

Instead of charging $X, why not charge $2X with prob 1/2 and $0 with prob 1/2? - amichail

Given that people are often irrational (e.g., they buy lottery tickets), would you make more money this way?
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nostrademons
I think you're interpreting people's irrationality in the wrong way. People
are often irrationally risk _averse_ : most people would much rather pay $X
with probability 1 than $2X with probability 1/2 and $0 elsewhere. The reason
lottery tickets sell is because utility functions are nonlinear. After buying
a $1 lotto ticket, they're still poor; they don't miss the dollar. But if they
win, suddenly they are _rich_ , which is qualitatively different from being
poor. Thus, the calculation is a small but nonzero chance of being rich, vs.
the certainty of being poor. Most people don't do the math to figure out just
how small.

There's a reason why people indulge "If I won the lottery..." fantasies.

~~~
azbob
Actually, people play the lottery because they can't do math.

~~~
anigbrowl
I'm not so sure about that. In California (and in several other places I've
lived) the odds of winning are written out on the back of the ticket. Sure, a
lot of people believe in not-systems like studying past numbers or drawing
numbers from their dreams or casting spells; but deep down I think most people
understand 'odds of winning = 1 in 57 million'.

Lottery addicts certainly can't do math since they waste a lot of money on
tickets. But a good many other people just buy one a week or just
occasionally, eg when there's a particularly large jackpot on offer. This
isn't so irrational; a regular player will make a few bucks back over the year
on small prizes, and the risk/reward ratio improves for a big jackpot even
though the odds don't.

It's worth recalling that while the odds on any individual ticket are awful,
enough people are playing that people do win big prizes on a semi-regular
basis. For small-spend players who can afford it, and may think of it as semi-
charitable given the uses to which lottery profits are put, is it really any
more irrational than certain kinds of insurance?

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lunchbox
As omegazero pointed out, there might be a selection bias if you don't do it
right -- people will back out if they see they are in the unlucky group of
folks who will get charged $2X.

If you make people commit before revealing the amount, the issue is trust: how
do customers know that the odds are actually 1/2 that they'll pay $0? How do
they know you aren't just charging everyone $2X? You'd have to use some
verifiably random bit, which gets complicated. People will smell a scam.

(Speaking of which: are there any commonly used publicly verifiable random
numbers, like a die roll, but outside of any party's control? I presume there
must be a need for them in a number of situations.)

~~~
gmazzola
I'm sorry if this response is off-topic, but your last question piqued my
curiosity so I would like to answer it.

There is an authoritative source of random numbers. In 1955, The RAND
Corporation (a Cold War-era think tank) published a wonderful book entitled "A
Million Random Digits with 100,000 Normal Deviates". Amazon.com has a copy of
it, including some amusing reviews: [http://www.amazon.com/Million-Random-
Digits-Normal-Deviates/...](http://www.amazon.com/Million-Random-Digits-
Normal-Deviates/dp/0833030477) .

For a good source of truly random numbers accessible from an API, I personally
use <http://random.org> . They use atmospheric noise to create random numbers,
which ultimately boils down to the true randomness that is Quantum Mechanics.
It's not suitable for high-security applications -- I could do some network
trickery and redirect your API request to my server that always returns 1.0 --
but it's better than the PRNGs on modern computers.

~~~
lunchbox
Thanks for the informative reply, gmazzola. Could someone who doesn't trust
random.org verify that the numbers are indeed random and impossible to rig?
What I have in mind is a number that (1) nobody has influence over, (2) can be
measured objectively, (3) is observable to everybody, and (4) is impossible to
predict.

For example, I could tell my friend that I'll do his laundry for a month if
Barack Obama's speech tomorrow contains an even number of words, and he'll do
my laundry otherwise. This would appear to be truly random, but what if I
secretly am friends with Barack Obama and can rig it in advance?

Is there some easy, practical way of producing a number whose randomness a
large number of mutually distrustful parties can agree on? (I am thinking of
something like asking each party to produce a number, and then publicly
summing everyone's numbers together.)

~~~
gmazzola
Sadly, this is outside my area of expertise. I will nonetheless attempt to
answer your question, but please take my words with a grain of salt.

Before we even begin delving into true RNGs, it is worthwhile to consider if
we're over-engineering the problem. Is a PRNG "good enough" for the task at
hand? In most cases, it is. A well-seeded PRNG, such as the ones present in
modern-day Operating Systems, are suitable for most tasks not involving
National Security.

However, if you have a genuine need for a true RNG, a computer algorithm
certainly won't be generating it. Computers are by nature deterministic, and
thus are very poor at behaving unpredictably. Thus, like with all good
problems, we are forced to enter the realm of physics.

The fundamental problem is, who will be observing the source of randomness? To
my knowledge, there isn't a physical source of randomness that is observable
to everybody. (I did some quick googling to confirm my suspicions, but if
you're planning on using my words to do anything useful, _please_ confirm my
statement!). Thus, as I see it, you have several options:

1) Your idea, where all parties derive a true random number from physics and
publically sum everyone's numbers together. Your qualifiers (2) through (4)
hold, but (1) is difficult. In this case, a certain number of rogue nodes will
be able to manipulate the computation. I remember a Professor of mine, who
does research in this field, stating the minimum number of truthful nodes
needed in a distributed computation is (2/3)n + 1, but again confirm this
number for yourself.

My point here is, using the public-summing method, you are faced with the
difficult problem of determining if a node is attempting to manipulate the
system. While a provable solution has been found, after decades of research
across the globe, my Professor still is working on the problem, thus
demonstrating it is not an easy task.

2) Have a single computer (say, random.org) that is observing a true RNG, and
publicizes the result for all to see. Of course you'd use asymmetric crypto so
that all parties can prove that they've received the correct number.

Again, your qualifiers (2) through (4) pass, but (1) presents a different
problem. We're back to where we started: do you trust random.org?

However, it's an easier task to make an authority trustable than a peer in a
distributed computation. We trust Verisign to be a certificate authority,
because we believe their security practices are half-decent, and they can be
audited. (Every year all CA's are independently audited by WebTrust.org using
pretty strict criteria.)

The same could be done for random.org: why not require certification and
frequent auditing of their RNG equipment?

The other nice thing about RNGs is that you can audit them yourself, given
enough time and expertise. When viewed correctly, poor RNGs will have distinct
patterns visible to the eye (example:
<http://www.cs.hku.hk/cisc/projects/va/index.htm> ).

The crux of my argument is: I don't know of a true RNG, that upon observation
by multiple parties, all will receive the same random number. My instinct and
my research says that none exist, but I would love to be proven wrong. Crypto
experts, correct me!

If you'd like more information, Wikipedia is always invaluable:
[http://en.wikipedia.org/wiki/Hardware_random_number_generato...](http://en.wikipedia.org/wiki/Hardware_random_number_generator)

~~~
lunchbox
That is really a fantastic answer, Greg! Thanks for the valuable information.

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patio11
People will "irrationally" learn that your product is valueless (after all,
you give it away for free) and you will attract pathological customers (the
kind who would put up with this pricing model, which _screams_ scam).

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omegazero
To sell your good a consumer must be both willing and able to pay. Under this
system that would be the 2X price since he doesn't know which price he will
actually get (if he knew ahead of time, or could back out of the deal after
learning the price, you'd always be giving them away).

There's always going to be less people you can afford 2X than X.

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nopassrecover
A clever idea but I worry what happens to the people that miss out. They are
either aware they've paid $2X (if you tell them) or they are aware that
they've been "ripped off" (you are prepared to give it away for $0 so you must
have at least 50% markup. Kind of like jewellery stores putting half price
sales on $10-20k diamond rings). Either way you are associating negative
feelings immediately and a sense of buyer's regret.

On a practical note, what stops them getting a refund and repurchasing until
they get it for free.

~~~
mechanical_fish
_On a practical note, what stops them getting a refund and repurchasing until
they get it for free._

Your other observation is good, too, but I think this sentence gets to the
heart of the problem. The double-or-nothing transaction is _irreversible_ ,
which is what makes it a bad one.

People like commercial transactions that can be reversed. Ideally, both
parties should walk away feeling like they got a fine deal, but that if the
deal goes sour at any point in the near future (because a part was broken;
because the customer had second thoughts) they would be both be willing to
"undo" it without much harm done.

~~~
harshavr
maybe you can make it reversible by refunding it on the same terms, i.e the
buyer has the right to return the good to the seller, and the seller pays 2X
or 0 with prob 1/2 to the buyer.

~~~
nopassrecover
Maybe, but a) there may be statutory rights issue, b) this just seems likely
to annoy people and c) you might run the risk of actually having to comply
with gambling laws if you take money from people and offer them a chance of
doubling it.

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byrneseyeview
No. A lottery ticket is a way to buy a fantasy: if you're a housekeeper who
doesn't speak much English and already has two kids, you know you'll never be
rich -- but for $1, you can spend a couple hours thinking it's a possibility.

To take advantage of this, you might charge 1.1X with a 10% chance of getting
10X worth of similar goods. But that wouldn't be too exciting, either.

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dxjones
I like the lottery ticket analogy some people have made, but here is my twist.

My service costs $X per month. So if you like it, you'll want to pay $X. ...
But for a just this month, there is a 1/10 chance your $X will get you the
service for the entire year!! ... and if you don't "win", you still get what
you paid for.

I think this might encourage people who are on the edge to sign up now, and
still feel good no matter what the outcome, plus they might tell their friends
about it.

\-- David Jones

~~~
sachinag
Just a note: we don't sign our posts/comments here. Your username does that
for you.

<http://news.ycombinator.com/item?id=198817>

~~~
rokhayakebe
This may just be me having a bad day, but I do sense a little arrogance in
your response. It does not hurt anyone if you add your name at the end of a
comment.

~~~
chuffwaffle
It hurts everyone. It uses up screen space and reading time and has absolutely
zero value.

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modoc
No. Buying a product/paying for a service isn't the same as gambling, and
without a potential high payoff (3 million dollars or whatever) you aren't
triggering the same neurochemicals.

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chaosmachine
A more common variation of this idea is "Win your purchase free!", with the
odds of winning being fairly low, but the price remaining the same.

Car dealerships seem to like this one, and Visa ran a similar contest here in
Canada recently (called "Win What You Buy").

The success of this kind of promotion is most likely proportional to the price
of your product.

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hugs
Sounds like the Neo-Futurists' pricing scheme: """Tickets are $9 + the roll of
a single six-sided die ($10 - $15, depending on your luck!)"""
[http://www.neofuturists.org/index.php?option=com_content&...](http://www.neofuturists.org/index.php?option=com_content&task=view&id=20&Itemid=45)

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known
<http://en.wikipedia.org/wiki/Global_Gillette> does it, right?

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schmoo
From experience in running various marketing campaigns, the magic 'number' is
1 in 10. Charging $X with the option of paying $1.1X (or just over, even) for
a 0.1 probability of getting the money straight back will get the most people
buying into the scheme. That'll be around 1 in 10 people too. Force the extra
payment and around half of them will walk away there and then(1). Bump the
price up to $1.1X without mentioning it, only that there's a 1 in 10 chance of
getting it free and you'll see the overall take-up go up anywhere from 25% to
100%.

Long story short: _Make your new price $1.1X without fanfare, offer a 1 in 10
chance of getting it for free and you all win. They get their chance at a
freebie at a cost they don't notice, you get your promotion vibe bumping up
sales_.

(1)I know that that's obvious, and it was dumb to run it - but we ran it
anyway for the sake of completeness.

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Rod
The expected value is the same:

(0.5 * 2X) + (0.5 * 0) = X = (X * 1.0)

but perhaps you would be able to attract more customers. I doubt it. While
it's certainly true that everybody loves a freebie, no one likes to pay twice
for something.

Why not charge X with probability (1-p) and charge zero with probability p?
The expected value would be reduced to (1-p) but perhaps you would attract
people looking for freebies. More customers is always a good thing, right?

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ajkirwin
There is a way that you can do this. You charge $X and simply state that every
Yth customer gets it free.

Problem solved.

