7 ms·

The Logic of Loss

31 points by soundsop 18y ago

briancooley 18y ago
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.
- DaniFong 18y ago
  While one can fold this type of difficulty into expected utility theory, this is not (apparently) true of all situations. People still overweight loss, overweight certainty, and overweight extremely low probabilities. The classic paper by Daniel Kahneman and Amos Tversky presents a pretty thorough critique of expected utility theory as a model for decision making, as an empirical question. c.f. www.hss.caltech.edu/~camerer/Ec101/ProspectTheory.pdf
- aaronsw 18y ago
  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 18y ago
    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.
  - briancooley 18y ago
    "negative to positive" - those are your words. If utility dictates that I should not risk $10,000 on a 99% chance of losing it all, it is unlikely that I have the bankroll to play the game as many times as would be required to overcome my risk of losing everything. And by playing multiple times, I have introduced a scenario with significant probability of losing much more than $10,000, which is obviously catastrophic if losing $10,000 means so much to me. The utility is certainly different, but I wouldn't necessarily claim it is better. It could in fact be worse, but I haven't studied it enough to assert either.
- amalcon 18y ago
  Exactly. It's important to remember that, while in theory you might win a particular game on average, that game does not exist in a vacuum. Suppose you're playing a game wherein the gambling is only a component, and you also have some other use for the currency (say, it's the metric that causes you to win). The player in the lead should typically not bet all his money on any gamble, no matter how good the expected payoff. edit: Of course, there are exceptions to that last rule of thumb. It's just a common case.
- CWuestefeld 18y ago
  Exactly. This is the economic principle of "marginal utility" -- see http://en.wikipedia.org/wiki/Marginal_utility http://en.wikipedia.org/wiki/Marginal_utility The principle is that I'm willing to buy a lottery ticket, even though the odds are slanted (the agency takes a large cut) because the $1 the ticket costs me is meaningless to my life, but the $1 million I might win would fundamentally change my life. The is why people buy insurance: the $1000 I spend every year on homeowner's insurance hurts only slightly, but the amount that I'd lose to a fire would destroy me financially. It's also the rationale for burglary: the thief is very likely to make a large sum of money, while he only has a small chance of a devastating loss (i.e., going to jail). The question is all wrapped up in the relative size and likelihood of the events, where the size is judged relative to the difference that it makes to you.
harpastum 18y ago
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_St._Petersburg_lotteries http://en.wikipedia.org/wiki/St._Petersburg_paradox#Finite_S...
- deleted 18y ago
  [deleted]
- johnrob 18y ago
  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.
mattmaroon 18y ago
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
- mhb 18y ago
  Along these same lines, it's very surprising how many people who could easily afford a new car have collision insurance.
- diego 18y ago
  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.
  - mattmaroon 18y ago
    Taxes alone don't necessarily make it EV negative. For me it wouldn't be since I already have substantial gambling income to deduct from. (Unless you're a professional gambler, you can't deduct more than you earn.) But you're right, for most people that one particular wager would, assuming they were going to get a 1099 if they won. (Most money made from gambling goes unclaimed, as it doesn't take place in a casino.) Startup investing is somewhat the opposite I suppose, where taxes actually makes it more profitable. If you lose, you can deduct the loss, if you win, you usually pay the much lower capital gains taxes. (Unless I'm misunderstanding the tax ramifications of a losing angel investment, which I may certainly be.)
gojomo 18y ago
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.
zedwill 18y ago
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
wallflower 18y ago
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 http://news.ycombinator.com/item?id=549998

31 points by soundsop 18y ago

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.

DaniFong 18y ago
While one can fold this type of difficulty into expected utility theory, this is not (apparently) true of all situations. People still overweight loss, overweight certainty, and overweight extremely low probabilities. The classic paper by Daniel Kahneman and Amos Tversky presents a pretty thorough critique of expected utility theory as a model for decision making, as an empirical question. c.f. www.hss.caltech.edu/~camerer/Ec101/ProspectTheory.pdf
aaronsw 18y ago
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 18y ago
  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.
- briancooley 18y ago
  "negative to positive" - those are your words. If utility dictates that I should not risk $10,000 on a 99% chance of losing it all, it is unlikely that I have the bankroll to play the game as many times as would be required to overcome my risk of losing everything. And by playing multiple times, I have introduced a scenario with significant probability of losing much more than $10,000, which is obviously catastrophic if losing $10,000 means so much to me. The utility is certainly different, but I wouldn't necessarily claim it is better. It could in fact be worse, but I haven't studied it enough to assert either.
amalcon 18y ago
Exactly. It's important to remember that, while in theory you might win a particular game on average, that game does not exist in a vacuum. Suppose you're playing a game wherein the gambling is only a component, and you also have some other use for the currency (say, it's the metric that causes you to win). The player in the lead should typically not bet all his money on any gamble, no matter how good the expected payoff. edit: Of course, there are exceptions to that last rule of thumb. It's just a common case.
CWuestefeld 18y ago
Exactly. This is the economic principle of "marginal utility" -- see http://en.wikipedia.org/wiki/Marginal_utility http://en.wikipedia.org/wiki/Marginal_utility The principle is that I'm willing to buy a lottery ticket, even though the odds are slanted (the agency takes a large cut) because the $1 the ticket costs me is meaningless to my life, but the $1 million I might win would fundamentally change my life. The is why people buy insurance: the $1000 I spend every year on homeowner's insurance hurts only slightly, but the amount that I'd lose to a fire would destroy me financially. It's also the rationale for burglary: the thief is very likely to make a large sum of money, while he only has a small chance of a devastating loss (i.e., going to jail). The question is all wrapped up in the relative size and likelihood of the events, where the size is judged relative to the difference that it makes to you.

harpastum 18y ago

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_St._Petersburg_lotteries http://en.wikipedia.org/wiki/St._Petersburg_paradox#Finite_S...

deleted 18y ago
[deleted]
johnrob 18y ago
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.

mattmaroon 18y ago

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

mhb 18y ago
Along these same lines, it's very surprising how many people who could easily afford a new car have collision insurance.
diego 18y ago
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.
- mattmaroon 18y ago
  Taxes alone don't necessarily make it EV negative. For me it wouldn't be since I already have substantial gambling income to deduct from. (Unless you're a professional gambler, you can't deduct more than you earn.) But you're right, for most people that one particular wager would, assuming they were going to get a 1099 if they won. (Most money made from gambling goes unclaimed, as it doesn't take place in a casino.) Startup investing is somewhat the opposite I suppose, where taxes actually makes it more profitable. If you lose, you can deduct the loss, if you win, you usually pay the much lower capital gains taxes. (Unless I'm misunderstanding the tax ramifications of a losing angel investment, which I may certainly be.)

gojomo 18y ago

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.

zedwill 18y ago

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

wallflower 18y ago

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