
$100 Invested in 100 $1 Lottery Tickets - magikbum
http://www.investinged.com/100-invested-in-100-1-lottery-tickets/
======
ChuckMcM
Ah probability, the science of denial :-)

Having lived in Las Vegas during my teen years I got to see first hand how
people rationalize their misunderstanding of statistics into winning 'systems'
that if they just had enough money would payoff. I cannot count the number of
times someone told me, in complete earnestness, that their system worked, they
had proved it worked using a small stake of $X (which was all gone now) and if
they had ($10X or $100X) of a stake their working system would return a
handsome profit. And you say "Gee if it worked how come you lost all your
money?" and they would say "You win and lose some, my system predicts when the
big wins will come based on what has happened so far and I make big bets on
that, and small bets on the ones we know are more likely to lose but to get
them out of the way." And you say "So if you had a coin and you flipped it you
would make a really big wager if the coin had just turned up heads 3 times in
a row?" and they say "EXACTLY! You know this system?"

~~~
lifeformed
I wonder what the best way is to illustrate to those people that that coin
example is ridiculous. It's so intuitive to us that the coin has no "memory".
However, I could see why someone would think that 3 heads in a row mean the
4th will be more likely to be heads. If you didn't think about it much, it is
a reasonable gut reaction to a layperson.

What if you told the person this: "What if you flipped a coin and it had come
up 3 heads in a row. Is it more likely that it'll come up heads again? Well,
what if you waited a minute before you flipped it again? What about an hour?
20 years? Would the odds go back to 50/50 then? At what point does the coin
'forget' its previous flips?"

I think putting it that way would help illustrate the absurdity of that way of
thinking.

As an aside, I think if I flipped a coin 100 times and it was heads all 100
times, I would be willing to make a big bet on the 101st flip being heads. The
odds of getting 100 heads in a row is so much smaller than the odds that
something is wrong with the system (the coin is weighted, there's some sleight
of hand going on, etc).

~~~
nazgulnarsil
If you don't know whether it is a fair coin 3 heads in a row is evidence that
the 4th will be heads with slightly greater probability than tails.

------
aresant
The lottery let's people gamble (which is illegal in most US states) because
of "the children".

EG lottery profits go to support additional money for public schools.

This is all after a 16% operating / administrative cost, of course, which
amounted to ~$4.83b in California alone in 2012 (2).

Back in 1988 an article appeared in the NYTimes suggesting that what was
actually happening with the money, only 3 years in, was that state budgetary
offices were simply using this newfound windfall to supplant existing
commitments.

Explained by the State Superintend at the time "the percentage of the state
budget spent on public schools declined from 39 percent four years ago to 37.5
percent last year. Lottery dollars, he said, have in effect been used to make
up the difference."

Part of my frustration with California's recent retroactive tax-raises,
ostensibly for education, is borne out of examples like these.

(1) [http://www.nytimes.com/1988/10/04/us/california-educators-
as...](http://www.nytimes.com/1988/10/04/us/california-educators-assert-
lottery-has-failed-to-pay-off-for-the-schools.html)

(2) [http://www.calwatchdog.com/2012/09/27/ca-lottery-states-
cash...](http://www.calwatchdog.com/2012/09/27/ca-lottery-states-cash-cow/)

~~~
btilly
I fully understand that, and support the tax raises anyways because if that is
the only way to get them, then we can get them that way.

The problem is that the state constitution and politics makes it easy to get
rid of revenue, but really hard to get it back. For instance consider Arnold
Schwarzenegger, one of whose original goals was to drop the vehicle licensing
fee from 2% of a car's worth to 0.65%. He got in office when times were good,
he reduced that tax. Then times turned bad, and it was impossible to reverse
that even though the state really couldn't afford it any more. This is about a
$6 billion/year hole in our budget. That's on par with the recent tax
increases.

Except that the vehicle licensing fee was part of our budget for decades. It
was stable and reliable. Our recent tax increases are temporary. What do we do
in the long run?

~~~
the_rosentotter
> vehicle licensing fee from 2% of a car's worth to 0.65%

In Denmark the fee is 180% of the car's worth... (sorry for OT)

~~~
cpeterso
How can poor people afford to buy a car? Public transportation isn't available
in all places and at all times of day.

~~~
the_rosentotter
Note that we hardly have poor people (by American standards) because of the
welfare state, which is partly funded by these extremely high taxes, but it is
difficult for low income people to afford a car (gasoline is heavily taxed
too). If they really need it they will buy an old beater and drive it a couple
of years until it dies, then repeat (which somewhat nullifies the rationale of
car registration fees helping the environment).

~~~
ams6110
"old beaters" also differ from American standards. I doubt the typical
American "beater" car would be considered roadworthy in Denmark.

------
mattmaroon
Lotteries are probably regulated to the point where this can't happen, but I
used to play poker at some quasi-legal charity games quite often. They sold
instant bingo tickets, which are very much like instant lottery tickets.
There's a box with a defined number of losers and each prize.

Most of the return from a box came from let's say 5 big prizes (out of let's
say 1,000 tickets). Let's suppose the return is 50%, and the ticket price $2,
so the total payout on a box is $1,000. There would be 5 $100 winners, and a
number of smaller winners that added up to the other $500.

The people selling them would watch and count how many of the $100 tickets
were redeemed. (Gamblers tend to not hold onto the winning ticket secretly,
they cash them in right away and buy more.) If there were, say, 2 of the big
winners left but only 100 tickets remaining in the box, the guy running it
would purchase them all. The two big winners would pay for the whole thing and
his profit would then be the sum of all of the small prizes left (which was
expected to be roughly equal to the 2 big tickets).

Since it was a charity game he was effectively stealing from the charity, but
also robbing the players collectively because any time you were near the end
of a box but still able to buy tickets you could be sure there were no big
prizes left.

I wonder if instant lotteries ever do this. If they see it's near the end and
they've got a disproportionate number of prizes left they could simply pull
all of the tickets.

~~~
rcxdude
I don't think that strategy cost the charity any money, unless the boxes would
not have sold out anyway. The return on the boxes is fixed regardless of who
buys the tickets.

~~~
nedwin
The cost is that people who know this strategy is in place will no longer
purchase any tickets if there is less than 100 tickets left.

Further if the ruse is revealed the general sale of all charity lottery
tickets will define because it could be assumed that it is rigged in favour of
the house.

------
CurtMonash
In the 1970s, when state lotteries were new, the Massachusetts lottery had a
parimutuel payout, akin to horse racing -- whoever had the winning 4-digit
number divvied up a payout. Based, I suppose, on anecdotal evidence, some guys
in the Harvard physics department judged which numbers were likely to be least
popular, and bet those, getting a positive return.

However, this arbitrage quickly went away. It seemed that organized criminals
started using the lottery as a low cost (indeed initially negative cost) way
of laundering money, using a similar scheme.

The upside is that this turned into a kind of state income tax on criminal
income.

------
marshray
If he can consistently reproduce the $41 return, he has it made.

He just needs to aggregate bundles of lottery tickets and sell them to
investors looking for a guaranteed -60% return, and then pocket the extra 1%.

~~~
stevewilhelm
I'll guarantee any desired negative return for just a 0.5% fee.

------
dice
I think the final paragraph sums it up, although the author seems to miss the
point:

>The thrill and rush of possibly winning started to wear off after about the
twentieth losing ticket. Each card had a couple of “Life” symbols on them, and
every time you got a second you just dreamed of seeing the third one under the
remaining graphite. However it never appeared and never will and it just kind
of turned depressing. How could people put themselves through this humiliation
and teasing every day of their lives? This is definitely an investment that is
not rigged in your favor and can never really bring you positive returns.

There is a thrill to knowing that, however small the chance, there is a large
payout potentially waiting for you. Most people don't buy 100 scratchers at a
time, or I would guess even one a day. Buying one lotto ticket a week, for
instance, is a trivial expense for many people which also happens to be fun
(the aforementioned thrill). The inevitability of the loss doesn't become as
apparent over those time scales: selective memory results in people
remembering their (typically small) wins and forgetting all of the losses in
between.

~~~
ttrreeww
Stock options: There is a thrill to knowing that, however small the chance,
there is a large payout potentially waiting for you.

~~~
gfodor
A lot of money can be made selling call options on high volatility stocks you
own that are way out of the money. You are essentially selling lotto tickets
to gamblers.

~~~
gburt
I bet not. In the short term, it looks like money can be made, but you're
dramatically under-estimating the likelihood of those high-sigma events.

Edit: tail risk from modelling error, in particular.

~~~
gfodor
The point is if you own the stock the high sigma event does not result in a
loss but a reduced gain. And we're talking way out of the money so it will be
a substantial gain if you get called away. Many call buyers are retail
investors speculating on price movements, and are using call options as a form
of leverage since they do not have the capital to go long the same amount of
stock. Whereas call sellers must own the stock (or be exposed to infinite
losses.) There are a few studies that show there are excess returns for option
sellers vs buyers but unfortunately don't have a link handy. (See "Expected
Returns" the book on amazon.)

edit: AAPL right now is an excellent example of a high volatility stock that
is underpriced demanding large option premiums. If you have the capital
picking up some AAPL to simply write calls until it goes back up to a fair
valuation is a reasonable way to make money, with the caveat that it relies
upon Apple breaking above being in the bottom 5% of the market valuation-wise.

~~~
TheCowboy
It's called a covered call position. If it was that risk-free and easy, then
every hedge fund would be already on top of this and quickly bring prices back
into parity.

Unfortunately, you still expose yourself to the risk of holding the stock,
while putting a hard cap on the upside.

You have to hold 100 shares to cover 1 option. A decline in the price can
quickly add up to a significant loss, not to mention when you actually have to
sell your position when the calls are exercised.

~~~
gfodor
I never said it was risk free or easy, and hedge funds do sell covered calls.
The point is there is a well known and understood asymmetry between the long
and short options markets due to the capital needed to write options.
Intuitively the reason there is alpha for selling options is likely at least
in part that you are letting people with little capital access leverage.

------
gojomo
Spending on scratchers is legal... and even encouraged by government
advertising.

But unless you're already rich enough to qualify as an 'accredited investor',
there are legal barriers to investing in private companies

Such irrational paternalism is insane.

~~~
thaumaturgy
The risks of scratchers (and other lotteries) is known, controlled, and
published. If you feel "ripped off" by a lottery, you are stupid.

The risks of startup investment are murky and subject to manipulation. People
can rip off other people. Some of the laws are there to protect people's
retirement savings from investment scammers.

(Whether those laws are effective or not is a debate I'm not qualified to
have.)

------
michaelbuckbee
Of note is that there is at least one documented case of someone (supposedly)
reverse engineering lottery algorithms to give themselves better odds:

[http://www.dailymail.co.uk/news/article-2023514/Joan-R-
Ginth...](http://www.dailymail.co.uk/news/article-2023514/Joan-R-Ginther-won-
lottery-4-times-Stanford-University-statistics-PhD.html)

~~~
Retric
The statistics are off, the odds of someone winning several times is based on
how many times they buy ticks but lot's of people play and winners often
change their behavior.

First off a lot of people have won once so you need to know how many winners
there where and how much they spent to get odds of a second win. Total ticket
sales are ~$78 billion assuming 1 winner per 50 million spent that's ~1,560
winners per year assuming they live another 40 years that's 62,000 people that
have one once alive at any one time. So now you figure how many tickets do
winners buy per year? Call it 5,000$ so now each year there is around 300
million spent by lotto winners on tickets. So, you would expect ~6 people to
win a second time each year.

But, this is where behavior's may really get out of whack. Of those 6 you
would expect people to think they where destined to win. Let's say 1 person
per year now spends 1/3 of there money on the lotto. As the payouts tends to
be ~1/2th of ticket sales (jackpot's are around 1/4 but I assume non jackpot
wins are rolled back in). They would then have a ~1/6 chance of a third win
and a 1/36 chance of a second win. Of course that's just looking at winners
for one year so around once every 20 years someone should win 4 times in a
row.

------
dtrizzle
Speaking of which, I need to buy a few Powerball tickets!

[http://www.usatoday.com/story/news/2013/05/17/saturdays--
550...](http://www.usatoday.com/story/news/2013/05/17/saturdays--550-million-
powerball-jackpot-could-get-even-bigger/2194135/)

------
pessimizer
>How could people put themselves through this humiliation and teasing every
day of their lives?

Skinner knows.

------
jmharvey
I think he's underestimating the time he invested in this project. He says he
scratched 100 tickets in 15 minutes. That's a pace of 9 seconds per ticket.
I've bought a sizable number of lottery tickets, and that's a blazingly fast
pace to scratch off (or otherwise remove) the latex, read the revealed
numbers, determine if you have a winner, tear the ticket at the perforation,
and sort the ticket into the appropriate pile.

------
Thrymr
It looks like he bought 100 consecutive tickets. If the winning tickets are
truly random, it wouldn't matter, but I wouldn't be surprised if the
distribution is controlled in some way that ensures winning tickets will be
more evenly distributed than random. Anyone know whether this is the case?

If it is, the variance at least (if not the expected return) could be
different if the tickets were purchased in 100 different places.

~~~
the_cat_kittles
usually you can see how many of the bigger prizes have been collected during a
run. If you didn't manually ensure they were not all clumped together, you
might run into cases where tickets could be deduced to have substantially
different odds (in either direction)... I think this has actually happened.
You wouldn't want all the big prizes to get claimed right at the beginning, I
imagine people would largely stop buying your tickets.

------
protomyth
In the 90's right before ND was part of PowerBall, I was asked to buy the
tickets for a whole office because I was going to MN. I bought $120 of tickets
and did not have one ticket with any winning numbers (never mind a powerball).
I was never asked to buy tickets again. I seem to remember the odds were
better to win than miss all (5/49 + 1/42 era).

Its a cute diversion for most and one of those weird office group things.

------
nmcfarl
nyud.net cached version, as I’m getting a DB error:

[http://www.investinged.com.nyud.net/100-invested-
in-100-1-lo...](http://www.investinged.com.nyud.net/100-invested-
in-100-1-lottery-tickets/)

------
johnward
I took a look at the odds in my state. The lower dollar amount tickets have
worse odds. The higher you go up in ticket price the better the odds get.

At $1 you might see odds up too 1:5 but all of the $20 tickets are <1:4. The
best I saw was 1:2.89. I'm not goot with stats but wouldn't have been better
to buy 5 $20 instead of 100 $1 tickets?

~~~
dghughes
It's the same with slot machines penny may be 80% (payback) but $1, $5 and up
may be 96% but that's over a million or even ten million spins.

------
quackerhacker
I love statistics and probability...but I thought this was going to start off
like one of those old mastercard commercials lol. Just a question...isn't the
odds and probability on the back of the scratchers???

100 $1 lottery tickets = $100 bucks

scratching tickets = 15 mins

learning ROI and tending to a cramped hand = priceless

------
johnohara
A second test would be to purchase 10 tickets from 10 different locations in
order to change the influence of the state's internal randomization procedure
during print production.

Would be interesting to see if the payouts lined up with the expected value as
well.

------
ImprovedSilence
good article. also:

"the lottery is a tax for people bad at math." - some dude.

~~~
breadbox
Joe Bob Briggs had a better quote, to the effect that lotteries are a tax on
desperation. The people who play lotteries are often those who have run out of
rational options. Seen in that light, lotteries are really a government
preying on its own least-protected citizens.

------
jaynos
It helps if the game isn't fully random:
<http://www.wired.com/magazine/2011/01/ff_lottery/all/>

It's Jonah Lehrer, but I doubt it's completely fabricated.

------
neogodless
Previous discussion: <https://news.ycombinator.com/item?id=4398665>

Also note that winning a $4 ticket will net you $6 :-) So the actual expected
ROI is -64%

------
johnward
You just need to find a way to hack the lottery:
<http://www.wired.com/magazine/2011/01/ff_lottery/>

------
pclark
My friend once went to a concert where entry cost "5 scratch cards" – there
were about 150 people in attendance. I always wondered how the concert
organisers did…

~~~
justncase80
The next day they were probably wishing they had just gotten $5 instead.

~~~
maaku
And a sore wrist ;)

------
drmr
"spend just $1 and be rewarded in prizes that are worth exponentially more"

Any exponent of 1 is 1. So you wouldn't be able to win anything 'more' than
that at all. Exponentially.

~~~
SEMW
When people say a quantity like $x is exponentially increasing, they generally
mean it's going as $x(1 + k)^t for some k, not as ($x)^t.

(And remember, any non-unitless quantity will be 1 in _some_ units, nothing
special about $1).

------
jvanderwal
I wonder if there's any sort of somewhat even distribution to the winning
tickets. If it's entirely random, there's shouldn't be. However, I knew a guy
who worked at a gas station and he'd watch whenever people bought a bunch of
tickets. If they scratched them off right there and didn't win anything, he'd
buy the next few tickets. I believe he spent about $50-$100/week, but
regularly won about $150/week.

~~~
gus_massa
Check that he is reporting each and every time that he is playing. Ideally he
should be writing the gambling in an Excel or Googledocs spreadsheet. Every
one of them for at least three months.

A common problem is that the people report only the good events and forget the
bad strikes. Other problem is partial compensations: "I won +$50 and +$10$ and
I only lost once -$30." really means "The firs week I won +$50. The second
weak y lose -$40, but it not a lose because they come from the money I had won
in the first weak. The third weak I won again +$10. I only was unlucky in the
fourth weak because I lose -$30."

It's not voluntary lying. Lucky strikes are interesting anecdotes, unlucky
strikes are expected and boring. And bad memory and "compensations" are normal
human bias. So write down everything systematically, or it's not useful to
make statistics.

------
networked
>But wouldn’t it be great if you could just on a whim plop down $1 and buy a
ticket that changed your life?

Aside from the monetary loss this might not even be a good thing to _dream
about._ Consider <http://lesswrong.com/lw/hl/lotteries_a_waste_of_hope/>.

~~~
SomeCallMeTim
Awesome link! I've made a similar (though not as well-presented) argument
myself on a thread on Reddit (in r/frugal -- people were actually defending
buying a ticket using exactly the linked arguments). Glad to know the thinkers
at lesswrong.com agree. :)

------
joering2
Just out of curiosity, does anyone know they do it at the power ball? I know
the system shuts down long before drawing, but what else do they do? Some sort
of DB dump and lock it in the safe or something? What are chances that an
employee leaves a virus that randomly insert a row with winning numbers after
being drawn?

------
ctdonath
Compute the average payoff. If it's positive, it's investing. If it's
negative, it's gambling.

~~~
tunesmith
Occasionally, a large jackpot can return a positive average payoff, if it's
powerball style and they accrue from round to round. However, the odds are so
astronomically against any one ticket winning, that it would still be
considered gambling. If a billionaire could risk enough of their fortune to
gain a high probability of getting that winning ticket and therefore making an
overall profit, then perhaps it would be investing from his perspective, but
if you or I blows our $50k emergency fund and still has a 99% chance of losing
it all, it's still gambling.

~~~
T-hawk
This strategy fails because multiple winners would split the jackpot. If one
billionaire sees a positive return in buying up the entire probability space
to get the jackpot, he must assume that another billionaire would also come to
the same conclusion. No player can assume they're the only one applying the
strategy; they each must assume the jackpot will split until a ticket is no
longer positive value.

------
jack-r-abbit
It would have been interesting to see him continue the investing with the $41
for a second round. If you go into it already willing to lose $100,
reinvesting the winnings gives you more chances to win that big prize.

------
elmuchoprez
I'm always amused that when they list the overall odds of "winning", they
include the odds of just getting your money back ($1 prize on a ticket that
cost $1), which isn't "winning" at all in my book.

~~~
neogodless
Ha, well in your book. But once you buy a ticket, the $1 is sunk cost and you
currently have $0 left of your $1. If you then get $1 from the ticket, you did
"win" it and are $1 better off than you would have been if the ticket was not
a winner. If you're willing to shell out the $1 in the first place, you should
be happier winning $0.23 then being stuck with a losing ticket.

------
lifeguard
I prefer to buy stocks that pay dividends.

------
amalag
He showed how to pay the 'stupid tax'

------
dmak
I did this once. I bought $100 worth of scratchers and won $500. It was a
great day!

------
tyang
Kind of like startup investing on speed without the extra zeroes.

------
justncase80
If by investment you mean "waste of money". Then sure.

~~~
justncase80
Or as the expression goes: Gambling is a tax for those who are bad at math.

------
tlarkworthy
Is it worth doing this on rollovers. The expectation is actually positive then

~~~
tunesmith
No... see above. Even if expectation is positive, it is still likely a bad
decision. Google Kelly Criterion - it tells you what percentage of your
bankroll you can risk on those kinds of bets. For most of us, it would work
out to a fraction of a penny.

------
geetee
And that's how probability works?

------
rhapsodyv
Invested?? "ok"...

~~~
chiph
Negative examples can sometimes be the best examples. :)

~~~
rhapsodyv
Sure. An example of a gamble that is a little better is "Capitalisation
Titles" (at least we have this in Brazil). You pay a fixed monthly fee and
participate in some type of raffle with good prizes. In the end of the period,
the bank gives all your money back with monetary correction.

In other words: a lottery that you at least have your money back.

