Tall, Dark, and Mysterious


‘A journalist doesn’t think she should know statistics. Bloody hell.’

File under: Sound And Fury, Queen of Sciences, I Read The News Today, Oh Boy. Posted by Moebius Stripper at 9:38 pm.

Thus commented Geoff the other day. Timely remark, that one, for tonight a whopping eighty-five percent of Canadian adults waited eagerly to see if they took home the Lotto 6/49’s record-breaking $40 million jackpot, and we all know what that means: it means that it’s time for journalists nationwide to present us with a panel of mathematical geniuses who regret to inform you, Joe Ticketbuyer, that you’re probably not going to win:

The results of the biggest lottery jackpot in Canadian history will be announced tonight, but experts are warning people not to get their hopes up.

For the uninitiated: you play the Lotto 6/49 by selecting 6 numbers out of 49. You win (part of) the jackpot if all six of your numbers all match the six numbers drawn.

According to experts, this event - whose probability, by the way, I had my never-were-any-good-at-math-and-always-hated-the-subject psych majors compute in my discrete math class last year, and most actually managed to do so correctly - is unlikely.

What are the chances that your ticket will hit the $40 million Lotto 6/49 jackpot?

Not good, according to Simon Fraser University Professor (well, senior lecturer, but who’s keeping track? - Ed.) Malgorzata Dubiel. She has calculated that the odds are just short of one in 14 million.

All the while muttering to herself: “For this I got a Ph.D.?”

Semantic quibble: the odds are slightly better than one in 14 million; they’re one in 13 983 816. So I take issue with the use of the phrase “just short”, which implies “a bit less than”, no?

Anyway, is followed by three paragraphs about the would-be philanthropist who said he’d donate half his winnings to charity if he won the jackpot (he didn’t), and then this:

[Dubiel] also debunked the myth that a person can “crack the code” of lotteries.

“Everything we know about mathematics says no, it can’t be done.”

This makes it sound as though the sum total of the mathematical canon to date, from Archimedes to Zariski, was brought to bear on the age-old question of “Stochastic Processes: Totally Stochastic, Or Just Kind Of?”. And, at last, produced the long-awaited conclusion that as a matter of fact, God occasionally does play dice with the universe, at least when He’s choosing the Lotto numbers. On top of that, I wince at the “everything we know” wording, which is reminiscent of Underwood Dudley’s dealings with aspiring angle trisectors. Many of those sorry folks explained their obsession with the problem with something along the lines of “mathematicians say that trisecting an angle using compass and straightedge alone is impossible, but they’re just not trying hard enough.”

But I digress: whether or not the lotto code is crackable isn’t a mathematical question, dammit. If the code is crackable, it’s because the random number generator selecting the numbers is somehow not completely random, and seriously? Take it to a computer scientist, dude. (Except that…lotto numbers are still selected by that spinny thing with the balls, no? And we’re asking a mathematician if it gets all spinny on the balls in a crackable way? Is this what people start thinking when they watch shows like Numbthreers?)

Dubiel admitted that there have been cases of people winning multiple times, but put it down to luck.

Note the use of the transitional term ‘but’, which is typically used to contrast one idea with an ostensibly opposed one. As in, there’s an apparent contradiction between the existence of multiple lottery winners, and the absence of mathemagical gnomes that select them deterministically.

“People simply put too much faith in something that is just coincidence,” she said.

They’re also too easily wowed when mathematicians remind them of the stuff they saw in Chapter 8 in their grade twelve high school math text, but that’s neither here nor there.


  1. When no one won the $30 million jackpot, I thought about the odds of winning and it occured that if someone had a bankroll of $28 million, they could have bought every possible combination and won $2 million. And if the jackpot was just $2 million more this time, they could have made money even if one other person won and still broke even if two others won. That’s a story! (”Canadian buys 14 million tickets and wins big”)

    I found this fact most interesting, though:

    The biggest winner will be the provincial lottery coffers. Saturday’s $30 million jackpot brought in $55 million worth of tickets, but there was no winner.

    About 29 per cent of the money goes to provincial governments, a further 18 per cent is split between operating costs, payments to sellers and the federal government.

    For this lotto, only $10 million of the $55 million in sales goes back into the jackpot. That’s 450% profit. And it’ll be even more tonight. What a markup! 50% Or should I call that profit? Or maybe, I should call it taxes (shorter, editorial-length commentaries here.

    - Nicholas — 10/27/2005 @ 12:11 am

  2. State-run lotteries are definitely a form of tax, and they can be pretty efficient, too, in that you don’t have to worry about getting people to pay the tax. Even people who know the odds gamble. You can’t win if you don’t play, and the cost of a single ticket is usually so low that most people figure buying one ticket couldn’t hurt.

    I find state-run lotteries morally repugnant, akin to the state selling crack cocaine. A little more bread and fewer circuses please.

    - meep — 10/27/2005 @ 1:37 am

  3. yes, it is a form of tax. but a friend of mine once pondered…a tax on what? he finally decided: a lottery is simply a tax on stupidity.

    - Polymath — 10/27/2005 @ 4:56 am

  4. They might be a form of tax, but mostly they’re a cheap way to buy a few day’s worth of dreaming, at least among the reasonably well-educated. (I would . . . quit my job and become a cabinetmaker! I would . . . travel around the world! I would . . . get my nutty sister out of the house! Not that I’ve, you know, thought this through very carefully or anything.)

    - wolfangel — 10/27/2005 @ 5:36 am

  5. For the record, I did not buy a ticket for this lottery.

    - wolfangel — 10/27/2005 @ 5:37 am

  6. 8 out of 5 people are bad with statistics.

    - Wacky Hermit — 10/27/2005 @ 5:48 am

  7. Well, even though I screwed up my figures above, it’s good I didn’t have $28 million, because I would have lost about $500,000 last night, although my extra spending would have boosted the prize enough to make me come out in the black. Damn, a good plan didn’t work twice, and only because I didn’t have tens of millions of dollars!

    Polymath–by that logic, cigarette and alcohol taxes are also taxes on stupidity. (And in Canada, those products are taxes on our medicare system as well.) Many excise and sales taxes can be called taxes on stupidity: car registrations in cities with public transit, moving taxes on frivolously expensive properties, sales taxes on junk food, etc. Many of these taxes are hidden and regressive, which makes them more taxes on the ignorant (the ignorant being the vast majority of the population).

    Oh, and I thought of the snarkiest ending line to a letter to the editor on this topic: “Oh, and for those who are saddened by not winning $54 million, I have some good news: the governments’ gas profits are huge.”

    - Nicholas — 10/27/2005 @ 6:13 am

  8. Polymath: Lotteries can also be interpreted as taxing (not stupidity, but) hope.

    - sjt — 10/27/2005 @ 6:24 am

  9. Hey! Alcohol is good!


    - meep — 10/27/2005 @ 7:26 am

  10. Ah, the pitiable lot of the expert asked to play ‘expert’ on some cable news show. I remember my father (a doctor of sleep medicine) once being asked to comment on some story by the local paper and being horribly misquoted by a reporter who didn’t know the first thing about science in general, let alone medicine.

    What’s interesting to me about the whole lottery ordeal is that the statistics aren’t being twisted, they’re just being ignored. Ticket buyers seemingly acknowledge, and then dismiss, the Saganesque odds against winning: “Sure, the odds against winning are a zillion to one, but imagine if I won! Hope, it would seem, trumps reason.

    PS: It occurs to me that the odds of winning when there is a huge and well-publicized jackpot must be much, much lower than when there is a smaller jackpot. If you really wanted to improve your odds, you’d buy tickets when the prize was only $4 million or so. $4M may be less than $40M but it will still buy you a metric shitload of shiny consumer goods.

    PPS: This seems a good excuse to break out one of my favorite musings on statistics. Quoth Arthur Koestler:
    “Statistics is like a bikini. What they reveal is suggestive. What they conceal is vital.”

    - Geoff — 10/27/2005 @ 9:29 am

  11. There was a group of folks several years ago who did have a bankroll and tried to buy *all* the tickets (there was a magazine article explaining the scheme and how it played out). I seem to recall the team was Australian but don’t recall if it was an Australian lottery or not. Turns out, it’s kind of hard to buy 13+ million tickets and they wind up only buying something like 90% of the possible combinations. But they did win the jackpot and as I recall did make a profit. [But it was a while ago and my memory may be faulty on the details.]

    - William — 10/27/2005 @ 10:06 am

  12. Semantic quibble: the odds are slightly better than one in 14 million; they’re one in 13 983 816. So I take issue to the use of the phrase “just short”, which implies “a bit less than”, no?

    Yeah, “one in just short of 14 million” would be more appropriate. Although perhaps one could justify the “just short of one in 14 million” wording by pointing out that one in 14 million is, idiomatically, long odds, and that one in 13 983 816 is slightly less so. But given the apparent carelessness of the rest of the article, I doubt that the writer thought it through.

    - Q. Pheevr — 10/27/2005 @ 10:11 am

  13. Geoff: Players dismiss the odds because, in most cases, they are mainly playing for fun. Sure, the expected value of my profit from buying a single lottery ticket is negative, but I think many people get enjoyment from choosing their lottery numbers and checking to see if they are chosen. To some people, that enjoyment is worth a dollar.

    (Mind you, I’m not one of these people. I played the lottery a few times when I became old enough, and found it terribly boring. I’d rather put that money toward seeing a movie or something.)

    That’s not to say that there aren’t lottery addicts, or people who don’t understand that, in the long run, playing the lottery is a losing proposition.

    - Chris Phan — 10/27/2005 @ 10:26 am

  14. Ha Ha, I had the same reaction to the lottery coverage I saw (but I didn’t write a funny post about it). Math is kryptonite to the media. When they go near it, they get all weak and befuddled and they run away screaming in pain. Mostly, they just don’t go near it.

    Even when the CBC did a documentary a few years back on the people who used (use) math to beat the one government lottery you can (some of the time) outwit (the sports lotteries), they pretty much just said, ’so and so found a way to beat the system’ without really going into any detail, choosing to focus on the ‘human elements’ (read: not involving numbers) of the story.

    - Declan — 10/27/2005 @ 10:29 am

  15. Geoff makes an interesting argument: would you be better off buying tickes only when the prize is low - so that there are fewer sold, or only when the prize is high - so you’ll win more?). Buying into a large lottery means there’s also a chance more than one will win, and you’ll have to split it with less-deserving people.

    Here in the US we have lotteries all over the place. And invariably, people win buckets full of money (a good part of which they have to give back to the government in the form of taxes).

    - Mike — 10/27/2005 @ 10:50 am

  16. Well, in the 6/49, whether 1 ticket, 14 million tickets, or 50 million tickets are sold doesn’t change your chances of winning at all. (It does change your chances of having to share the jackpot, obviously.) So the real question is — assuming you are playing because it is fun to “just imagine if” — is it more fun to play for a lower jackpot or a higher one? (I have high standard, so imagining winning a mere 3 million is no fun at all.)

    - wolfangel — 10/27/2005 @ 10:56 am

  17. Geoff: “It occurs to me that the odds of winning when there is a huge and well-publicized jackpot must be much, much lower than when there is a smaller jackpot.”

    Same odds of winning, but with a larger jackpot you have a higher probability of splitting the jackpot. The real question is which will give you the higher* expected return on investment.

    Unless you are seeing the high jackpots split 10 or more ways on a regular basis (not what I’ve seen from similar lottery jackpots, but your experience may be different), you are better off betting when the jackpot is high. For example, if your hypothetical $4,000,000 jackpot is split 1.1 ways (mean), your expected ROI is approximately -$0.74 (assuming $1 per ticket). If your hypothetical $40,000,000 jackpot is split 3 ways (mean), your expected ROI is approximately -$0.05, a much better deal.

    (All of these ROIs assume that the jackpot is payed in untaxed cash, of course. I don’t know how Canadian lotteries work, but that is wildly incorrect for US lotteries, which usually pay 40-50% of the stated jackpot amount in taxable cash; that is, the actual bankable cash payout is around 25% of the stated jackpot.)

    * In most cases, “higher” in this context means “closer to zero”.

    - Doug Sundseth — 10/27/2005 @ 10:56 am

  18. That’s astonishing. I constantly complain about how terrible the media portrayals of technology are (medicine in particular), but I had no idea how bad it was in the case of math. Perhaps they should teach in J-school that not all issues actually have two sides.

    - Amanda — 10/27/2005 @ 1:54 pm

  19. Statistics are particularly horrible. Pretty much every correlation that’s “statistically significant” is reported on worthlessly in the press. The worst part is that causation is always assumed and explained. The actual p values are never reported. And most of the time, they don’t tell you which variables were controlled for and how.

    - meep — 10/27/2005 @ 1:57 pm

  20. Doug & wolfangel: You’re right of course, I was thinking of a traditional simple lottery and wasn’t paying attention to the mechanics of 6/49.

    - Geoff — 10/27/2005 @ 2:10 pm

  21. Well, this post definitely holds the record for “longest comments thread before I joined in”. But an excellent one it is.

    Coupla comments - one, regarding lottery-as-tax - you know, I just started thinking about how lottery revenue goes to find things like education…and that in Canadian (and American) schools, we have far more students studying calculus than, oh…probability and statistics. Funny, that! And, I reckon that a more statistically-savvy population would buy fewer lottery tickets, so.

    Declan - oh, yes, “human element” stories about topics that involve math. I believe you’ll recall a more recent, and larger-scale, example of that one, which took place, what, six months ago in our fair province? It took a research expert to find a single newspaper article that told us how STV worked, but throw a dart and you’d find one that told us just how hard the mathematics behind it was!

    Amanda - perhaps they should teach that not all issues have two sides - oh, god, YES, hallelujah AMEN to that.

    - Moebius Stripper — 10/27/2005 @ 3:18 pm

  22. Too true, MS. In biology, for instance, there are three sides: evolution, intelligent design, and flying spaghetti monsterism. (All other possibilities are of course absurd.)

    - wolfangel — 10/27/2005 @ 7:26 pm

  23. When the government sponsors a lottery, it tells its citizens that the way to get ahead in life is neither to study, nor to work hard, nor to save, but to depend on random chance. This is deeply immoral. It is no wonder that the government does not emphasize the mathematics of the lottery, or the expectation of winning.

    Did that reporter have an editor, by any chance?

    - Eric Jablow — 10/27/2005 @ 7:31 pm

  24. I’m with Eric. Government sponsorship of lotteries (especially when accompanied by intense advertising) is far more harmful than allowing lotteries to be conducted by private parties, because of the message it sends from a purported moral authority.

    - David Foster — 10/28/2005 @ 10:13 am

  25. Ha ha! “Moral Authority!” The government! Very funny, David and Eric.

    hee hee…

    - Samwise — 10/28/2005 @ 12:06 pm

  26. There are lots of reasons I find state lotteries offensive. Part of what’s the worst part of it is the state monopoly — it’s like those states here in the U.S. where all liquor stores are owned by the government. If there’s going to be gambling, I’d rather it just be legal and run wholly by private companies; the states can just impose a sales tax on lottery tickets. Of course, the margin they’ve got now is much higher than most sales taxes.

    The worst part is the disingenuousness. “It will bring in more revenue for schools!” Ha. Govt revenues are fungible — inevitably, they’ll just reduce the allocation to schools from the general taxes. The total amount won’t budge that much; and what is extra will likely go to more bureaucrats as opposed to the actual schools.

    - meep — 10/28/2005 @ 3:01 pm

  27. Related: Delcan points us to an article about some people who didn’t win the jackpot. I can’t tell you how glad I am that there is so little of importance happening in the world today that we can fill newspapers with stories about things that didn’t happen.

    I’d like to add a reason to the many given in these comments for why governments shouldn’t run lotteries - because they lead to such inane crap. Oh, I know - much of what we read in the newspapers is of low quality - but we’re really scraping the bottom of the barrel here.

    (To be honest, I don’t have much of an opinion on governments running lotteries. I would, however, like for said governments to commit to increasing numeracy to the point that everyone who passes through a Canadian high school can understand just how unlikely they are to win, without the front-page mathematical whiz kidz spelling it out to them. Reckon we’d see lottery ticket sales go RIGHT down if that happened.)

    - Moebius Stripper — 10/28/2005 @ 8:04 pm

  28. Lotteries got nothing on slot machines. Thinking about it, imagine that you’re a person who has a lousy, low-paying job with no hope of improvement, and you have $10 of disposable income per week. You could save all that money and have a crappy retirement. Or, you could play the lottery, and have a high chance of having a crappy retirement because you didn’t save all your money. But at least you have a small shot of coming out way ahead and having a nice life at some point. My point is that amount of money is not necessarily equal to the VALUE of that money, so lotteries could be good.

    Slot machines, on the other hand, are much worse. Occasionally, slot machines offer very large prizes at very bad odds, but most of the time, they don’t, and people play them anyway. The way this works is, basically, you insert money, press a button, and then you keep doing it until you are out of money. Slot machines often have features for convenience where you can play as many as 30 “lines” at once (meaning, essentially, that you are playing 30 pulls at a time). The payoffs on slot machines are usually something like 90 cents on the dollar, but remembering that people who play them play thousands of times…

    BTW, I disagree with Meep that the government shouldn’t run lotteries. Essentially, the lottery lets many states have no (or very few) other forms of gambling, and as low as it is to take money from poor, undereducated people, I’d much rather the government do it than casino owners or illegal gambling operations; at least that money comes back to society in some form. I think gambling, like smoking and alcohol, is too engrained in society to eliminate by an all-out ban, like we do with crack for instance, even though that still doesn’t work.

    Heck, if people are going to have crack anyway, the government might as well be the one selling it.

    - Moses — 10/28/2005 @ 10:47 pm

  29. Yeah, it’s much better that the government, which already has taxing power, exploits poor people. Why is govt more pure in its intentions than private enterprise? The margins the govt gets on lotteries can be much higher than private enterprise, because they’ve got no competition. If there were private lotteries, then the companies would have to compete on payoffs and ticket prices.

    I think it’s pretty crappy of government, which can create monopoly industries, to set up something that by its nature screws people over. And if the money received from lotteries is substantial, then the govt now has the incentive to perpetuate the bad behavior. So, if the govt sold crack, then it would have an incentive to defund any drug rehab programs.

    - meep — 10/29/2005 @ 7:01 am

  30. Rather than bashing journos over the head, you people ought to think about betting on unpopular numbers in the Canadian lottery. The systematic lottery player can have an edge, although it would take longer than a lifetime to exploit with any confidence.More subtle than some of you seem to think. See pages 44-50 of Bill Ziemba’s appendix: http://www.cfapubs.org/rf/issues/v2003n6/pdf/FullAppendix.pdf

    - Guy — 10/30/2005 @ 7:22 am

  31. although it would take longer than a lifetime to exploit with any confidence.

    Whereas bashing journos over the head takes five minutes to do with confidence. I think there’s a clear winner here, in terms of expected satisfaction.

    - Moebius Stripper — 10/30/2005 @ 8:45 am

  32. meep - The problem is democracy. If the government decided to get rid of the lottery and replace it with higher taxes on the rich, then the people who are currently being exploited by the lottery would vote them out in favour of a government that promised to cut taxes and bring the lottery back. It’s not really that crappy of the government to run a lottery at all, they are reflecting the will of the people.

    - djfatsostupid — 10/30/2005 @ 8:55 am

  33. Yes, the people are idiots.

    Still, if we’re wanting to go with the will of the people, why isn’t pot legal yet?

    What I’m really irritated about is that North Carolina has a lottery now. For years they kept voting down a lottery, but I guess the influx of Yankees finally overpowered the local prejudice against gambling. Of course, I guess I should’ve seen that coming with the loosening of the liquor laws there. I guess the “religious right” doesn’t even have sufficient power in its own backyard.

    - meep — 10/30/2005 @ 9:42 am

  34. Late-night thoughts on the lottery: Some say it’s a tax on stupid people. I wouldn’t go that far. I’d say rather that it’s the price we pay for not having studied probability more diligently.

    - Mike — 11/3/2005 @ 12:39 pm

  35. The lottery does have some uses. About 7 years back, after being a pack a day smoker (and hating it, but somehow unable to quit) for almost a decade, I decided that every day I went without smoking, I would buy a lottery ticket.

    Even though I’d never played the lottery before (having given up gambling at age 6 when I wasted all $15 of my birthday money trying to win a stuffed California Raisin playing The Claw, back when the Claw was only $.25 to play) I was convinced that I was due some monumental reward for the noble act of quitting smoking. Everyday, instead of obsessing about quitting smoking, I obsessively fantisized about the obscene amount of money I was going to win.

    At the end of each day, I woud go buy my lottery ticket, playing the numbers made up off of my quit date and the tax stamp off of my last pack of cigarettes. I religiously avoided checking the winning numbers or listening to the news, and spent each day thinking not of cigarettes, but how I was going to spend all that cash.

    After about three weeks, I figured if someone had one the lottery I would have heard about it, and I was getting tired of standing in line every day to spend $1 for a stupid piece of paper, so I cashed in all my tickets, and I have been smoke free ever since.

    - Scooby — 11/5/2005 @ 3:09 pm

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