Having lived in Las Vegas during my teen years I got to see first hand how people rationalize their misunderstanding of statistics into winning 'systems' that if they just had enough money would payoff. I cannot count the number of times someone told me, in complete earnestness, that their system worked, they had proved it worked using a small stake of $X (which was all gone now) and if they had ($10X or $100X) of a stake their working system would return a handsome profit. And you say "Gee if it worked how come you lost all your money?" and they would say "You win and lose some, my system predicts when the big wins will come based on what has happened so far and I make big bets on that, and small bets on the ones we know are more likely to lose but to get them out of the way." And you say "So if you had a coin and you flipped it you would make a really big wager if the coin had just turned up heads 3 times in a row?" and they say "EXACTLY! You know this system?"
I wonder what the best way is to illustrate to those people that that coin example is ridiculous. It's so intuitive to us that the coin has no "memory". However, I could see why someone would think that 3 heads in a row mean the 4th will be more likely to be heads. If you didn't think about it much, it is a reasonable gut reaction to a layperson.
What if you told the person this: "What if you flipped a coin and it had come up 3 heads in a row. Is it more likely that it'll come up heads again? Well, what if you waited a minute before you flipped it again? What about an hour? 20 years? Would the odds go back to 50/50 then? At what point does the coin 'forget' its previous flips?"
I think putting it that way would help illustrate the absurdity of that way of thinking.
As an aside, I think if I flipped a coin 100 times and it was heads all 100 times, I would be willing to make a big bet on the 101st flip being heads. The odds of getting 100 heads in a row is so much smaller than the odds that something is wrong with the system (the coin is weighted, there's some sleight of hand going on, etc).
There might be a sort of disease of anthropomorphism in modern (Western) culture. From a young age, kids are exposed to talking trains and animals and all manner of other things.
This probably makes people very susceptible to ascribing properties to things that can't have them: "hot" slot machines, "lucky" dice, and so on.
Its a memory thing :-) Other conversations that fall into the general theme:
"This technology is going to disrupt (really big co) and with only 1% of their market I'll be a zillionaire."
"The proprietary use of carefully designed magnetic fields on the water actually turn it into fuel which allows us to generate power too cheap to measure."
"I have done all the homework I need to do before the weekend is over."
This is true, as someone who learned to count cards because everyone on college assumed since I was from Vegas I could count cards, on a visit home I won about $1,500 at the MGM Grand when they were dealing single deck blackjack. After the third time I doubled down on like a 14 the dealer just stopped dealing. Security came over and waited for me to collect my stuff and leave.
I make sure to get in on the lottery pool at work. I'd hate to be the one guy that shows to work after everyone else wins and quits. Yeah, the odds are extremely thin, but consider it $2 to keep myself from committing suicide.
The lottery let's people gamble (which is illegal in most US states) because of "the children".
EG lottery profits go to support additional money for public schools.
This is all after a 16% operating / administrative cost, of course, which amounted to ~$4.83b in California alone in 2012 (2).
Back in 1988 an article appeared in the NYTimes suggesting that what was actually happening with the money, only 3 years in, was that state budgetary offices were simply using this newfound windfall to supplant existing commitments.
Explained by the State Superintend at the time "the percentage of the state budget spent on public schools declined from 39 percent four years ago to 37.5 percent last year. Lottery dollars, he said, have in effect been used to make up the difference."
Part of my frustration with California's recent retroactive tax-raises, ostensibly for education, is borne out of examples like these.
This is all after a 16% operating / administrative cost,
of course, which amounted to ~$4.83b in California alone
in 2012.
You're reading that completely wrong.
You can see their audited financial statements online.[1]
In 2012, the total lottery expense was $4.4B, into the following categories:
3.6% to operating / administrative, 1.7% to game costs, 6.8% to retailer costs, 58.6% to prizes, and 29.7% went to education.
That 3.6% represents $143mm in total cost (not $4.8B). Of that, $63mm went to salaries, $47mm went to advertising, $6.4mm went to PR and POS, $13mm to 'other professional services', $8mm to depreciation, and $5mm to G&A.
I fully understand that, and support the tax raises anyways because if that is the only way to get them, then we can get them that way.
The problem is that the state constitution and politics makes it easy to get rid of revenue, but really hard to get it back. For instance consider Arnold Schwarzenegger, one of whose original goals was to drop the vehicle licensing fee from 2% of a car's worth to 0.65%. He got in office when times were good, he reduced that tax. Then times turned bad, and it was impossible to reverse that even though the state really couldn't afford it any more. This is about a $6 billion/year hole in our budget. That's on par with the recent tax increases.
Except that the vehicle licensing fee was part of our budget for decades. It was stable and reliable. Our recent tax increases are temporary. What do we do in the long run?
If pensions are the issue, then the solution is probably a little more detailed than "cut spending". You show me someone with a 2 word fiscal solution and ill Sheila you a fool.
The bigger issue is that California's tax revenue is hugely cyclic, since it depends on income taxes on people whose incomes depend on the performance of investments. Thus during a boom, California gets lots of money, during a crash, the government is strapped.
But yeah, pensions need to be reformed. However even if you did so, the state would still regularly run out of money.
You could find a way to give just about any government billions more in "revenue" (my, what a polite euphemism for theft) and they'll still find ways to spend more money than they take in.
The problem isn't finding enough "revenue", it's simply spending within their means.
That's the fee that you need to pay each year to update the license on the car. I'm quite sure that in Denmark you don't pay 180% of the car's worth every year.
The fee for me to license a car I bring to denmark is 1/3rd the figure you cited.[1] Do you know why there is such a disparity? Would you mind explaining the rationale for such a high fee?
(I realize its not your personal policy, I am just curious about what the government says about the fee. As an American it sounds strange but I imagine such a low % here in the states is equally as strange to you. Thanks for indulging my curiosity.)
The 180% is for private cars. They give breaks for vehicles with special registration (commercial, foreigners etc.), I guess to not stifle business / foreign workers too much.
I think the rationale for the high fee is (a) Denmark likes taxes (around 50% income tax on average) to run our comprehensive welfare state, and progressive taxation that taxes wealthier people more is seen as the best approach (new car buyers sort of fit into this), and (b) "the environment", we have very good public transportation (and, famously, bicycle facilities) which the government wants to encourage.
I don't agree 100% on those points but there it is.
How does anyone afford 180% the value per year? It seems like it would make buying any car more than a few thousand DKK only possible for a very small rich few.
It depends on where you are. Public transit in London, for example, is amazing. The longest wait for a train at my local station (Zone 2) was around 12 minutes off peak. Night buses take over for the tube late at night. They'll take you where you need to go, albeit a little slowly. A yearly pass costs £1216 (Zone 1-2). Good luck getting insurance and petrol for much less than that.
There's an argument to be made that public transportation isn't available because poor and middle class people can afford cars.
Note that we hardly have poor people (by American standards) because of the welfare state, which is partly funded by these extremely high taxes, but it is difficult for low income people to afford a car (gasoline is heavily taxed too). If they really need it they will buy an old beater and drive it a couple of years until it dies, then repeat (which somewhat nullifies the rationale of car registration fees helping the environment).
This happens in Ohio too. From the Columbus Dispatch:
"School leaders have complained for years that the state engages in a shell game; for every extra dollar generated by the lottery that goes to schools, a dollar is taken out of the state’s general-fund allocation to districts across the state.
The shell game — difficult to prove in a multibillion-dollar state budget — was briefly exposed in late 2001 when Ohio added Powerball to the lottery. The state estimated $40 million would go to schools from the new game, so lawmakers promptly reduced general-fund money for schools by $40 million."
The reason states started running lotteries was actually to deny business to the mob. Mafia used to run the numbers games right alongside the protection racket. Revenue was mostly a side effect of a law and order decision.
I can't say I understand how anyone would be more or less upset about taxes due to the fact that lottery money goes to schools.
I hate this phenomenon. It's so easy for an organization to misappropriate targeted funds, simply by removing & redirecting regular funding equal to the amount of the targeted funds.
It's why I am very hesitant to donate to my alma mater. I want to, but I know no matter what I tell them I want done with my donation, a little wizardry on the books and they can send it wherever they please.
Something to think about: In some countries where general prostitution is illegal but government sanctioned version is, the government collects tax from johns.
Lotteries are probably regulated to the point where this can't happen, but I used to play poker at some quasi-legal charity games quite often. They sold instant bingo tickets, which are very much like instant lottery tickets. There's a box with a defined number of losers and each prize.
Most of the return from a box came from let's say 5 big prizes (out of let's say 1,000 tickets). Let's suppose the return is 50%, and the ticket price $2, so the total payout on a box is $1,000. There would be 5 $100 winners, and a number of smaller winners that added up to the other $500.
The people selling them would watch and count how many of the $100 tickets were redeemed. (Gamblers tend to not hold onto the winning ticket secretly, they cash them in right away and buy more.) If there were, say, 2 of the big winners left but only 100 tickets remaining in the box, the guy running it would purchase them all. The two big winners would pay for the whole thing and his profit would then be the sum of all of the small prizes left (which was expected to be roughly equal to the 2 big tickets).
Since it was a charity game he was effectively stealing from the charity, but also robbing the players collectively because any time you were near the end of a box but still able to buy tickets you could be sure there were no big prizes left.
I wonder if instant lotteries ever do this. If they see it's near the end and they've got a disproportionate number of prizes left they could simply pull all of the tickets.
The charity is going to get the same no matter what. All of the variations of this I've seen works this way:
A charity approaches a bar with a box of tickets with the total of the ticket face value of X. The total prizes are in the range of X/4 to X/3. The bar buys the whole box for X/2 and keeps all of the proceeds.
Or, to put it another way:
There are 2000 tickets and each ticket costs $1. The bar buys the whole box for $1000, which goes directly to the charity. The total prizes in the box is $500. The bar sells the tickets out bringing in $2000, pays out $500 in winning tickets, recovers the $1000 paid to the charity and keeps the remaining $500 as profit. Then they call up the charity for another box.
Most of the boxes come with displays that list out the various prizes and most places will cross out the big ones when they're paid out... mostly so they employees can keep track and buy out the box when there's a favorable amount of big tickets left.
I don't think that strategy cost the charity any money, unless the boxes would not have sold out anyway. The return on the boxes is fixed regardless of who buys the tickets.
While it doesn't literally cost the charity anything this go-around, it is pretty unseemly behavior in a charity event. If I was a player in said charity's poker tournament and saw the organizers gaming the system to their own profit, I would be much less inclined to come back to next year's tournament. Many of these tournaments see lots of return players year to year, and it is in their interest to create an environment that maximizes the feelgood effect on players and charity donations. Many players will donate winnings back to the charity. Somehow it seems like these clever folks who are trying to outsmart the charity's game might not be so altruistic.
Some of the value of running an event like that is get people to feel involved and make them feel good while doing so.
By buying out the last portions of tickets it prevents much of the good will the event was supposed to generate.
Knowing this strategy I would not run an instant raffle, second if for case the raffle type was not under my control I would make it clear that such strategies by volunteers would nto be allowed. An Volunteer who went ahead with the strategy after being told that it reduced the potential gain of the event would not be worth retaining.
The cost is that people who know this strategy is in place will no longer purchase any tickets if there is less than 100 tickets left.
Further if the ruse is revealed the general sale of all charity lottery tickets will define because it could be assumed that it is rigged in favour of the house.
I work for a lottery that sells the type of tickets you're referring to i.e. a set amount of tickets a business purchases knowing how many of each winner is in the box. Only the business that purchased the box could cash winning tickets, each batch of tickets had a unique serial number.
The tickets have recently been changed with a new feature a barcode which allows the ticket to be cashed at any store that sells lottery products.
I couldn't find anything about this kind of product on google. Could you disclose the name of your product or what should I google to find more about it (not necessarily your company's product)?
If the one running the lottery is able to know which tickets it sold had which prizes, then it could simply stop selling the tickets the moment the collective prizes from the remaining tickets exceeded the collective price of the remaining tickets -- if that ever happened.
One way the charity itself could do that is by using its own account to "buy" the rest of the tickets. If someone else does it from their own pocket, then they have a guaranteed winner on their hands, but they aren't stealing from the charity -- merely using insider information to get a better deal than the rest of the players, and not returning the profits from this information back to the charity.
Of course, in a way this is cheating. The lottery issuer has more information than the players. But if it's for a good cause, then I guess it's fine :)
In the 1970s, when state lotteries were new, the Massachusetts lottery had a parimutuel payout, akin to horse racing -- whoever had the winning 4-digit number divvied up a payout. Based, I suppose, on anecdotal evidence, some guys in the Harvard physics department judged which numbers were likely to be least popular, and bet those, getting a positive return.
However, this arbitrage quickly went away. It seemed that organized criminals started using the lottery as a low cost (indeed initially negative cost) way of laundering money, using a similar scheme.
The upside is that this turned into a kind of state income tax on criminal income.
I think the final paragraph sums it up, although the author seems to miss the point:
>The thrill and rush of possibly winning started to wear off after about the twentieth losing ticket. Each card had a couple of “Life” symbols on them, and every time you got a second you just dreamed of seeing the third one under the remaining graphite. However it never appeared and never will and it just kind of turned depressing. How could people put themselves through this humiliation and teasing every day of their lives? This is definitely an investment that is not rigged in your favor and can never really bring you positive returns.
There is a thrill to knowing that, however small the chance, there is a large payout potentially waiting for you. Most people don't buy 100 scratchers at a time, or I would guess even one a day. Buying one lotto ticket a week, for instance, is a trivial expense for many people which also happens to be fun (the aforementioned thrill). The inevitability of the loss doesn't become as apparent over those time scales: selective memory results in people remembering their (typically small) wins and forgetting all of the losses in between.
A lot of money can be made selling call options on high volatility stocks you own that are way out of the money. You are essentially selling lotto tickets to gamblers.
The point is if you own the stock the high sigma event does not result in a loss but a reduced gain. And we're talking way out of the money so it will be a substantial gain if you get called away. Many call buyers are retail investors speculating on price movements, and are using call options as a form of leverage since they do not have the capital to go long the same amount of stock. Whereas call sellers must own the stock (or be exposed to infinite losses.) There are a few studies that show there are excess returns for option sellers vs buyers but unfortunately don't have a link handy. (See "Expected Returns" the book on amazon.)
edit: AAPL right now is an excellent example of a high volatility stock that is underpriced demanding large option premiums. If you have the capital picking up some AAPL to simply write calls until it goes back up to a fair valuation is a reasonable way to make money, with the caveat that it relies upon Apple breaking above being in the bottom 5% of the market valuation-wise.
It's called a covered call position. If it was that risk-free and easy, then every hedge fund would be already on top of this and quickly bring prices back into parity.
Unfortunately, you still expose yourself to the risk of holding the stock, while putting a hard cap on the upside.
You have to hold 100 shares to cover 1 option. A decline in the price can quickly add up to a significant loss, not to mention when you actually have to sell your position when the calls are exercised.
I never said it was risk free or easy, and hedge funds do sell covered calls. The point is there is a well known and understood asymmetry between the long and short options markets due to the capital needed to write options. Intuitively the reason there is alpha for selling options is likely at least in part that you are letting people with little capital access leverage.
Well, mathematically you're constructing a synthetic put.
You're giving up the potential upside in the stock while keeping all the downside risk. The "premium" or lotto ticket you're selling is your compensation for foregoing any upside past the option's strike.
People seem to forget that, in general, options are fairly priced.
Higher chance of payout, yes. But lower amount of payout.
If you adjust for the payout amount, the liquidity difference, the amount of risk, and the amount of work involved, I say they work out to be roughly the same.
Remember, no one can dilute your lotto tickets after the fact :)
The risks of scratchers (and other lotteries) is known, controlled, and published. If you feel "ripped off" by a lottery, you are stupid.
The risks of startup investment are murky and subject to manipulation. People can rip off other people. Some of the laws are there to protect people's retirement savings from investment scammers.
(Whether those laws are effective or not is a debate I'm not qualified to have.)
The statistics are off, the odds of someone winning several times is based on how many times they buy ticks but lot's of people play and winners often change their behavior.
First off a lot of people have won once so you need to know how many winners there where and how much they spent to get odds of a second win. Total ticket sales are ~$78 billion assuming 1 winner per 50 million spent that's ~1,560 winners per year assuming they live another 40 years that's 62,000 people that have one once alive at any one time. So now you figure how many tickets do winners buy per year? Call it 5,000$ so now each year there is around 300 million spent by lotto winners on tickets. So, you would expect ~6 people to win a second time each year.
But, this is where behavior's may really get out of whack. Of those 6 you would expect people to think they where destined to win. Let's say 1 person per year now spends 1/3 of there money on the lotto. As the payouts tends to be ~1/2th of ticket sales (jackpot's are around 1/4 but I assume non jackpot wins are rolled back in). They would then have a ~1/6 chance of a third win and a 1/36 chance of a second win. Of course that's just looking at winners for one year so around once every 20 years someone should win 4 times in a row.
I think he's underestimating the time he invested in this project. He says he scratched 100 tickets in 15 minutes. That's a pace of 9 seconds per ticket. I've bought a sizable number of lottery tickets, and that's a blazingly fast pace to scratch off (or otherwise remove) the latex, read the revealed numbers, determine if you have a winner, tear the ticket at the perforation, and sort the ticket into the appropriate pile.
It looks like he bought 100 consecutive tickets. If the winning tickets are truly random, it wouldn't matter, but I wouldn't be surprised if the distribution is controlled in some way that ensures winning tickets will be more evenly distributed than random. Anyone know whether this is the case?
If it is, the variance at least (if not the expected return) could be different if the tickets were purchased in 100 different places.
usually you can see how many of the bigger prizes have been collected during a run. If you didn't manually ensure they were not all clumped together, you might run into cases where tickets could be deduced to have substantially different odds (in either direction)... I think this has actually happened. You wouldn't want all the big prizes to get claimed right at the beginning, I imagine people would largely stop buying your tickets.
In the 90's right before ND was part of PowerBall, I was asked to buy the tickets for a whole office because I was going to MN. I bought $120 of tickets and did not have one ticket with any winning numbers (never mind a powerball). I was never asked to buy tickets again. I seem to remember the odds were better to win than miss all (5/49 + 1/42 era).
Its a cute diversion for most and one of those weird office group things.
I took a look at the odds in my state. The lower dollar amount tickets have worse odds. The higher you go up in ticket price the better the odds get.
At $1 you might see odds up too 1:5 but all of the $20 tickets are <1:4. The best I saw was 1:2.89. I'm not goot with stats but wouldn't have been better to buy 5 $20 instead of 100 $1 tickets?
I love statistics and probability...but I thought this was going to start off like one of those old mastercard commercials lol. Just a question...isn't the odds and probability on the back of the scratchers???
100 $1 lottery tickets = $100 bucks
scratching tickets = 15 mins
learning ROI and tending to a cramped hand = priceless
A second test would be to purchase 10 tickets from 10 different locations in order to change the influence of the state's internal randomization procedure during print production.
Would be interesting to see if the payouts lined up with the expected value as well.
Joe Bob Briggs had a better quote, to the effect that lotteries are a tax on desperation. The people who play lotteries are often those who have run out of rational options. Seen in that light, lotteries are really a government preying on its own least-protected citizens.
My friend once went to a concert where entry cost "5 scratch cards" – there were about 150 people in attendance. I always wondered how the concert organisers did…
Maybe it was a tax evasion scheme - in some places governments don't tax lottery winnings.
Of course, in many jurisdictions, the concert organisers probably would be liable for sales / income tax for the scratch cards, but perhaps they believed they had less risk of legal consequences for not counting this as income.
I wonder if there's any sort of somewhat even distribution to the winning tickets. If it's entirely random, there's shouldn't be. However, I knew a guy who worked at a gas station and he'd watch whenever people bought a bunch of tickets. If they scratched them off right there and didn't win anything, he'd buy the next few tickets. I believe he spent about $50-$100/week, but regularly won about $150/week.
Check that he is reporting each and every time that he is playing. Ideally he should be writing the gambling in an Excel or Googledocs spreadsheet. Every one of them for at least three months.
A common problem is that the people report only the good events and forget the bad strikes. Other problem is partial compensations: "I won +$50 and +$10$ and I only lost once -$30." really means "The firs week I won +$50. The second weak y lose -$40, but it not a lose because they come from the money I had won in the first weak. The third weak I won again +$10. I only was unlucky in the fourth weak because I lose -$30."
It's not voluntary lying. Lucky strikes are interesting anecdotes, unlucky strikes are expected and boring. And bad memory and "compensations" are normal human bias. So write down everything systematically, or it's not useful to make statistics.
Awesome link! I've made a similar (though not as well-presented) argument myself on a thread on Reddit (in r/frugal -- people were actually defending buying a ticket using exactly the linked arguments). Glad to know the thinkers at lesswrong.com agree. :)
Just out of curiosity, does anyone know they do it at the power ball? I know the system shuts down long before drawing, but what else do they do? Some sort of DB dump and lock it in the safe or something? What are chances that an employee leaves a virus that randomly insert a row with winning numbers after being drawn?
Occasionally, a large jackpot can return a positive average payoff, if it's powerball style and they accrue from round to round. However, the odds are so astronomically against any one ticket winning, that it would still be considered gambling. If a billionaire could risk enough of their fortune to gain a high probability of getting that winning ticket and therefore making an overall profit, then perhaps it would be investing from his perspective, but if you or I blows our $50k emergency fund and still has a 99% chance of losing it all, it's still gambling.
This strategy fails because multiple winners would split the jackpot. If one billionaire sees a positive return in buying up the entire probability space to get the jackpot, he must assume that another billionaire would also come to the same conclusion. No player can assume they're the only one applying the strategy; they each must assume the jackpot will split until a ticket is no longer positive value.
This is kind of a crude definition. If you knew a certain slot machine in Vegas had a positive expected payout, sure, you'd be rich, but is it an investment? Also, there are plenty of people legitimately investing in companies that have less than even odds of a return.
Investing to me is more about mindset and the manner in which you deploy capital for a return, and how much you are relying upon luck, guesswork, and chance.
And every once in a while somebody walks into a casino, puts a coin in a slot machine, wins the jackpot and leaves with 100000x their initial "investment".
In general, over the long term, investing makes money.
In general, over the long term, gambling loses money.
It would have been interesting to see him continue the investing with the $41 for a second round. If you go into it already willing to lose $100, reinvesting the winnings gives you more chances to win that big prize.
I'm always amused that when they list the overall odds of "winning", they include the odds of just getting your money back ($1 prize on a ticket that cost $1), which isn't "winning" at all in my book.
Ha, well in your book. But once you buy a ticket, the $1 is sunk cost and you currently have $0 left of your $1. If you then get $1 from the ticket, you did "win" it and are $1 better off than you would have been if the ticket was not a winner. If you're willing to shell out the $1 in the first place, you should be happier winning $0.23 then being stuck with a losing ticket.
No... see above. Even if expectation is positive, it is still likely a bad decision. Google Kelly Criterion - it tells you what percentage of your bankroll you can risk on those kinds of bets. For most of us, it would work out to a fraction of a penny.
Sure. An example of a gamble that is a little better is "Capitalisation Titles" (at least we have this in Brazil). You pay a fixed monthly fee and participate in some type of raffle with good prizes. In the end of the period, the bank gives all your money back with monetary correction.
In other words: a lottery that you at least have your money back.
Well for him it was an investment, because he was writing this article and it formed the basis thereof. So for him the expected reward of (monetary return + pleasure of playing) was bolstered by (increase in value of the resultant article by having a physical illustration).
Having lived in Las Vegas during my teen years I got to see first hand how people rationalize their misunderstanding of statistics into winning 'systems' that if they just had enough money would payoff. I cannot count the number of times someone told me, in complete earnestness, that their system worked, they had proved it worked using a small stake of $X (which was all gone now) and if they had ($10X or $100X) of a stake their working system would return a handsome profit. And you say "Gee if it worked how come you lost all your money?" and they would say "You win and lose some, my system predicts when the big wins will come based on what has happened so far and I make big bets on that, and small bets on the ones we know are more likely to lose but to get them out of the way." And you say "So if you had a coin and you flipped it you would make a really big wager if the coin had just turned up heads 3 times in a row?" and they say "EXACTLY! You know this system?"