
The Case for Buying a Powerball Ticket - khc
http://www.nytimes.com/2015/02/12/upshot/the-case-for-buying-a-powerball-ticket.html
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Chinjut
I hate the argument that, on the grounds that the aggregate money spent on
lottery tickets is typically larger than the aggregate money paid out on
lottery tickets, purchasing a lottery ticket is inherently irrational.

The same is true of insurance, yet few people consider the purchase of
insurance to be intrinsically irrational by the same argument.

People are free to have whatever preferences they want. Some people prefer a
life with a slim possibility of a tremendous windfall (and but a negligible
loss in the more likely alternative) to a life of certain continuation with
the status quo grind. More power to them.

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dragonwriter
> The same is true of insurance, yet few people consider the purchase of
> insurance to be intrinsically irrational by the same argument.

The offsetting argument for insurance is that it provides risk management
against unaffordable, catastrophic expenditures -- it is a trade-off of a
certain expenses, against the risk of a much larger uncertain expense, with an
expected net cost in _financial_ terms, but that it is rational in some cases
given the decreasing marginal utility of net income (which, conversely, means
that there is an _increasing_ marginal _cost_ of high expenses.)

Of course, the trade-off in the lottery is you are paying a certain, low cost
for a chance at unlikely larger payoff -- this has not only a negative
expected financial value, but -- given the declining marginal utility of
income -- an even _larger_ expected negative _utility_ in most cases,
considering utility of money on its own.

Of course, it may be rational _if_ the utility provided to a particular player
by "playing the lottery" (the entertainment value, etc.) exceeds the expected
net disutility associated with financial expectations.

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Chinjut
If some people do, in fact, prefer situations in which there is a slim chance
of tremendous windfall and large chance of small loss to guaranteed status
quo, who is the economist to tell them "No, no, this is incompatible with the
theory of diminishing marginal vNM-utility. Your preferences are misguided!".

Utility is just a construct for describing people's preferences; to turn
around and demand that people's preferences ought change to match some
textbook model of utility is to put the cart before the horse.

People can reasonably have all kinds of different personal preferences, right?
If your theory doesn't account for that, that may not be an example of muddled
thinking on your subjects' part; it could just as well be a problem with your
theory. I mean, what is actually factually misinformed about preferring the
risk profile afforded by a lottery ticket to the alternative?

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qq66
Because it's hard to imagine that anyone _actually_ has a increasing marginal
utility of money. If they did, over wide enough of a range, they'd bet their
entire life savings on the Powerball.

What's much more likely is that they're getting some entertainment out of
playing the lottery, or they're poor calculators of risk and reward.

~~~
Chinjut
I don't have to imagine that anyone prefers occasionally playing the lottery
to never playing the lottery. I can see it in action any time I please, and
while some of the people doing so may be laboring under delusions as to the
quantities involved, I see no reason to conclude that all are. (I will proffer
myself as an example.)

A person might well prefer the risk profile resulting from occasionally
playing the lottery (small chance of tremendous gain, large chance of minor
loss) to both the risk profile resulting from never playing the lottery
(guarantee of no gain or loss) and the risk profile resulting from betting
their entire life savings on Powerball (large chance of catastrophic loss,
small chance of tremendous gain); these are all different risk profiles, so
they can all perfectly well be valued arbitrarily differently.

[And I do mean arbitrarily differently. What rule of rationality demands that
anyone who might want to play the lottery from time to time for the risk
profile it produces ought further prefer to bet their entire life savings on
the lottery? Whoever claims that to be a rule of rationality, I say they're
the irrational one.]

Whether you would describe someone with such preferences as having "increasing
utility of money" or not is up to you. But I see nothing problematic in having
and acting on such preferences.

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zorrb
This article is trash. First he makes a dumb argument that comes down to,
what's $2 in exchange for the warm fuzzies of imagining where you'll move with
that money.

And then goes on to explain why now's the best time to waste your money if you
like wasting your money because of the ridiculously obvious point that the
jackpot is larger now.

This is abysmal garbage and the author should feel bad and so should everyone
who upvoted this. I rarely ever get mad but the lottery is one of my biggest
pet peeves, and this brings no insight or elaboration on the issue besides,
"gee wouldn't it be great to instantly have millions of dollars."

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jmiwhite
There are a number of things you can spend a small amount of money on with
ultimately nothing to show for it but some brief enjoyment. It seems the
author is encouraging his (non-addict, non-destitute) audience to reframe
their thinking about what the lottery provides as entertainment value rather
than simply being 'a tax on people who are bad at math' \- even if you don't
ultimately play, you don't have to view those who do in a negative light.

That's certainly how I used to feel, but once I started thinking of it as a
lark rather than a blight, it just didn't seem like that big of a deal.

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geoelectric
Buying one ticket is a much bigger benefit over buying none than buying two is
over buying one.

Buying one ticket does seem reasonable to me (even with excellent math
skills). Buying two is just silly.

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pixelcort
"It’s actually more complicated than that, because that calculation doesn’t
account for the fact that there could be multiple jackpot winners who must
split the pot."

In other articles, it's been said that when the jackpot is high, the expected
value actually goes down due to the increased chances of multiple winners.

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kryptiskt
I don't think there's anything wrong with buying a lottery ticket if its cost
is a trifle for you.

Buying one when the expected value is positive is not a sound gamble however.
Suppose there is a jackpot of $300M and you have a 1 in 150 million chance to
win. It's obvious that you have an edge, so you calculate how large part of
your bankroll you should bet with the Kelly criterion[1] and get: f=3.33e-9

Oh well, if you are a centimillionare you can buy a ticket and be rational.

[1][http://en.wikipedia.org/wiki/Kelly_criterion](http://en.wikipedia.org/wiki/Kelly_criterion)

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jrs235
You need to factor in ticket price, odds of winning, cash payout, taxes.
Powerball is $2 a ticket. The cash payout is around $338 million. The odds of
winning with a ticket is about 1 in 175. Assume taxes will take half. You
shouldn't buy a powerball ticket using reason unless the cash payout is at
least $700 million. Problem then is so many people are playing there's likely
more than one winning ticket which would mean the numbers don't work.

Edit: the payout tonight is $338m

~~~
kryptiskt
I assumed a $1 ticket in the example. The point is that even if the expected
value is high, buying a ticket means that you are likely overbetting by
several orders of magnitude.

~~~
jrs235
Yes. And even if you get to pot odds or better after taxes and decide to spend
$20 (10 tickets), $200 (100 tix), or even $2000 (1000 tix) because you're at
pot odds... 1 in 17.5 mil, 1 in 1.75 mil, even 1 in 175,000 are still very
long odds. So, you can't win and dream if you don't play but if you play buy
just one ticket. Buy it more for the fantasy you get to play in your dreams at
night in your head, because that's most likely the greatest payout you'll get.
$1 or $2 for a bottled drink or for some sweet dreams... Your choice, both are
okay choices in my mind.

Edit: typos.

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chrisbennet
We all know that there are negatives to winning the lottery or getting rich.
One big drawback would be never being able to make new ("poor") friends
without knowing if they were true friends or only friends because of your
wealth.

I can certainly see "rolling the dice" on a life changing outcome if you had
nothing to lose because you were miserable. I think it make less sense if you
are happy. Am I the only one who is so happy that I wouldn't take a chance on
wrecking my life?

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oaktowner
The lottery is a tax on people with bad math skills.

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Chinjut
You don't have to have bad math skills to play the lottery. For example, I am
a mathematician who has on occasion chosen to purchase lottery tickets. And I
see nothing at all irrational about this.

~~~
oaktowner
Oh, I'm not above buying the occasional ticket, either -- for that matter, I
like playing Blackjack and view any losses incurred as entertainment.

However, people at the lower end of the income spend a _lot_ more of their
money (proportionally) on lottery tickets. [1]

And states are increasingly dependent on those revenues [2], which means in
effect we've got a system where our schools become dependent on our lowest
income population wasting money on what is essentially a pipe dream.

Note: I'm not saying "we've got to stop lotteries!" As I said: I play myself.
Just noting that we are funding our government on the backs of people who are
making what is arguably a terrible investment.

In other words: lotteries are a tax on people with bad math skills.

[1] Lots of studies back that up; there's a pretty good list here:
[http://stoppredatorygambling.org/blog/category/research-
cent...](http://stoppredatorygambling.org/blog/category/research-
center/lotteries-who-really-plays/)

[2] [http://taxfoundation.org/article/gambling-tax-policy-
states-...](http://taxfoundation.org/article/gambling-tax-policy-states-
growing-reliance-lottery-tax-revenue)

