Some choice quotes from his Google+ post: "The lottery is not a tax on people who are bad at math. It's trading a little bit of expected-value for a lot of variance."
"There are many other cases in real life where mean/variance tradeoffs arise, and there are perfectly plausible objective functions under which it makes sense to follow a policy that doesn't maximize expected value.
The obvious example is insurance, where you pay a small bit of money each year to reduce the chance that you end up suddenly needing to pay a lot of money. Same with forming or joining a startup; on average you'll make less money than if you take a "normal" job, but there's some small chance that you'll have just joined the next Apple or Google and you'll end up rich.... "
One common assumption is that utility is logarithmic in money, i.e. that you become "one unit happier" not by adding $100K but by doubling your income. This matches actual human behavior fairly well, and implies that you should buy insurance (losing everything is really bad) but not lottery tickets (winning $BIGNUM makes you less happy than you'd think).
Actually, according to this article, certain kinds of insurance are less effective at optimizing happiness, because we are psychologically equipped to adapt to new (bad) circumstances:
Obviously, certain kinds of disaster pose a greater threat to happiness than others. For example, health insurance may be a worthwhile investment for some, while property insurance may not.
People in Colin's circles are probably not the desperate, poor, uneducated lottery players that opponents of the lottery are concerned about. Colin's right not to judge his friends who choose to entertain themselves with the lottery fantasy every so often. They can afford it.
Yeah, when you think about it the lottery and insurance are surprisingly similar ideas, though a bit in reverse. Getting in an accident and winning the lottery are both unlikely. By buying insurance you remove the small chance of a large loss. By playing the lottery you create the small chance of a large win. Both reduce your expected value, and doing both even more so. If you buy both, your variance is still high but in the positive direction.
>Yeah, when you think about it the lottery and insurance are surprisingly similar ideas, though a bit in reverse. Getting in an accident and winning the lottery are both unlikely.
Getting into an accident is far more likely. And everyone has health issues sooner or later, so the probability of that is 1.
The probability of being hit by lightning is massively diluted by the fact that most people don't live places where lightning is a serious threat. I've heard it's actually a serious risk some places.
> on average you'll make less money [in a startup] than if you take a "normal" job
I disagree. If he's using "average" in the sense of "mean" (not median), then he's saying that starting a startup has a lower expected return and is higher risk than working a normal job, meaning it's inferior in both regards (assuming diminishing marginal utility). Entrepreneurship is a classic "high risk, high return" venture. It has a higher expected return than a conventional job; that's what makes it financially attractive to founders and VCs in the first place. The astronomical success of the minority offsets the lack of success of the majority.
In a similar vein I disagree with his assertion that joining a startup (taking a risk) is like buying insurance (avoiding a risk). They are opposites.
Do you have any proof that, on average, startup founders make more money than people employed in regular jobs, once you take into account all of the ones that make no money and then collapse?
The mean YC startup about a year ago [1] $22.4 million, let us assume 3 founds on average and 3 years of work, and that they hold 1/3 of the value, and you get an average return well north of 500k a year per founder.
And most of that money doesn't actually go to the founders - YC owns a chunk of them, and so do other investors (as PG says, 94% of them get funding from elsewhere too).
That's a good question. Would be interesting to see if someone can dig up any studies on this. e.g what % of the country's wealth is owned by founders (and their heirs), divided by the % of people who are current or former founders.
My argument is founded not on experimental data but rather on the axioms of utility theory. If startups had higher risk AND lower expected payoff, it would make no financial sense to found or invest in one, since that would be a textbook example of a bad investment:
There is a massive difference between founding a startup and investing in startups.
Professional investors (VCs, Angels, Incubators) choose the best startups (most efficient choices) and do not fund the rest which eliminates a huge number of founders who simply fail and get zero return for their work. On top of that, there are a number of VCs and angels who are completely unsuccessful picking startups and end up out of the business unable to raise additional institutional money or who lose their additional investment capital.
The expected return of investing in startups is very likely negative if you add all the smart and non-smart investors together. (I don't have data, and can't even imagine where to get it, so I'm saying "likely".)
Using the security market line to prove your point isn’t really fair since not much research has been done on applying it to startups. One of the major issues with applying the SML is the fact that it is very hard to calculate beta of startup investments since they have very long term time horizons. SML has more to do with portfolio construction and how you can get a portfolio which doesn’t deviate from the benchmark too far while still producing Alpha. (Alpha is active return). The Tryenor ratio is more about making sure public equity managers are not doing really crazy stuff.
Overall my point is that there is no evidence that suggests the expected return from investing is startups in net positive. Whether founding or working for a startup produces positive expected returns or not is also very hard to know, but I would estimate that working for early stage startups for lower than market pay has a negative expected value even after considering the possibility of huge exits (a lot of companies fail that you have never heard of).
Where I think startups have a much higher expected return comes with the experience and growing up you can do while working in a small company. When you calculate total earnings over a lifetime for people who join even failed startups early on, I would not be surprised if they made more and had more enjoyable lives, even if they ended up at big stable companies later. When you add the possibility of a big exit to the higher future earnings I think the expected value goes net positive.
I've rarely heard people try and sell startups as a way to make oodles of cash. It's more frequently sold as a way to be your own boss. As such I'd expect it to attract people of a particular personality type, who want to drive their own ideas forward and do things their own way, without anyone telling them what they can or cannot do. As such I'm not convinced that it is always a rational decision (or, at least, not an entirely rational one - there's definitely emotional input there).
Looking at all of the people who applied to YCombinator and seeing how many of them have successful businesses a couple of years later would be fascinating.
>Entrepreneurship is a classic "high risk, high return" venture.
Sure, for the ones investing capital. For the workers, I can't imagine startup's mean pay being anywhere near as high as a "normal" job. A mean will cut out the Zuckerbergs, Serg, Brin, etc. Also, remember you can't compare mean startup salary to mean "normal" job salary since the bulk of startups are in the valley. To get a closer estimate you'd need to give the same weight to "normal" jobs in a given area as number of starups they have there (e.g. lots in SV, some in NYC, etc.).
>It has a higher expected return than a conventional job; that's what makes it financially attractive to founders and VCs in the first place.
In the exact same sense than a lottery has a "higher expected return that a conventional job", just with slightly better odds.
>The astronomical success of the minority offsets the lack of success of the majority.
That doesn't make sense. Except in the light of something lke the Dunning-Krueger effect, where most people involved in startups expect they will be that "minority".
The point of a lottery is to generate income for the government/company running it, which would not be possible if players collectively won more than they spent.
tl;dr there are circumstances where the expected value is greater than 1, due to the accumulation of prize money when nobody wins several times in a row.
In aggregate, all lottery runs put together take in more than they pay out. But an individual lottery run might be -EV for the state if the jackpot has grown enough; however, that only happens after no one wins the lottery for weeks on end, at which point the state has run even bigger profits than before. Once someone wins that big jackpot, the state may pay out more than it took in that particular week, but still less than it took in for the several weeks leading up to the jackpot finally being won.
"Some choice quotes from his Google+ post: 'The lottery is not a tax on people who are bad at math. It's trading a little bit of expected-value for a lot of variance.'"
If you want high variance, wouldn't you then want to make high-risk investments in the stock market? I'm not very knowledgeable on the subject, but my understanding is that the expected value rises with increased variance on the stock market, rather than decreasing.
Some vaguely interesting statistical analysis, but here's the money quote at the end (TL;DR)-
"So why do I still buy lottery tickets? <b>Definitely not for the expected monetary return on investment.</b> I think of it as a discretionary entertainment spend. I get literally hours of enjoyment from fantasizing what I’d do if I won."
I believe the author is trying to convey that even a remote possibility of winning fuels his fantasy. It is impossible to win without buying a lottery ticket.
$10M in US $100 bills would take up over 100 liters of volume, which would fill about five rather large briefcases. The cash itself would weigh over 200 pounds. Strictly speaking, it's impossible for someone to walk up to you on the street and simply "hand" you a briefcase full of $10M. They would have to wheel them to you on a cart, which would undoubtedly attract far more attention than is safe for this sort of transaction.
Incidentally, it's amusing to note that $100 bills are actually more valuable than gold relative to their weight. The obvious next question would be, what's an even denser store of value. For one amusing example, Cristiano Ronaldo has a transfer value in excess of $130 million by last valuation, and weighs less than 200 pounds, making him more than ten times as valuable as $100 bills per unit weight, let alone gold. Judging from the transfer market, it would seem that many top-flight athletes are literally worth their weight in gold.
Yeah, that's why we abolished the $500 bill in this country. I'm surprised the EU has currency in that amount. I didn't think to investigate other currencies because the guy I was replying to said 10 million dollars. Perhaps 10 million euro would fit in a single large briefcase (and be worth more than 10 million dollars to boot).
By weight you are absolutely right but considering density it is a much closer call. A kilo of Ronaldo (assume 75kg) costs 1700k and takes about 1dm3. In this space you can fit 19.3 kg of gold worth 1016k. So impressively Ronaldo is worth more than a solid statue of himin Gold.
The obvious next question would be, what's an even denser store of value.
Interestingly, high-denomination casino chips, some professional players don't cash them out since it's much easier to transport them to their place of staying.
You're assuming that there is actually someone walking around out there with a briefcase full of $10M that he or she intends to give to someone. At least with the lottery you know that someone is actually getting a lot of money.
Per the Kelly Criterion, unless you have a big bankroll, the minimum bet is an overbet, which turns it into a losing strategy.
Suppose you have $100,000, and repeatedly bet .001% of your net worth on a single ticket in the lottery at 100,000,000:1 with a 2x EV (disregarding that you can’t bet more or less than the price of a ticket). You do it 2,000,000 times, and then you hit the jackpot – pretty lucky since the odds are 100,000,000 to 1, right? But by the time you hit the jackpot, your bankroll has been so depleted that winning 200m x your bet, you only get back to 41% of your original net worth – because you overbet!
In the book "Thinking fast and slow" by Daniel Kahneman, it is claimed that there is a growing body of evidence that we really have two brain systems. A fast one, which uses heuristics to quickly approximate the answer, and a slow one, capable of deliberate and rational thought. He argues that the fast brain system is really responsible for a lot of our cognitive biases.
For example, our fast brain does not really understand probability. It only knows three categories: either something is impossible, it is possible, or it is a certainty. A lot of human behaviour with regards to probability can be explained by this simple assumption.
Why do people buy lottery tickets? For their intuition, it moves an impossibility into a possibility. The fast brain system that fuels their intuition does not care what the actual probability is and does not understand anyway.
While I deeply respect Daniel Kahneman's work, please note that his two system "theory" is pretty awful. He uses it as a justification for some strange results, and made no effort to test it. Now, there is some evidence that humans have numerous different reasoning systems, but this is a complicated and controversial area, and we have no idea how many, its somewhere between 1 and n, where n could range from 0 to at least 10.
Lottery, as a form of innocent betting, can really provide a lot of fun for a small price. I would be bored to death to watch a soccer game, but when I bet 1€ on it, it suddenly becomes 2 hours of fun. And I don't expect to "win the ticket", cause I already got more than I paid for.
Looking at everything from the profit/cost point of view can lead to a very boring life, for most of the people.
Lotteries are a tax on people who are desperate, not ignorant. Even if you understand the math, your utility function changes so that you're willing to trade a small expected loss for the long shot chance of solving all your problems. I don't buy the idea that swathes of lottery players really think they're making a value bet. Just because they respond with anecdotal evidence when you confront them with the true odds, doesn't mean they're really arguing the facts, they're just protecting their hopes.
I've been interested in the topic for a long time as I have a relative who spends most of his income on lottery tickets. Any time I can, I ask people who play the lottery why they do it. Most of them spend a tiny amount and it's something they have a little bit of fun with their workmates or family, these are the "normals". But about 20% of the players account for 80% of the ticket revenue, these are the people playing out of desperation because they are in a poverty trap and they have no other way out. They are foregoing essentials to pay for the lottery tickets, so if they didn't play, they wouldn't accrue the money they "saved". These people are often on the brink: depressed, panicked and alone. A lottery ticket is a temporary "self medication" with which they can temporarily quiet their anxieties, until of course, they need the next hit.
Simple evidence that gambling (rather than just lotto) is a tax on poor people - check out where the gaming/'slot' machines are. Last time they ran the map in the paper, the venues were heavily clustered in the poorer northern and western suburbs of Melbourne, with another cluster down in Frankston.
Then of course there's the simple point that less money comes out of lotto than goes in, simply to pay for overheads and profit of the gaming company (as with all gambling) plus a bit of tax on the ticket. The ticket sale simply can't be a zero-sum game; less has to make it back to the winners than was paid in the first place.
That being said, I also pay the idiot tax every month or two, and for the same reasons as the author - entertainment.
By this line of reasoning, anything that is more popular among poor people is a tax on them? People pay to gamble to get something in return (entertainment as you say) and that makes it not a tax. It is quite natural that the gaming company makes a profit on that, just like, say, a movie theater company.
There is certainly some truth in the vision of the poor guy being a more vulnerable gambling victim but I would not generalize that to non-addicts. Gambling vs. other kinds of entertainment is a matter of personal preference.
Actually gambling is quite popular among rich people, in the form of financial speculation...
By this line of reasoning, anything that is more popular among poor people is a tax on them?
The argument is that gambling houses are taking advantage of people's poor education to bilk them out of money. In principle, everyone in developed nations should know that gambling is a poor investment, but it takes good financial sense to really understand that. People with good financial sense usually aren't very poor.
At low income levels, taxation is generally low. We've tended to avoid flat income taxes because they impact those with low-incomes more than high-incomes because poor people spend a higher percentage of their money than rich people.
So when you look at how poor people spend money, the rational economist would never advocate spending the money on the lottery. The utility is low, and even if the expected value is positive, the variance makes it a bad idea. Poor people would be better off spending money on things with greater returns.
The problem is that poor people don't spend their money on things with greater returns. They spend far too much of their money on lottery, and it's probably combination of psychological factors and financial illiteracy. I could be off on this, but I remember a statistic showing that there isn't much deviation on how much money any random household spends on the lottery. So a household with $100,000 in incomes spends as much on the lotter as a household with $20,000 in income. The result is that the lottery has become a regressive tax.
So when you look at how poor people spend money, the rational economist would never advocate spending the money on the lottery. The utility is low [...]
This misses the point of the article, which is that gambling should not be regarded as an investment, but as entertainement. But I agree that poor people are possibly more likely to see it the wrong way, i.e. as a good investment.
The result is that the lottery has become a regressive tax.
By the same argument you can conclude that potatoes are a regressive tax since they cost a higher fraction of the poors' revenues.
When you give money to the government with nothing in return (except as a member of the collectivity), that is a tax. Not when you give money to a private company in exchange for some kind of entertainment.
When there is a high jackpot, it almost is a break even proposition.[1] Of course this is not zero-sum in the medium term because this situation only occurs because it was not won previous weeks. It takes a jackpot of around $120m to be 'fair' (on the powerball lottery).
That ignores taxes and multiple winners. The Megamillions jackpot hit 640 million and it still had negative expected value. There happened to only be 3 winners, but there could have easily been far more than that.
PS: Powerball tickets also cost 2$ now which means you need a larger jackpot to break even.
This is all bad probabilities if you don't take into account the fact that you repeatedly buy tickets. I'd like to see a more detailed study counting the probability of never winning when playing systematically for 20 years, for example.
But nevertheless. Yes, the lottery is a tax for the poor. And if you expect your life to change for the better by winning a big bag of money (that you will have taken to the other suckers who lost, minus the organiser's fee), then you just need to reconsider what makes a happy life. You should also consider how many people get isolated after they have won, not knowing how to deal with such a change, such a "responsibility", such a social pressure from family and friends after they have won.
I'd never play the lottery not because of the ridiculously low chances of winning (I also am a statistician), but because what I would win would change nothing to my human condition. I prefer reading Epictetus instead. It's cheaper and the effect lasts longer.
It is most certainly a tax on the poor and undereducated. The level of cognitive dissonance required to believe that there is not a massive information asymmetry at hand is simply staggering. Yes, some people are perfectly able to calculate the probability of winning the lottery and know that they should gain enjoyment just from playing, not from the belief that they'll win. These are not the people who are victims. The victims are the high school dropouts who don't understand that their chances of getting hit by lightning while simultaneously getting hit by a bus while crossing the street are still better than winning the lottery. Many, if not most, of these people don't really have the discretionary spending ability to lose hundreds of dollars a month on merely dreaming of winning the lottery. But somehow we pretend everything's fine.
There certainly are people like you describe but I'd say most do understand that their chances are minuscule -- even if they really don't understand the numbers. But they don't care; they're desperate and don't exactly have many options so they grasp for the only thing they know that might change their condition.
> their chances of getting hit by lightning while simultaneously getting hit by a bus while crossing the street are still better than winning the lottery
While I agree with you in philosophy, I wonder if that is the best example. I don't think I've ever seen a news report of someone getting hit by lightning and a bus at the same time, but people do seem to win the lottery on a fairly regular basis. This suggests that winning the lottery may be the more likely of the two.
Someone winning the lottery is more likely than someone getting hit by a bus while being struck by lightening. You specifically winning the lottery is probably less likely than you specifically getting hit by a bus at the same time as being struck by lightening.
A quick survey of the literature seems to indicate that gambling activity (including lottery play) is positively correlated with income.
If it was a tax on the poor and undereducated, the correlation should be negative, yet the first three articles I found on the matter said it's positive, and that income is the strongest determinant of gambling activity.
It's more complicated than that. First of all you have to separate the different gambling activities. Some activities, like card games at a casino, are more positively correlated to income and education, while most studies on activities like the lottery and scratch tickets show negative correlation to both income and education.
Secondly simply looking at the number of times person partakes in an activity or just how much they spend only gives a small and incomplete picture. The really important number is what proportion of their total income is spent on gambling. Most studies seem to find that the poor spend a higher proportion of their income on lottery tickets than richer people.
I highly doubt that, given the choice between a sandwich and a lottery ticket, a starving person would choose the ticket. Death from starvation in societies where lotteries exist for the masses is quite low. For example in France where I live, people don't need food to survive. There are enough government subventions for food banks and NGOs to help.
A big bag of money buys your more trouble than food, it buys you restlessness and an insecure future. A regular income from a stable job, for instance, provides food as well, without buying you the trouble of having to secure the money you've got by chance.
And no, that's not presumptuous. We know of plenty of people who were happy with little, nowhere needing the cash that big lotteries pretend you can have.
Yes its played by the poor, yes the odds are riciculously low. These people don't 'expect' to win, instinctively they know the odds are low but it is the only chance they see themselves as having. The lottery is a tax on desperation.
If you're analyzing lotteries, one thing you have to think about is the diminishing utility of money. ( http://en.wikipedia.org/wiki/Diminishing_marginal_utility ). Your first dollar is a lot more useful than your millionth dollar. Or another way, having a million dollars is not a million times as useful as having one dollar - it's a lot less useful than that. This makes a lottery a pretty bad investment even when the expected-returns are in your favor.
Not to mention all those stories of people who win the lottery and then lose all their friends out of jealousy. But that's harder to analyze.
It seems to me that if you already have, say, 100000$, then that utility changes completely. Losing 1$ would be meaningless for you, whereas gaining 1 million dollars would be a huge improvement.
While having a million dollars isnt a million times as useful as having 1 dollar, it is monumentally more useful than having a million 1 dollar bills that cannot be combined. So i'd still rather have a million dollars in a lump sum than a million 1 dollar bills that i can only use one at a time.
The only weekend when casinos did not make a profit, in the entire history of Las Vegas, was when the annual U.S. statisticians conference was organized in Las Vegas :)
The variation I heard was the the American Chemical Society (ACS) held their 1997 meeting in Vegas. The casinos didn't make enough money from the 13,000+ people who were there, and don't want the chemists back. Checking now, there hasn't been an ACS national meeting there since then, and the schedule, which goes up to 2019, doesn't show any future meetings there.
For what it's worth, neither does the American Statistical Association.
lol. Mine was told to me by a chemist. Did a physicist tell you the APS version? Looking at the APS calendar, they also have no upcoming meetings in Vegas.
I don't see how this makes sense. The casino's odds are always not in favor of the players, so the more the merrier from the casino's POV. Even if you're a card counting wiz, the margins are pretty poor and you're easily caught.
I imagine the real problem would be crowding your casino with people who just showed up for the buffet but refused to gamble.
I think your latter assertion is the point - the statisticians refused to gamble and many of the hotels' services are provided at a loss to help bring in gamblers.
Many businesses are run this way - restaurants make a loss on food to make their margins on drinks... I wouldn't be surprised if casinos make a reduced profit (or even a loss) on alcohol so as to make a profit on the gambling.
Casinos will comp you a room, meals, drinks if you gamble just the right amount, and it's sometimes possible to get +EV once you factor the "value" of these things into account. No card counting required.
Poor statistics on the chance of winning aside, there is one reason for me to spend $1-$2 a week on tickets: Having a ticket ensures you have a chance of winning, while not having one ensures none at all. Losing the $50-$100 per year isn't too big of a deal for me, especially for the entertainment value.
Only if you enjoy sports. Also very few sports bets pay out a million times the money. Even a bet like France beating Canada in the ice hockey world championship only pays 33 times the money, and the prospect of winning $66 on a $2 bet is hardly exciting.
I buy one or two lottery tickets every year. This gives me a non-zero chance of winning, with negligible cost. Going from zero to non-zero chance is a more important step than the one from almost-zero to still-almost-zero chance that buying 1 ticket a week would give me, at least psychologically.
Oddly, his real reasons for why he plays the lottery has nothing to do with probability and statistics, and is in the last two paragraphs. I feel the essay would have been better serveed if he had started with that, then said "But, given that, let's still explore what the actual expected return on investment is for the fun of it."
I always wonder about these calculations. According to http://www.michiganlottery.com/where_the_money_goes out of every $1 players spend on the Michign lottery, $.58 goes to player prizes. Assuming they're actually counting that correctly, doesn't that mean the expected monetary return (to you, of course it's nice that you're donating to the school system) of $1 spent on the lottery has to be $.58?
That's over the course of the whole run; accordingly the average expected value of $1 spent on the Michigan lottery would be $.58 if you bought a ticket for every game every week. But you don't do that. Some weeks the jackpot is higher so you buy a ticket, some weeks you don't. When the jackpot is higher, the EV for that week rises, but since the lottery itself plays every week it doesn't matter so much to them.
But when the jackpot is bigger, more people buy tickets, too, which makes the EV for that week go down. It's not at all clear to me which effect is bigger. (Indeed, I wonder if your best bet is to buy the first week the jackpot rolls over, but not when it has rolled over multiple times.)
At any rate, if the expected return over long periods is $.58 for $1, I sure wouldn't expect it to even get close to $1 on the best weeks.
- If you're so poor that paying 1 USD is a hardship, then you shouldn't play the lottery. Otherwise, where's the harm?
- The argument, "the lottery is a tax on poor / stupid people" is valid but useless when talking about small amounts of money.
- The difference(s) between winning the lottery and someone just giving you millions of dollars? - 1) You know where the money came from; 2) The person just giving away the millions isn't receiving payment for giving away the money.
Saying that the lottery is a tax on poor people is like saying that buying a bottle of Coke is a tax on poor people. Both of these events are completely voluntary. No government agency was involved in making you spend the money. You are not obligated to do it. And, if you choose not to spend the money you are not violating any laws. It is not a tax. That's the most ridiculous idea I've ever heard.
One could argue that spending money on a lottery ticket is actually better for you than spending the same amount of money on a soft drink. One gives you hope and entertainment and might have other positive "feel good" side-effects. The other fills you with sugar (high fructose corn syrup) and is not good for anything at all.
You are not obligated by law to buy lottery tickets, therefore, it cannot, by any stretch of the imagination, be called a tax. Period. They can advertise all they want. You can still say "no".
In fact, you can stand in front of a government lottery official, extend your arm out, point a finger at them and laugh out hysterically while loudly proclaiming that you will not buy their tickets. Try telling the IRS that you will not pay taxes because, well, you don't want to.
"No government agency was involved in making you spend the money."
and I was careful to make the distinction between "encouraging" and "forcing" people to spend.
I would rather the government get out of the lottery business, because it seems like a basically useless activity. If we need money, let's ask for money. But it's not a high priority for me. Living in CA, there are plenty of other, much bigger problems than lotto.
I have always had a hard time equating ROI on any windfall probability. I view lottery systems as a windfall system in that the chance of winning is zero and the expense of playing is trivial, so any investment has no expectation of return it only allows for the possibility of windfall. The $1600 investment over 30 years would not have noticeably increased or decreased my QoL so it is not a lose in my mind, only a technicality.
Best entertainment value ever: When one of the big jackpots was making the news I bought one as much to head off the conversation of why not than anything, but it triggered these incredible technocolor daydreams! I was not bored on the subway for days. Diminishing returns though, since then the occasional ticket never had the same internal result.
In Australia there is no tax on winnings from any form of gambling and all Australian lotteries (like this one) pay in one lump sum 14 days after the draw.
Not that the Government doesn't take their cut, it's just already been factored into the advertised prizes.
I love this argument. It gets juicy quick. Sugary, like cake. When they tell you "you can't win if you don't play", and you say, "nonsense, I can find a dropped lottery ticket on the ground that turns out to be the big one" and they say "really?? what are the chances of that happening?". Black forest, cherry on top. Just wonderful.
If aside from entertainment value it makes sense to buy one ticket,then it makes sense to buy two. And three and four. But in fact aside from entertainment value it does not make sense to buy one, because that change from 45,379,619:0 to 45,379,619:1 on a windfall is accompanied by a change from 1:1 to 0:1 chance on keeping your original dollar. And in the vast bulk of lottery scenarios, it all multiplies out to a negative expected return.
Its increasingly lower returns for each dollar, thus I don't see the point of anything above the minimum. The expected return may be negative (further hence the minimum investment) but its negligible.
I was initially confused and annoyed by the author's lack of justification. But I enjoyed his conclusion, that there's an 'entertainment' value attached to the purchase.
For me, the opposite. I thought from the title it was going to be about gaming the lottery, but it's a matter of fact analysis and doesn't go into using strategies like picking under-loved numbers to overcome the odds.
You may be able to increase your expected value by choosing numbers that are less popular. It would be interesting to research the psychology behind number selection and choose combinations less likely to have a multi-payoff outcome.
Interestingly, this means that common "lucky" numbers are actually unlucky, to a degree inversely proportional to their perceived luckiness across the population.
'The decision of whether to buy a lottery ticket shouldn’t be based on the probability of winning, or the expected return of a ticket, but on the entertainment value that comes from imagining a different life.'
https://plus.google.com/107814003053721091970/posts/6sPpxMo6...
Some choice quotes from his Google+ post: "The lottery is not a tax on people who are bad at math. It's trading a little bit of expected-value for a lot of variance."
"There are many other cases in real life where mean/variance tradeoffs arise, and there are perfectly plausible objective functions under which it makes sense to follow a policy that doesn't maximize expected value.
The obvious example is insurance, where you pay a small bit of money each year to reduce the chance that you end up suddenly needing to pay a lot of money. Same with forming or joining a startup; on average you'll make less money than if you take a "normal" job, but there's some small chance that you'll have just joined the next Apple or Google and you'll end up rich.... "