
I am a statistician and I buy lottery tickets - realize
http://simplexify.net/blog/2012/5/6/i-am-a-statistician-and-i-buy-lottery-tickets.html
======
tytso
I really like Colin McMillen's comments on this matter:

[https://plus.google.com/107814003053721091970/posts/6sPpxMo6...](https://plus.google.com/107814003053721091970/posts/6sPpxMo6JTM)

Some choice quotes from his Google+ post: "The lottery is not a tax on people
who are bad at math. It's trading a little bit of expected-value for a lot of
variance."

"There are many other cases in real life where mean/variance tradeoffs arise,
and there are perfectly plausible objective functions under which it makes
sense to follow a policy that doesn't maximize expected value.

The obvious example is insurance, where you pay a small bit of money each year
to reduce the chance that you end up suddenly needing to pay a lot of money.
Same with forming or joining a startup; on average you'll make less money than
if you take a "normal" job, but there's some small chance that you'll have
just joined the next Apple or Google and you'll end up rich.... "

~~~
lunchbox
> on average you'll make less money [in a startup] than if you take a "normal"
> job

I disagree. If he's using "average" in the sense of "mean" (not median), then
he's saying that starting a startup has a lower expected return _and_ is
higher risk than working a normal job, meaning it's inferior in both regards
(assuming diminishing marginal utility). Entrepreneurship is a classic "high
risk, high return" venture. It has a _higher_ expected return than a
conventional job; that's what makes it financially attractive to founders and
VCs in the first place. The astronomical success of the minority offsets the
lack of success of the majority.

In a similar vein I disagree with his assertion that joining a startup (taking
a risk) is like buying insurance (avoiding a risk). They are opposites.

~~~
AndrewDucker
Do you have any proof that, on average, startup founders make more money than
people employed in regular jobs, once you take into account all of the ones
that make no money and then collapse?

~~~
lunchbox
That's a good question. Would be interesting to see if someone can dig up any
studies on this. e.g what % of the country's wealth is owned by founders (and
their heirs), divided by the % of people who are current or former founders.

My argument is founded not on experimental data but rather on the axioms of
utility theory. If startups had higher risk AND lower expected payoff, it
would make no financial sense to found or invest in one, since that would be a
textbook example of a bad investment:

<http://en.wikipedia.org/wiki/Security_market_line>

Yet there are lots of (otherwise) smart/rational people founding and investing
in startups.

~~~
wtvanhest
There is a massive difference between founding a startup and investing in
startups.

Professional investors (VCs, Angels, Incubators) choose the best startups
(most efficient choices) and do not fund the rest which eliminates a huge
number of founders who simply fail and get zero return for their work. On top
of that, there are a number of VCs and angels who are completely unsuccessful
picking startups and end up out of the business unable to raise additional
institutional money or who lose their additional investment capital.

The expected return of investing in startups is very likely negative if you
add all the smart and non-smart investors together. (I don't have data, and
can't even imagine where to get it, so I'm saying "likely".)

Using the security market line to prove your point isn’t really fair since not
much research has been done on applying it to startups. One of the major
issues with applying the SML is the fact that it is very hard to calculate
beta of startup investments since they have very long term time horizons. SML
has more to do with portfolio construction and how you can get a portfolio
which doesn’t deviate from the benchmark too far while still producing Alpha.
(Alpha is active return). The Tryenor ratio is more about making sure public
equity managers are not doing really crazy stuff.

Overall my point is that there is no evidence that suggests the expected
return from investing is startups in net positive. Whether founding or working
for a startup produces positive expected returns or not is also very hard to
know, but I would estimate that working for early stage startups for lower
than market pay has a negative expected value even after considering the
possibility of huge exits (a lot of companies fail that you have never heard
of).

Where I think startups have a much higher expected return comes with the
experience and growing up you can do while working in a small company. When
you calculate total earnings over a lifetime for people who join even failed
startups early on, I would not be surprised if they made more and had more
enjoyable lives, even if they ended up at big stable companies later. When you
add the possibility of a big exit to the higher future earnings I think the
expected value goes net positive.

------
FelixP
Some vaguely interesting statistical analysis, but here's the money quote at
the end (TL;DR)-

"So why do I still buy lottery tickets? <b>Definitely not for the expected
monetary return on investment.</b> I think of it as a discretionary
entertainment spend. I get literally hours of enjoyment from fantasizing what
I’d do if I won."

~~~
commieneko
Interestingly, I can fantasize about winning the lottery and spending all that
lovely, lovely money too. All without buying a lottery ticket.

~~~
libria
I believe the author is trying to convey that even a remote possibility of
winning fuels his fantasy. It is impossible to win without buying a lottery
ticket.

~~~
eridius
On the other hand, someone could walk up to you on the street and hand you a
briefcase full of $10M. It's not out of the realm of probability.

~~~
philwelch
$10M in US $100 bills would take up over 100 liters of volume, which would
fill about five rather large briefcases. The cash itself would weigh over 200
pounds. Strictly speaking, it's impossible for someone to walk up to you on
the street and simply "hand" you _a_ briefcase full of $10M. They would have
to wheel them to you on a cart, which would undoubtedly attract far more
attention than is safe for this sort of transaction.

Incidentally, it's amusing to note that $100 bills are actually more valuable
than gold relative to their weight. The obvious next question would be, what's
an even denser store of value. For one amusing example, Cristiano Ronaldo has
a transfer value in excess of $130 million by last valuation, and weighs less
than 200 pounds, making him more than ten times as valuable as $100 bills per
unit weight, let alone gold. Judging from the transfer market, it would seem
that many top-flight athletes are literally worth their weight in gold.

~~~
adrianN
500€ notes are the method of choice for transporting large amount of money.

<http://en.wikipedia.org/wiki/500_euro_note#Crime>

~~~
philwelch
Yeah, that's why we abolished the $500 bill in this country. I'm surprised the
EU has currency in that amount. I didn't think to investigate other currencies
because the guy I was replying to said 10 million dollars. Perhaps 10 million
euro _would_ fit in a single large briefcase (and be worth more than 10
million dollars to boot).

------
RockyMcNuts
Per the Kelly Criterion, unless you have a big bankroll, the minimum bet is an
overbet, which turns it into a losing strategy.

Suppose you have $100,000, and repeatedly bet .001% of your net worth on a
single ticket in the lottery at 100,000,000:1 with a 2x EV (disregarding that
you can’t bet more or less than the price of a ticket). You do it 2,000,000
times, and then you hit the jackpot – pretty lucky since the odds are
100,000,000 to 1, right? But by the time you hit the jackpot, your bankroll
has been so depleted that winning 200m x your bet, you only get back to 41% of
your original net worth – because you overbet!

A longer discussion (by me) of why only millionaires should play Powerball -
[http://blog.streeteye.com/blog/2011/11/why-only-
millionaires...](http://blog.streeteye.com/blog/2011/11/why-only-millionaires-
should-play-powerball/)

------
codehotter
In the book "Thinking fast and slow" by Daniel Kahneman, it is claimed that
there is a growing body of evidence that we really have two brain systems. A
fast one, which uses heuristics to quickly approximate the answer, and a slow
one, capable of deliberate and rational thought. He argues that the fast brain
system is really responsible for a lot of our cognitive biases.

For example, our fast brain does not really understand probability. It only
knows three categories: either something is impossible, it is possible, or it
is a certainty. A lot of human behaviour with regards to probability can be
explained by this simple assumption.

Why do people buy lottery tickets? For their intuition, it moves an
impossibility into a possibility. The fast brain system that fuels their
intuition does not care what the actual probability is and does not understand
anyway.

~~~
disgruntledphd2
While I deeply respect Daniel Kahneman's work, please note that his two system
"theory" is pretty awful. He uses it as a justification for some strange
results, and made no effort to test it. Now, there is some evidence that
humans have numerous different reasoning systems, but this is a complicated
and controversial area, and we have no idea how many, its somewhere between 1
and n, where n could range from 0 to at least 10.

------
markokocic
Lottery, as a form of innocent betting, can really provide a lot of fun for a
small price. I would be bored to death to watch a soccer game, but when I bet
1€ on it, it suddenly becomes 2 hours of fun. And I don't expect to "win the
ticket", cause I already got more than I paid for.

Looking at everything from the profit/cost point of view can lead to a very
boring life, for most of the people.

------
tdubhro1
Lotteries are a tax on people who are desperate, not ignorant. Even if you
understand the math, your utility function changes so that you're willing to
trade a small expected loss for the long shot chance of solving all your
problems. I don't buy the idea that swathes of lottery players really think
they're making a value bet. Just because they respond with anecdotal evidence
when you confront them with the true odds, doesn't mean they're really arguing
the facts, they're just protecting their hopes.

~~~
JoachimSchipper
This is a really interesting idea. Do you have any evidence, anecdotal or
otherwise?

~~~
tdubhro1
A good starting point for more rigorous evidence:
[http://stoppredatorygambling.org/category/research-
center/lo...](http://stoppredatorygambling.org/category/research-
center/lotteries-who-really-plays/)

I've been interested in the topic for a long time as I have a relative who
spends most of his income on lottery tickets. Any time I can, I ask people who
play the lottery why they do it. Most of them spend a tiny amount and it's
something they have a little bit of fun with their workmates or family, these
are the "normals". But about 20% of the players account for 80% of the ticket
revenue, these are the people playing out of desperation because they are in a
poverty trap and they have no other way out. They are foregoing essentials to
pay for the lottery tickets, so if they didn't play, they wouldn't accrue the
money they "saved". These people are often on the brink: depressed, panicked
and alone. A lottery ticket is a temporary "self medication" with which they
can temporarily quiet their anxieties, until of course, they need the next
hit.

~~~
gfodor
thanks for the link. I have never spent much time thinking about the ethics of
the lottery and this was quite stunning.

------
vacri
Simple evidence that gambling (rather than just lotto) is a tax on poor people
- check out where the gaming/'slot' machines are. Last time they ran the map
in the paper, the venues were heavily clustered in the poorer northern and
western suburbs of Melbourne, with another cluster down in Frankston.

Then of course there's the simple point that less money comes out of lotto
than goes in, simply to pay for overheads and profit of the gaming company (as
with all gambling) plus a bit of tax on the ticket. The ticket sale simply
can't be a zero-sum game; less has to make it back to the winners than was
paid in the first place.

That being said, I also pay the idiot tax every month or two, and for the same
reasons as the author - entertainment.

~~~
jkn
By this line of reasoning, anything that is more popular among poor people is
a tax on them? People pay to gamble to get something in return (entertainment
as you say) and that makes it _not_ a tax. It is quite natural that the gaming
company makes a profit on that, just like, say, a movie theater company.

There is certainly some truth in the vision of the poor guy being a more
vulnerable gambling victim but I would not generalize that to non-addicts.
Gambling vs. other kinds of entertainment is a matter of personal preference.

Actually gambling is quite popular among rich people, in the form of financial
speculation...

~~~
ssharp
At low income levels, taxation is generally low. We've tended to avoid flat
income taxes because they impact those with low-incomes more than high-incomes
because poor people spend a higher percentage of their money than rich people.

So when you look at how poor people spend money, the rational economist would
never advocate spending the money on the lottery. The utility is low, and even
if the expected value is positive, the variance makes it a bad idea. Poor
people would be better off spending money on things with greater returns.

The problem is that poor people don't spend their money on things with greater
returns. They spend far too much of their money on lottery, and it's probably
combination of psychological factors and financial illiteracy. I could be off
on this, but I remember a statistic showing that there isn't much deviation on
how much money any random household spends on the lottery. So a household with
$100,000 in incomes spends as much on the lotter as a household with $20,000
in income. The result is that the lottery has become a regressive tax.

~~~
jkn
_So when you look at how poor people spend money, the rational economist would
never advocate spending the money on the lottery. The utility is low [...]_

This misses the point of the article, which is that gambling should _not_ be
regarded as an investment, but as entertainement. But I agree that poor people
are possibly more likely to see it the wrong way, i.e. as a good investment.

 _The result is that the lottery has become a regressive tax._

By the same argument you can conclude that potatoes are a regressive tax since
they cost a higher fraction of the poors' revenues.

When you give money to the government with nothing in return (except as a
member of the collectivity), that is a tax. Not when you give money to a
private company in exchange for some kind of entertainment.

~~~
evandijk70
In a lot of countries, lotteries are heavily regulated and the government is
the only one allowed to run one.

------
subtenante
This is all bad probabilities if you don't take into account the fact that you
repeatedly buy tickets. I'd like to see a more detailed study counting the
probability of never winning when playing systematically for 20 years, for
example.

But nevertheless. Yes, the lottery is a tax for the poor. And if you expect
your life to change for the better by winning a big bag of money (that you
will have taken to the other suckers who lost, minus the organiser's fee),
then you just need to reconsider what makes a happy life. You should also
consider how many people get isolated after they have won, not knowing how to
deal with such a change, such a "responsibility", such a social pressure from
family and friends after they have won.

I'd never play the lottery not because of the ridiculously low chances of
winning (I also am a statistician), but because what I would win would change
nothing to my human condition. I prefer reading Epictetus instead. It's
cheaper and the effect lasts longer.

~~~
Locke1689
It is most certainly a tax on the poor and undereducated. The level of
cognitive dissonance required to believe that there is _not_ a massive
information asymmetry at hand is simply staggering. Yes, some people are
perfectly able to calculate the probability of winning the lottery and know
that they should gain enjoyment just from playing, not from the belief that
they'll win. These are _not_ the people who are victims. The victims are the
high school dropouts who don't understand that their chances of getting hit by
lightning while simultaneously getting hit by a bus while crossing the street
are still better than winning the lottery. Many, if not most, of these people
don't really have the discretionary spending ability to lose hundreds of
dollars a month on merely _dreaming_ of winning the lottery. But somehow we
pretend everything's fine.

~~~
Stratoscope
> their chances of getting hit by lightning while simultaneously getting hit
> by a bus while crossing the street are still better than winning the lottery

While I agree with you in philosophy, I wonder if that is the best example. I
don't think I've ever seen a news report of someone getting hit by lightning
and a bus at the same time, but people do seem to win the lottery on a fairly
regular basis. This suggests that winning the lottery may be the more likely
of the two.

~~~
danssig
_Someone_ winning the lottery is more likely than _someone_ getting hit by a
bus while being struck by lightening. _You specifically_ winning the lottery
is probably less likely than _you specifically_ getting hit by a bus at the
same time as being struck by lightening.

------
paulhodge
If you're analyzing lotteries, one thing you have to think about is the
diminishing utility of money. (
<http://en.wikipedia.org/wiki/Diminishing_marginal_utility> ). Your first
dollar is a lot more useful than your millionth dollar. Or another way, having
a million dollars is not a million times as useful as having one dollar - it's
a lot less useful than that. This makes a lottery a pretty bad investment even
when the expected-returns are in your favor.

Not to mention all those stories of people who win the lottery and then lose
all their friends out of jealousy. But that's harder to analyze.

~~~
Tichy
It seems to me that if you already have, say, 100000$, then that utility
changes completely. Losing 1$ would be meaningless for you, whereas gaining 1
million dollars would be a huge improvement.

------
mukaiji
It might be an urban myth, but it's still funny:

The only weekend when casinos did not make a profit, in the entire history of
Las Vegas, was when the annual U.S. statisticians conference was organized in
Las Vegas :)

~~~
drzaiusapelord
I don't see how this makes sense. The casino's odds are always not in favor of
the players, so the more the merrier from the casino's POV. Even if you're a
card counting wiz, the margins are pretty poor and you're easily caught.

I imagine the real problem would be crowding your casino with people who just
showed up for the buffet but refused to gamble.

~~~
aplusbi
I think your latter assertion is the point - the statisticians refused to
gamble and many of the hotels' services are provided at a loss to help bring
in gamblers.

~~~
chimeracoder
Many businesses are run this way - restaurants make a loss on food to make
their margins on drinks... I wouldn't be surprised if casinos make a reduced
profit (or even a loss) on alcohol so as to make a profit on the gambling.

~~~
mukaiji
alcohol in casinos is ___FREE_ __lol. So yeah, you bet they take a hit on the
booze and compensate with gambling.

------
fukumimi
Poor statistics on the chance of winning aside, there is one reason for me to
spend $1-$2 a week on tickets: Having a ticket ensures you have a chance of
winning, while not having one ensures none at all. Losing the $50-$100 per
year isn't too big of a deal for me, especially for the entertainment value.

~~~
Drbble
If you bet on sports with your friends, you get the same entertainment for
lower cost.

~~~
dagw
Only if you enjoy sports. Also very few sports bets pay out a million times
the money. Even a bet like France beating Canada in the ice hockey world
championship only pays 33 times the money, and the prospect of winning $66 on
a $2 bet is hardly exciting.

~~~
markokocic
But winning those $66 while your friend just lost $2, (or the other way round)
could be fun ;)

------
scott_s
Oddly, his real reasons for why he plays the lottery has nothing to do with
probability and statistics, and is in the last two paragraphs. I feel the
essay would have been better serveed if he had started with that, then said
"But, given that, let's still explore what the actual expected return on
investment is for the fun of it."

------
colomon
I always wonder about these calculations. According to
<http://www.michiganlottery.com/where_the_money_goes> out of every $1 players
spend on the Michign lottery, $.58 goes to player prizes. Assuming they're
actually counting that correctly, doesn't that mean the expected monetary
return (to you, of course it's nice that you're donating to the school system)
of $1 spent on the lottery _has_ to be $.58?

~~~
philwelch
That's over the course of the whole run; accordingly the average expected
value of $1 spent on the Michigan lottery would be $.58 if you bought a ticket
for every game every week. But you don't do that. Some weeks the jackpot is
higher so you buy a ticket, some weeks you don't. When the jackpot is higher,
the EV _for that week_ rises, but since the lottery itself plays every week it
doesn't matter so much to them.

~~~
colomon
But when the jackpot is bigger, more people buy tickets, too, which makes the
EV for that week go down. It's not at all clear to me which effect is bigger.
(Indeed, I wonder if your best bet is to buy the first week the jackpot rolls
over, but not when it has rolled over multiple times.)

At any rate, if the expected return over long periods is $.58 for $1, I sure
wouldn't expect it to even get close to $1 on the best weeks.

------
squozzer
\- If you're so poor that paying 1 USD is a hardship, then you shouldn't play
the lottery. Otherwise, where's the harm? \- The argument, "the lottery is a
tax on poor / stupid people" is valid but useless when talking about small
amounts of money. \- The difference(s) between winning the lottery and someone
just giving you millions of dollars? - 1) You know where the money came from;
2) The person just giving away the millions isn't receiving payment for giving
away the money.

------
robomartin
Saying that the lottery is a tax on poor people is like saying that buying a
bottle of Coke is a tax on poor people. Both of these events are completely
voluntary. No government agency was involved in making you spend the money.
You are not obligated to do it. And, if you choose not to spend the money you
are not violating any laws. It is not a tax. That's the most ridiculous idea
I've ever heard.

One could argue that spending money on a lottery ticket is actually better for
you than spending the same amount of money on a soft drink. One gives you hope
and entertainment and might have other positive "feel good" side-effects. The
other fills you with sugar (high fructose corn syrup) and is not good for
anything at all.

~~~
mturmon
The government _is_ involved in making you spend the money, because they
advertise the lottery.

This advertising presumably motivates citizens who would not ordinarily buy
tickets, to buy tickets.

They are not forcing you, of course, but they certainly are encouraging you.

~~~
robomartin
Oh, please.

You are not obligated by law to buy lottery tickets, therefore, it cannot, by
any stretch of the imagination, be called a tax. Period. They can advertise
all they want. You can still say "no".

In fact, you can stand in front of a government lottery official, extend your
arm out, point a finger at them and laugh out hysterically while loudly
proclaiming that you will not buy their tickets. Try telling the IRS that you
will not pay taxes because, well, you don't want to.

~~~
itstriz
I'm pretty sure the term "tax" is meant as metaphor.

~~~
danudey
I think the point is that it's a disingenuous assertion.

------
frankydp
I have always had a hard time equating ROI on any windfall probability. I view
lottery systems as a windfall system in that the chance of winning is zero and
the expense of playing is trivial, so any investment has no expectation of
return it only allows for the possibility of windfall. The $1600 investment
over 30 years would not have noticeably increased or decreased my QoL so it is
not a lose in my mind, only a technicality.

------
sammyo
Best entertainment value ever: When one of the big jackpots was making the
news I bought one as much to head off the conversation of why not than
anything, but it triggered these incredible technocolor daydreams! I was not
bored on the subway for days. Diminishing returns though, since then the
occasional ticket never had the same internal result.

~~~
sammyo
Oh that's funny, I went and actually read the article and his conclusion is
exactly this point.

------
knowtheory
Amused at the claim that 1 & 1/4 million is 'just over [...] a million"

I tend not to think of an added 1/4th as "just over" but perhaps that's a
difference in perception.

------
penetrator
let's not forget about the real tax from winning and the payment. govt always
wants his share and the lottery won't pay in lump sum.

~~~
planetguy
I've always wondered about that aspect of US law. If lottery winnings are
taxed, does that mean lottery tickets are tax-deductible?

~~~
dhugiaskmak
You can deduct gambling losses up to the amount of gambling winnings (if any),
yes.

~~~
galfarragem
In Portuguese stockmarket, if you have 1 winner stock and dozens of looser
stocks, you still pay tax from the winner one..

------
nirgle
I love this argument. It gets juicy quick. Sugary, like cake. When they tell
you "you can't win if you don't play", and you say, "nonsense, I can find a
dropped lottery ticket on the ground that turns out to be the big one" and
they say "really?? what are the chances of that happening?". Black forest,
cherry on top. Just wonderful.

------
icc97
It makes perfect sense to simply purchase 1 lottery ticket. Takes your chances
from 45,379,619:0 to 45,379,619:1, for a negligible cost.

Beyond that your time is wasted, statistician or not.

~~~
sopooneo
If _aside from entertainment value_ it makes sense to buy one ticket,then it
makes sense to buy two. And three and four. But in fact _aside from
entertainment value_ it does not make sense to buy one, because that change
from 45,379,619:0 to 45,379,619:1 on a windfall is accompanied by a change
from 1:1 to 0:1 chance on keeping your original dollar. And in the vast bulk
of lottery scenarios, it all multiplies out to a negative expected return.

~~~
icc97
Its increasingly lower returns for each dollar, thus I don't see the point of
anything above the minimum. The expected return may be negative (further hence
the minimum investment) but its negligible.

------
andrewfelix
I was initially confused and annoyed by the author's lack of justification.
But I enjoyed his conclusion, that there's an 'entertainment' value attached
to the purchase.

------
hypervisor
It reminds me of this <http://www.wired.com/magazine/2011/01/ff_lottery/all/1>

~~~
mmahemoff
For me, the opposite. I thought from the title it was going to be about gaming
the lottery, but it's a matter of fact analysis and doesn't go into using
strategies like picking under-loved numbers to overcome the odds.

------
dalke
The first rejoinder which came to mind is: "I am a lung cancer doctor and I
smoke cigarettes." :)

------
aneth
You may be able to increase your expected value by choosing numbers that are
less popular. It would be interesting to research the psychology behind number
selection and choose combinations less likely to have a multi-payoff outcome.

~~~
thedufer
Interestingly, this means that common "lucky" numbers are actually unlucky, to
a degree inversely proportional to their perceived luckiness across the
population.

~~~
ufo
I remember hearing a story once about six people that shared a lottery prize
because they used a number from a fortune cookie.

~~~
thedufer
Six people? Try 3,100 when the number 7-7-7-7 came up.

Source:
[http://articles.nydailynews.com/2010-04-02/news/27060744_1_l...](http://articles.nydailynews.com/2010-04-02/news/27060744_1_lottery-
winners-number-seven)

------
penetrator
'The decision of whether to buy a lottery ticket shouldn’t be based on the
probability of winning, or the expected return of a ticket, but on the
entertainment value that comes from imagining a different life.'

sounds like college, s/entertainment/networking

------
theoa
It's posts and comments like these where I so miss the down vote click.

There's not even a hint of irony.

It's all about the 'entertainment' value.

Am I seeing a remake of the book/movie 'Hunger Games'?

"Oh Nigel, do kindly pass me two of your Entertainment cards. You'll get a
treat if you do..."

