
The Logic of Loss - soundsop
http://www.aaronsw.com/weblog/logicofloss
======
mattmaroon
He's misunderstanding. For it to "make sense" for you to pay $9,000 for a 1%
shot of winning a million, you don't need to have to be able to make that same
wager many times. You have to look at the long term.

Life will present you with many different wagers with positive expectation,
but it often won't present you with the same one multiple times. Maybe it will
give you that shot, then the next time give you a +EV chance to invest in the
startup, then later give you the opportunity to play the St Petersburg game
for $2, etc. Keep taking the +EV wagers over your lifetime and you'll end up
way ahead, even if you never take the same exact one twice.

You don't need a good sample size for an individual wager to be a good idea,
just for all wagers combined. All of that assumes, of course, that taking any
one wager doesn't prevent you from many others. Taking the $9k wager if you
have $9k to your name will. Taking it if you have $10m to your name won't and
therefore is a no-brainer.

*Edited to account for Kelly Criterion. Thanks Aston

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diego
It's not a no-brainer. Does "winning one million" means that you have to do
absolutely no work, spend no time at all and the money is tax-free? The answer
most likely will be no. Taxes alone make the expected value negative.

The more important problem is that many times it's hard to determine whether a
"wager" has a positive or negative expectation, compounded by the fact that
the positive value has to be utility to you rather than just money.

~~~
philwelch
I think you're missing the point of the exercise. It's like you're assigned a
physics problem about point masses on frictionless surfaces and you answer the
question by saying it's irrelevant in the real world because masses are
distributed over volumes and surfaces are never frictionless.

Yes, of course you have to factor in taxes and time and so on and so forth.
But that's not what the question was about in the first place. You never see
idealized physics problems in the real world either but what you learn from
naive, simplified applications of classical physics still gets you somewhere
in real world problems. Same with EV calculations.

The point is that EV is an incomplete measure of value when it comes to
evaluating gambles, not that you have to pay taxes. EV doesn't work on one-off
situations, like if you're on a game show with Howie Mandel.

~~~
diego
No, I understand that point perfectly. My point was that in order for you to
be able to evaluate whether a gamble makes sense _repeatedly_ , you have to be
sure that each instance has a positive EV.

Say that you planned to do the 9k with %1 chance of a million payout enough
times to take advantage of probabilities. You could have found out much later
that the gamble had a negative EV. This is my point: the parent made it sound
like you can evaluate all decisions as if the EV was easy to establish. In
reality that's a rare case.

~~~
philwelch
In reality, there are no point masses or frictionless surfaces, either. Maybe
you perfectly understand the point and you're moving on to various niggling
contingencies. That's fine. The article is trying to explain something more
basic than what you're talking about. You're doing the equivalent of butting
into a freshman physics lecture and pointing out everything they've
oversimplified, which is just plain obnoxious.

~~~
diego
I'm not commenting on the article. I agree with the article, which in fact
talks only about wagers with quantifiable EV. My comment was a reply to
mattmaroon's observation that over the course of a lifetime someone can find
enough wagers with a positive value to eventually come out ahead. Please read
the entire thread.

<http://news.ycombinator.com/item?id=560109>

~~~
philwelch
I have read the entire thread and I just don't understand the point of your
comment. Of course people have to pay taxes and spend time on investments.
That doesn't make diversified investing a fool's errand. It's like we're
trying to build a go-kart and you're saying "it'll never work because there's
friction." Maybe there's friction, and we'll work out what that friction is,
just as we'll calculate the post-tax EV of our investments.

~~~
diego
To summarize: life usually doesn't offer a succession of quantified wagers
like one would ideally like. Nothing to do with friction, you just don't know
the expected value of anything other than lotteries or other chance games
where a trustworthy entity backs them up. You simply can't assume that you
will always be able to pick "real life" wagers with positive expected values.
The closest you can get are "traditional investments" for which you can look
at past returns and hope for the future to repeat the past. For new
situations, there simply isn't enough data.

If you decide to start a startup today, what's your expected value? Do you
have access to data about all startups ever started, costs involved and
payouts? How does that change if you segment it by startup type, decade, etc?
Can you say for sure that starting it has a positive expected value in terms
of utility to you as opposed to the probabilistic certainty of the expected
value of the 9k wager?

~~~
philwelch
Thanks for the clarification.

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briancooley
There's a concept for this called utility. It has nothing to do with how many
times you get to play, but rather with how much use you have for the money.

If the $10000 means little to you, you might even take a negative expected
value for a chance at a big score (people do this every day with $1 lottery
tickets), regardless of how many times you get to play.

Edit: The reason that repeating the game has some allure is that you are
changing the game from a low probability of winning a large payout to a higher
probability of winning a distribution of payouts computable via the binomial
expansion. It also changes the utility equation.

~~~
aaronsw
If "repeating the game ... changes the utility equation" from negative to
positive, how can you possibly say "it has nothing to do with how many times
you get to play"?

~~~
philh
It's be a mistake to say it has nothing to do with that, but the number of
times you get to play is subsumed into the utility equation. It would be
irrelevant if utility was linear.

The point is that $10,000 to me is worth more than 1% of the value to me of
$1,000,000. Whereas I would probably pay $1.10 for a 1% chance of winning
$100, though not on a regular basis.

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harpastum
I was a little confused when I read the section on the St. Petersburg Lottery,
so I looked around to see what it was all about.

In order to find the expected value, you simply multiply the probability of
the event by its expected payout. Then to find the total expected value, you
sum all of the possible outcomes. So the probability of the first flip being
tails (1/2) times the payout ($1), gives the expected value of that flip
($0.50). The rest of the flips follow in a similar way: 2nd (1/4)x($2)=0.50,
3rd (1/8)x($2)=0.50, 4th (1/16)x($4)=0.50, etc.

If you take the sum of these values to an infinite number of flips
(.50+.50+.50+...), you end up with an expected value of infinity. On the other
hand, even if the bank is ridiculously wealthy [1] (i.e. US GDP), the expected
payout is ridiculously small. That, to me, is the crux of the fallacy. It
reminds me of the legend of the creator of chess who asked for one grain of
rice for the first square of the chessboard, two for the second, four for the
third, etc. which becomes greater than the world production of rice after a
few dozen squares.

[1][http://en.wikipedia.org/wiki/St._Petersburg_paradox#Finite_S...](http://en.wikipedia.org/wiki/St._Petersburg_paradox#Finite_St._Petersburg_lotteries)

~~~
johnrob
This is a paradox only because we are allowing infinite winnings. That's not
possible in the real world. The solution is to end the game when the 'casino'
can no longer pay the amount on the table.

In this case, the expected value is simply .50 * log 2 C, where C is the total
cash available.

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zedwill
From my limited experince (you HN regulars correct me if I am wrong) VC does
not behave like the article say.

It is true that the VC diversifies on different inversions, not to put all the
eggs in the same basket and to invest on different markets/ideas

But VCs do not invest on a lot of startups. The companies I know have a very
limited portfolio (sometimes less than ten). They do not have big inversions,
I suppose because they can not handle the risk or the workload

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wallflower
This is one of the purported three questions that Larry Summers was asked in
his D.E. Shaw interview:

<http://news.ycombinator.com/item?id=549998>

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gojomo
If someone -- or more interestingly, some speculative project -- offers you a
1% chance at $1 million, for only $9,000, as many times as you want to take
it, then the issue becomes one of finance.

If your society has strong contracts, the corporate abstraction, norms of
honesty and disclosure, and a pool of wealthy investors (or operational
investment groups) which can weather a few bad runs, you'll likely raise the
money, and everyone wins.

If your society fails in one or more of those dimensions, it may be impossible
to raise the money. Too little respect for contracts/corporations (such as via
ex post facto wealth redistribution), too much dishonesty/secrecy, or too few
wealthy people/groups could make the costs of assembling the investment exceed
the returns. Thus the valuable project is never undertaken, and society is
poorer.

