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    People are still suggesting that the lottery is not a waste of hope, but a service which enables purchase of fantasy—"daydreaming about becoming a millionaire for much less money than daydreaming about hollywood stars in movies".  One commenter wrote:  "There is a big difference between zero chance of becoming wealthy, and epsilon. Buying a ticket allows your dream of riches to bridge that gap."

    Actually, one of the points I was trying to make is that between zero chance of becoming wealthy, and epsilon chance, there is an order-of-epsilon difference.  If you doubt this, let epsilon equal one over googolplex.

    Anyway:  If we pretend that the lottery sells epsilon hope, this suggests a design for a New Improved Lottery.  The New Improved Lottery pays out every five years on average, at a random time—determined, say, by the decay of a not-very-radioactive element.  You buy in once, for a single dollar, and get not just a few days of epsilon chance of becoming rich, but a few years of epsilon.  Not only that, your wealth could strike at any time!  At any minute, the phone could ring to inform you that you, yes, you are a millionaire!

    Think of how much better this would be than an ordinary lottery drawing, which only takes place at defined times, a few times per week.  Let's say the boss comes in and demands you rework a proposal, or restock inventory, or something similarly annoying.  Instead of getting to work, you could turn to the phone and stare, hoping for that call—because there would be epsilon chance that, at that exact moment, you yes you would be awarded the Grand Prize!  And even if it doesn't happen this minute, why, there's no need to be disappointed—it might happen the next minute!

    Think of how many more fantasies this New Improved Lottery would enable.  You could shop at the store, adding expensive items to your shopping cart—if your cellphone doesn't ring with news of a lottery win, you could always put the items back, right?

    Maybe the New Improved Lottery could even show a constantly fluctuating probability distribution over the likelihood of a win occurring, and the likelihood of particular numbers being selected, with the overall expectation working out to the aforesaid Poisson distribution.  Think of how much fun that would be!  Oh, goodness, right this minute the chance of a win occurring is nearly ten times higher than usual!  And look, the number 42 that I selected for the Mega Ball has nearly twice the usual chance of winning!  You could feed it to a display on people's cellphones, so they could just flip open the cellphone and see their chances of winning.  Think of how exciting that would be!  Much more exciting than trying to balance your checkbook!  Much more exciting than doing your homework!  This new dream would be so much tastier that it would compete with, not only hopes of going to technical school, but even hopes of getting home from work early.  People could just stay glued to the screen all day long, why, they wouldn't need to dream about anything else!

    Yep, offering people tempting daydreams that will not actually happen sure is a valuable service, all right.  People are willing to pay, it must be valuable.  The alternative is that consumers are making mistakes, and we all know that can't happen.

    And yet current governments, with their vile monopoly on lotteries, don't offer this simple and obvious service.  Why?  Because they want to overcharge people.  They want them to spend money every week.  They want them to spend a hundred dollars for the thrill of believing their chance of winning is a hundred times as large, instead of being able to stare at a cellphone screen waiting for the likelihood to spike.  So if you believe that the lottery is a service, it is clearly an enormously overpriced service—charged to the poorest members of society—and it is your solemn duty as a citizen to demand the New Improved Lottery instead.

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    43 comments, sorted by Click to highlight new comments since: Today at 10:45 PM

    You jest, but somewhere, someone is reading this blog post and putting your ideas into action ...

    That person is me. Check out I'd like to think it is more than just randomness this system you knowledge and group wisdom leads to who wins the lotteries.

    Surely one could easily replicate this "lottery" by buying path-dependent options with low exercise probability on the financial markets. People are not doing this, so this service must be less appealing than it intuitively seems.

    You can't buy such an option from a vending machine in a grocery store; if you could, perhaps it would be as popular as lottery tickets.

    zzz, I think you underestimate how people perceive gambles. Investing in financial markets isn't perceived as a bet, since we like to believe that if you only knew enough, you could make the right choices (whether you actually can or not is another matter). With lotteries and other forms of gambling, it doesn't matter how much you know, you can't anticipate the outcome any better than if you had no additional information. That, I think, is part of why gambling is much more popular than investment: even the least skilled person has the same chance of winning as the most.

    Gordon, I recommend the Satiricon of Petronius for some fantastic confirmation of your model of gambling applied to life success in general. It's fairly difficult for Americans, raised on meritocracy, and perhaps before than on the assumption of wise and just gods, to relate to the strong desire, expressed by many characters, for an unjust and capricious world. I suppose that if people imagine "lucky", "blessed", or "well fated" to be personal traits they can then easily believe that they are above average on those traits. The last, in particular, is not easily disconfirmed.

    Surely one could easily replicate this "lottery" by buying path-dependent options with low exercise probability on the financial markets. People are not doing this, so this service must be less appealing than it intuitively seems.

    I wonder what the odds actually are on "striking it rich" in a short period of time by treating financial markets as a gambling game. Is it better or worse than, say, the roulette wheel in a casino? If you bet $30,000 on a single number in a roulette wheel, you have a one in 38 chance of getting a 35x payout of $1,050,000. Can the financial markets give you a better than 1 in 38 chance of turning $30,000 into over $1,000,000 within a year before you lose your initial stake?

    Can the financial markets give you a better than 1 in 38 chance of turning $30,000 into over $1,000,000 within a year before you lose your initial stake?

    If you assume that option prices are well-calibrated, you could just buy $30,000 of any kind of option that would pay off $1,050,000 if it ended up in-the-money. Not sure that's a fair assumption though.

    Someone has to be selling such options, and I'm not aware of anyone who is.

    Eliezer, did you mean to evoke stock markets with "You could feed it to a display on people's cellphones"?

    Surely financial markets are well-calibrated for events that happen once a month. Then an option that such an event will happen tomorrow is should be about right. Some claim that there is systematic bias in options against rare events, that on a long shot you do better than even.

    Eliezer, did you mean to evoke stock markets with "You could feed it to a display on people's cellphones"?

    Perhaps so, but stock market investors are not trying to "strike it rich" for a single dollar, or even to earn a 3500% return. They have a large stake in the game, and their greatest worry is that a market crash may wipe out their investment.

    This idea is intriguing, but I don't know if it would be as popular as the other lottery. It can be hard to maintain excitement about something for a long period of time (with the regular lotto you can recharge between when you find out you've lost and when you buy your next ticket). You also couldn't gather around the T.V with your family/friends and their tickets, because you'd have to spend an undefined amount of time waiting.

    Some economist once stated something like, the stock market is like a casino with odds against the "house". It means the expected gain is not zero, but positive.

    If the market grows at g, with a little financial engineering, it should be possible to create a portfolio with expected gain somewhere between zero and g, with a very very long tail, i.e., a non-zero chance of huge payoffs.

    I think that's just called a "portfolio". I mean, isn't that basically what investors do?

    Such a lottery can be had. If there is an epsilon chance that a given lottery ticket is a winner, there is also an epsilon prime chance that a winning ticket will be lost and that you will find it, for zero dollars expenditure on your part. Thus, there is an epsilon multiplied by epsilon prime chance that you will be a lottery winner without actually buying into the lottery. If you get your hopes up for this scenario, are you a free-loader?

    _Gi: you have described exactly my lottery strategy, as well as that of Patti Smith:

    Every night before I go to sleep I find a ticket, win a lottery Scoop them pearls up from the sea Cash them in and buy you all the things you need...

    Or we could just start a lottery where: a) You deposit money into a bank account b) You let it gather interest for 90 days. c) Use the interest to pay for handling fees d) Distribute 100% of the money back to the people who deposited it.

    That is the service the public thinks we're selling: a uniform income distribution generator thingy.

    It exists in the UK, it's called "Premium Bonds"...

    For those who labor under the delusion that a 'premium bond' means the usual things about pars and coupons, it turns out that in the UK, a Premium Bond is something much more interesting:

    A Premium Bond is a lottery bond issued by the United Kingdom government's National Savings and Investments agency. The bonds are entered in a regular prize draw...There are many different prizes ranging from £25 to the top prize of £1,000,000 (between 2005 and 2009, there were two £1m prizes each month and the minimum prize was £50, but prizes were reduced after the large 2009 drop in interest rates). Investors can purchase bonds at any time; bonds need to be held for a full calendar month after the month in which they are bought, e.g. purchase in January, eligible for March. Numbers are entered each month, with an equal chance of winning any prize, until the bond is cashed in....From 1 January 2009 the odds of winning a prize for each bond number held was 36,000 to 1. In October 2009, the odds returned to 24,000 to 1 with the prize fund interest rate increase.[3] Around 23 million people own Premium Bonds,[citation needed] over one third of the UK population.

    However, I don';t think most premium bond holders (I am one, to a very modest extent) live their lives in a state of blissful anticipation.

    Probably not, yeah, but what that means is unclear. A refutation of the claim for regular lotteries that they're a good source of hope? Eliezer's justifications for a lottery 2.0 almost exactly like Premium Bonds? Some sort of adaptation? A flaw in Premium Bonds which would be fixed if they moved to a faster setup like draws every hour?

    I thought the empirical datum might be of interest. One can draw ones own conclusions from data.

    You know what? The government should do this. It would be a definite improvement for people who are going to buy tickets anyway, because at least they could afford a better education, and have more free time, which means that they might eventually learn not to buy lottery tickets.


    This theme is illuminated in the short novel Bear v. Shark.

    This isn't entirely relevant, but it's a good story, so... I recently heard from one of my mom's friends that my fifth grade teacher won the lottery, and continued teaching afterward. This makes me very happy, because he's a fantastic teacher (he has a reputation, actually, for making his classes really fun, like using remote-control cars for an Oregon Trail activity), and, as has been mentioned on this site, a lot of people don't end up being very happy once they've one the lottery. I'm glad Mr. Lesh was smart enough to keep teaching his class, which he obviously loved doing.

    The New Improved Lottery pays out every five years on average, at a random time—determined, say, by the decay of a not-very-radioactive element. You buy in once, for a single dollar, and get not just a few days of epsilon chance of becoming rich, but a few years of epsilon. Not only that, your wealth could strike at any time! At any minute, the phone could ring to inform you that you, yes, you are a millionaire!

    Given the huge fluctuations in value, it strikes me that buying up on Bitcoin is pretty much exactly this, and also part of the reason why I enjoy owning them.

    Those lotteries appear to be instant, which is different from what Eliezer was suggesting. In Eliezer's lottery, you pay in once, and the massive payoff could come any day now.

    I think there already is a New Improved Lottery that is played by many -- it's called drug addiction. Heroin addicts spend repeated minutes for their repeated fantasies. And their behavior at work or shopping is actually not that different from what you describe.

    However, for us non drug-addled folks, there is a problem with sustained repeatable fantasy -- it doesn't exist. Buying one lottery ticket gets me one minute of fantasy, but buying 9 more tickets does not get me nine more minutes of fantasy, even if they are from different drawings. Lots of people dream about winning the lottery -- how many people dream about winning the lottery twice?

    Or you could just fantasize about finding a billion dollars on the ground. After all, it could happen, so there's an epsilon chance of it happening without doing anything.

    I think there's a flaw in this reasoning. You're assuming that the harm from lotteries increases monotonically with the time spend dreaming about winning. The form of your argument is: "a huge amount of dreaming is harmful (because it stops you improving your life in more effective ways), therefore a small amount is harmful (i.e. worse than none)".

    Non sequitur. A tablespoon of salt in your soup makes it taste terrible, therefore a pinch of salt makes it taste worse than no salt?

    It may well be that spending $1 per week to buy 10 minutes of false but pleasant hope is the best use of that 10 minutes and $1, or at least, no worse than any other use you're likely to make of it. E.g. if you're taking that time and money out of your leisure budget, then you may well use it instead on smoking, or beer, or fries.

    And if you instead allocate it to thinking about how to get a promotion, sure you could do that, but why not do both? (I.e. spend a different 10 minutes on your promotion.) So this is a false dilemma. People who play the lottery may exaggerate the probability of winning, but I doubt they make plans - and it's not clear they displace other attempts at self-improvement - on the assumption they'll win.

    This random gratitude dynamic is exactly what social media platforms use to make their apps addicting. I remember having a conversation about it with a friend and she said something along the lines of, "Man, if Instagram gave me all my notifications at noon, the rest of the day I'd look really stupid. But because there's always a random chance of getting notifications, I check my phone all the time." The lottery system is obviously a bit different because you get a call rather saying you won, rather than you have to call them, to see if you've won. Nevertheless, even if there is a more positive feedback loop it's still as addictive, if not more...

    Surely, since the human condition is to wish for gratification as soon as possible, noone would buy into this system, in preference to the lotteries where you buy in and get same-day gratification, despite the risk being higher (similarly to how people bet on green in roulette, or take 15-1 odds in betting shops).

    This essay had a very good insight for things to come: Bitcoin and other cryptocurrencies fit the above description.

    They actually don't. Glossing over all the details, anyone who bought bitcoin 13 years ago (and just left it alone) received far better return than anyone buying into the proposed lottery would have. Results matter.

    There would be some handsome winners, as in the case of Bitcoin early adopters, also for this lottery. You mean average returns? In any case, expected average future returns should be zero for both.

    It is similar enough, that no matter what fancy justification or narrative is painted over, most cryptocurrency investors own crypto because they believe it will make them rich. Possibly very fast. And that possibility can strike at any time.

    Bitcoin might be a desperate get-rich-quick scheme. However, the odds are not as small as Eliezer's lottery. Also, some people use it to purchase illegal goods and services, so there's that. There are similarities, but there are also important differences. Also, there is an upper limit to how much you can lose with the lottery - not so with crypto.

    In short, crypto currencies are similar to Eliezer's lottery only to the extent that all day trading is gambling. Which is true often enough, but not always.

    I mean, to be completely fair, you can't exactly phrase distracting you from your work as a good thing. Perhaps a less distracting lottery would be better?

    "People are willing to pay; it must be valuable. The alternative is that consumers are making mistakes, and we all know that can’t happen."

    It can actually be both.  Value is subjective, and the idea that consumers can't make mistakes is a gross oversimplification of the way the market selects against mistakes on average, in the long-run.

    People are willing to pay for lottery tickets because the possibility of winning a pile of cash for a small investment makes them happier.  Whether or not that's a mistake depends on if there is some other opportunity they could spend their money on that would make them more happy than the lottery ticket.  To you and I it would seem obvious that there should be.  But both value and happiness are entirely subjective and gambling for entertainment isn't objectively worse than watching movies or playing computer games or commenting on rationality blogs.

    There have been long-term (multiple years of selling tickets between drawings) lotteries in the past.  I don't know of any with randomized drawing times though, so that could be a fun innovation.  Pity there's a government monopoly on lotteries so nobody's allowed to try it...  Waiting for a particular block hash value on the Bitcoin chain or something publicly visible would be a good way to determine drawing time these days actually...  Would be pretty easy to set up with a little math.