematically ill-behaved. I could build real-world example of lottery situations where people's choice cannot be determined by the maximisation of a function of EV and SD.

* The point inside parentheses is here to explain to some people why I always push all in every hand when there is no money involved.

So why do people play $5 lotteries even if it is EV- ? Why don't people play lotteries (either in my example or at the bubble of the WSOP ME) although it's EV+ ? Beause they have different preferences. Utility functions are a convenient mathematical way to convey this information, in most (but not all) situations.

Did you read the OP? He is deliberately taking a -EV decision. The fact that I would take an entirely different decision from you on a lottery that is +EV is neither here nor there.

Utility functions are functions of the 'amount of some commodity' (in this case, money), to the set of Real numbers.

It is certain that a utility function w.r.t money is monotone increasing (you always prefer to have some larger amount of money). a priori the function is continuous on it's domain since it has a discrete domain. In the case of any sensible choice for utility function it is also concave downwards.

Because they enjoy giving money to charity. The OP did not express this preference. He is playing the lottery out of a desire to get a 'balling lifestyle'. He asked if it was a bad decision. It is.

OP clearly points out the fact that people play lottery for a reason other than raw EV. Winning $1M or $5M clearly doesn't change the deal, because it's an amount which changes your life.

"Utility functions" can be taken as function of whatever you want which is a parameter of the problem and over which you will optimize. Say you have the choice between $1, $2 on the result of a coin flip or $1000 one time out of 1000. You need a way to express your willingness of gambling to decide. So your utility function is not only a function of the average amount of money you'll make. In 'amount of some commodity', you can have 'commodity' be the risk (ie. variance or SD). There may be multiple commodities which are not commensurable to others (how do you trade risk against EV ? That's a complex problem in stock markets for instance)

It is not a bad decision for him because changing lifestyle can be worth it if he decides it is. We are human and money matters to us only through what we can afford with it. We, as poker players, tend to only look at expected value because we have the Law of Large Numbers with us.

Of course if an 80 yr olds main concern is to give it to their grandkids, its valuable for them to play. but what about individual satisfaction?
I still don't know if its a 'bad decision' - i mean, if you're lucky enough to win the lotto, and lets face it someone has to win, then you've skipped a lifetime of hard work at a young age (if you start young). Money when you're young - can it get any better?
Obviously this doesn't mean spending your weekly wage on lotto tickets, but around $50 a week could pay off ?

To reduce the issue to very simple terms, assume someone plays a lottery once a week for $10 and it pays the winner $1000 with any player having a 0.5% chance to win. On a dollar basis, the EV$ is .005*$1000 -$!0 = -$5. Now, if winning $1000 is at least 200 times as pleasurable as the pain of losing $10, then on a utility basis, the lottery is +EV.

To show this, assume the following:

U(+$1000) = 250 utils and U(-$10)= 1 util..

Then

EVutils = .005*250 - 1 = 1.25-1 = + 0.25

This is why most people gamble on pure games of chance like roulette. They know intellectually that it is minus EV$ but the pleasure in possibly beating the system or just the excitement of watching the little ball roll around and around is worth the dollar cost.

So, I guess OP's point is that for a younger person, the difference in utility in winning the lottery compared to the lottery investment utility is much greater than that of an older person. While this may be true in general, much would depend on individual circumstances. For example, if the older person had to find funds to pay for care for his seriously ill wife, then the lottery may be an attractive option.

The normal utility function from 'money' to 'utility' can solve this problem. There is no need to graph 'risk' or 'variance' against 'utility' as doing so doesn't help you solve any additional problems whatsoever.

In your proposed example we have some function from R->R (assume money is continuous) We currently hold m money and our utility is f(m) We check which of f(m+1), 0.5f(m)+0.5f(m+2), 0.999f(m)+0.001f(m+1000) is greater. If your function from 'money' to 'utility' is linear it doesn't matter which you pick. If it's concave you should take $1. If it's convex you should the $1000 gamble. If it has a weird inflection point near $2 then perhaps you should take that. No need to introduce additional variables in our function.

Again a single line plotting 'money' against 'utility' can answer this problem. Deciding what the line should look like may be a complex problem, but adding extra variables beside 'money' and 'utility' does not help you solve it. The line will certainly be concave, or at least if some broker does not have a concave utility function you should reconsider investing with them.

OP,

I think you should do this and then write back in this thread when you win to rub it in our faces.

Sherman

Someone who starts playing the lottery at 20 will likely have spent aout $100,000 or more by the time he is 80.

Why not put the money in the bank?

The $100,000 you save will give you a great send off.

almost $2k/year?

hmmmm

i think OP is arguing that the theorhetical utility curve shifts downwards over time as the utility/$ is less bc of less opportunity to use it, poor health so not as fun etc.
I guess this makes sense. Lotto is still ******ed tho.

Precisely, but the OP ignores the need for generativity among the elderly. This is probably due to the fact that OP is 20 and therefore believes that it is much more important to have the money to spend for him/her self than to give to others. However, many older people would find it equally as rewarding to spend the money by giving it to others rather than on themselves. So to argue that having the money when you are 20 has more utility than having it when you are 80 simply ignores the goals of being 80.

Sherman

I 100% agree. I just think its a pretty pointless discussion bc its all based on utility which can only be defined (lol@that) for individuals or else as generalizations which are never going to be actually appliable.

I once heard the demand curve for poker chips slopes upward, thoughts?

wouldnt be suprised, i mean, you want more of them right?

UPDATE:
since i started this thread, i've won $80 and spent about $200.
Might have to abandon the dream