How Not to Be Wrong: The Power of Mathematical Thinking – with Jordan Ellenberg

Comments 100

  • These old airplanes must have had their fuel tanks elsewhere!

  • Hi,

    Can someone please explain how he got a 5.3% chance of getting no deuces with 7 tickets.

    Thank you.

    It's really bugging me because my calculations give me 2.53 %

  • I’ve just realised something about fire it could be used as mathematical binary base-2 number..🔥

  • All numbers should be viewed as spins. No spin zero positive spin 1 and negative spin minus 1. And sum of all positive is inverted negative 12. All numbers are powers of some other.

  • he talks by eroding his energies and never prove a point of math in simple lottery. Sorry son. negative…

  • Ellenberg? I am Ellenberg!!
    Where are your from?

  • Wald has many contribution to statistics. Thanks

  • Please don’t hate on him. It’s a misunderstanding. The title doesn’t explain that the title is the name of his book, so it basically half clickbait. That’s why he is talking about his book. The book is actually great!

  • Every now and then, he 'snorts' through his nose, which 'gusts' into the lapel mic!

  • wow sal's punishment is going really well!

  • How did he figure out the percentages of no deuces through 7 deuces?

  • Want to excel at math? Ban homework, ban exams…and no exam grading.

  • Can one of the people that didn't find him annoying explain to me the last part cause i couldn't make it to the end. Fell asleep yesterday but now i still want to know the answer

  • Misleading title don't watch

  • The short story he told is called survivor bias. Veritasium covered this in a very fun way.

  • If you have no other words but "fuselage" for it (wtf), you deserve bullet holes in it. Get some sensible words of your own, English.

  • Great presentation, very engaging and thought provoking , thank you RI!

  • Does he ever get to the point? He keeps going off into tangents

  • @ 8:06 the expected value of the lottery ticket is not 79.8 cents, it's 59.1 cents.
    The error is in assuming that a 'free ticket' has the value of the ticket price, when the value is actually the expected value of the ticket.

    This produces an equation like:
    n = 1/9.3 + 4/39 + 15/80 + 5/47 + n/6.8
    n-n/6.8 = 1/9.3 + 4/39 + 15/80 + 5/47
    5.8n = 6.8x(1/9.3 + 4/39 + 15/80 + 5/47)
    n = (6.8/5.8)x(1/9.3 + 4/39 + 15/80 + 5/47)
    which works out to be $0.5908…

  • One of the other speakers used the airplane story… can't remember the other one… watched too many so far…

  • I hope they left all the umms out of his book. If I had a dollar for every umm or uhh in this lecture I could buy a 1000 lottery tickets.

  • My observation has been that when using “quick picks,” the lottery appears to be set up to “share” by giving several people the same combination, thus spreading out a large winning and creating more winners with smaller amounts. Many large totals are split among several people who admit they used “quick picks.”

  • I believe the reason they controlled the numbers selected was to make finding the winning tickets easier.

  • Dr. T brought me here

  • This reminds me of the Chinese fortune cookie problem. In Canada they have a lotto called 6-49. Or in combinatronics 49 choose 6. Or 13.9 million combinations

    In many Chinese restaurants they give out fortune cookies with your bill. People would use these numbers for picking lotto numbers. Of course there was no better chance to win then using any other 6 numbers then the 6 that was on the fortune cookie. What people did not realize was the printer of the fortune cookies was lazy and they did not have a random number generator for the six numbers. So the printer printed a few thousand fortune cookies using the same 6 numbers. So purely by chance of course after many years the lotto number matching the fortune cookie came up. The lotto commission discovered many people won using the same 6 numbers and people were disappointed to share the jackpot with many others. At first the commission suspected fraud but soon found out that people were using the numbers on the fortune cookie. The commission talked to the printer and asked them to use more random numbers when printing fortune cookies. So the advise in Canada is to NOT use numbers from fortune cookies because it decreases your chance of sharing the jackpot.

  • If he stops and starts and umms and ahhs it is probably because he is slowing down his thinking, he has a tested IQ of 180.

  • Brillant, easily accessible, and containing a potent sociological subtext.

  • How about getting the number as "111" in that case you have all deuce..I hope lottery example outcome is 10P7 not 10C7. Considering repetition is allowed.

  • In the calculation of the expected value for the Mass Lottery, you used $2/6.8 for the contribution of winning a free ticket. But a free ticket isn't worth $2. As a first order estimate – as you point out – the ticket is worth 80 cents. Using simple feedback loop reveals the true value of a ticket as $0.59.

  • Badly explained. I very very much doubt that on roll down there was fix returns, I very very much doubt that you would know in advance exactly how much you would get for 4/5/6 matches. Rather, like for the Euro Millions, the money "not won on the jacpkot" in the previous runs is redistributed. This means that the state is not loosing money, the more people play, the more they gain. Even on those roll-down days. It stops when people stops playing on the "regular" weeks because they feel cheated.

  • It would appear that the 200 or so thumbs down people are all great speakers but……not too intelligent. If you want to learn things in life sometimes you have to forget the medium and focus on the information being transmitted. Great talk. Thank you.

  • misleading title, should be "How to be not wrong"

  • I was not expecting the whole talk to be about the lottery.

  • I am really disappointed in the audience for letting the Manhattan joke fall flat. Shame on you all!!

  • Fascinating! Great lecture – thank you for uploading.

  • I think that you are making an error in your presentation. The new odds on the roll down day were calculated on the basis that if the same number of tickets were sold as the previous non roll down day then the number of small prizes would equal the jackpot that had not gone down.

    Note that in a normal game if the jackpot goes off multiple times in the same game then the winners have to share the jackpot.

    This is not the case when there are smaller prizes.

    So the reason why the state could not see why the roll down days lost money is that under normal circumstances the number of people that play the lottery is static.

    But with the influx of money from the clubs then assumptions go out the window.

  • Here's a better idea – Only play the lottery if you think you will lose ! ie Dont play the lottery if you think you will win !

  • Imagine hearing this voice first thing in the morning…

  • I'm a mathematician and I gave up on this after fewer than 15 minutes. it doesn't help that he says "math" or that he stopped talking about dollars only to replace them with Euros, which we don't have in the UK either, whether we're playing Euro Millions or not. Whatever his point was, I wish he'd have got to it quickly.

  • Half way in to this video and this guy is still droning on about a lottery in massechusets and still has not addressed the title of his presentation.

    Why are americans always so manipulative.

  • My favorite Econ teacher would say Ummmm all the time. He was an amazing genius. As a result …Ummmmm…..I am in the top 5% of earners in the USA. i only wish I could be in the top 1% but I grew up in section 8 housing.

  • At 8:08, the prize for getting 2 matches is a "Free ticket" being sold at $2, and not $2 in cash. The actual worth of the ticket for the winner should be the expected value of the ticket. So the equation should read:
    x = ($ 1 million/9.3 million) + ($4000/39,000) + ($150/800) + ($5/47) + (x/6.8) where x is the expected value..
    Solving for x gives the expected value as 59 cents.
    So much for "Mathematical Thinking"!!

  • His book was insanely good

  • I recently saw an interview on 60 MInutes on CBS and it was on a rather clever gentleman, and his wife, who figured all this out and made many millions of dollars, over the years–and they are making a movie out of it! Coming soon…

  • This guy loves maths

  • That is actually interesting and I loved the contents of the speech but MAN, his voice, how annoying!

  • Yes, but can maths prove that white men are not always wrong about everything?

  • Nerds broke the lottery. I love that story so much.

  • I'd have a soar throat after 5 minutes and be gasping for air, lying on the ground.

  • Ya what's new.

  • Lotteries should be illegal

  • maths not math

  • Apparently none of the people in the comments has come across his book "How Not To Be Wrong: The Power Of Mathematical Thinking".. Try reading it and it'll remind you how ignorant you are.

  • Why didn't the state do anything about it? Because state employees are seldom M.I.T. graduates.

  • Great book… very entertaining read. Got it from the library, but when I finished I had to go buy a copy just to have, cus I love having cool books (especially cool math books). This is a cool one.

  • better at 1.5x… he already has a chipmunk voice so it seems a bit more natural somehow…Ummm, ya

  • At around 3:50, I understood that he was actually talking about "rational intuition" : intellectual constructs leading to science and philosophy (real philosophy, not Oprah's "feel good" psychology for lemmings). Mathematics is a "hardcore" consequence of such constructs, a tool that we've invented to aid us for such endeavor in "materialistic" science.

  • The talk is good. The book is great. I am on the 2nd read and find it to be one of the better maths books I have read. Any engineer or engineering student should get much from this book simply from the exposure to applied statistical mathematics. Thank you for a wonderful book.

  • So these people robbed a bunch of poor people? Nice!

  • Would've been nice if one of the regular players that lost money on that had sued the state for arbitrage

  • Expected, value IS what one would expect, however on average. So why not just use the term average expected value instead?

  • He made his explanation of why/how he chose his numbers much more complicated than it really had to be. His picks were simply the set of all 3 digit combinations that include a unique pair of 2 numbers. You will see that no combination will include the same 2 numbers (i.e you wouldn't use 1,2,3 and 2,3,4). There are 7 possible combinations which is why he said to select 7 tickets. Since you only need 2 number correct in order to win, you always win. So I would imagine that the MIT students did the same thing but scaled up and that the number of possible combinations using this method matched the number of tickets the MIT group was purchasing.

  • So Government is the largest Casino that always wins.

  • At the Royal Institute and he says "Math", he is wrong before he starts 😉

  • So the philosopher stone is real? url:

  • Why do people fail to recognise that the abbreviation of the plural word mathematics is "maths".  How can this be so difficult ??    Physics, another plural word has an "s". Do some simple learning !!!   [Aussie in BC]

  • Very nice, i'm going to keep my eye on the lottery in my state now.

  • this guy gave them literally one minute (while still talking) to pick 7 sets of 3 numbers from 1 to 7 before asking for someone to call out. and flashed a set as well. I still didn't understand the transylvanian lottery until he'd gamed it once. Way to ruin an opportunity for fun interactivity.

  • The "power" of mathematical thinking = Atomic bomb

  • This is what makes thi "mathematical" nonsense so boooooooriinnng.: the fact that its all done in order to figure out how to win at idiot games. My solution : Who Cares ? Maybe if he applied it to something interesting, it might be fun to listen. I'm leaving.

  • Slow-moving goofball. Needs to speed it up. He's not funny.

  • This is miraculous work. I love it. Great job presenting this information ℹ️ 🌀🌀🌀

  • TLDR; "I'll tell you a half story about how young kids at MIT won the lottery several times and you have to buy my book to know how it ended"

  • And the moral is … don't do the lottery :0)

  • I consider myself VERY fortunate to have been exposed to formal logic in an 'advanced' 9th grade class, as a subset of… GREEK PHILOSOPHY?!? This stuff should be taught to EVERYONE, starting in the third grade, until everyone 'gets it.' The only problem would be, it would kill off the advertising industry, people would have to make products that WORKED right, not sound attractive. The churches would take a big hit, too. I went on to study logic more deeply, out of interest, but jeepers, you can really get the gist of it spending several minutes reading up on 'logical fallacies' over at Wikipedia, then train yourself to APPLY it. Oh
    wait… what he's talking about the lottery is the tip of the iceberg, our entire economy depends on a whole bunch of people acting really, really stupid.

  • Damn the delivery is painful…

  • "There's" is a contraction of "there is" and refers to a singular person, place or thing. Your grammar indicates that you do not understand the notion of "singular" and "plural". "Plural" refers to more than one person, place or thing. "They're" or "there are" is the word that you seem unaware of. "They're more than you can imagine…".

  • Man this was tough to get through… His speech paterns are off putting.

  • You don't need any weird geometry to hedge your bets on the lottery tickets, this overcomplicates things dramatically. You just need to avoid picking the same numbers too much and not picking other numbers enough. As a programmer, I find this natural… as you generate tickets, just keep track of how many times you've picked each number, and always pick from the least-picked ones.

  • Lotteries are a TAX on the masses who buy tickets!!!!

  • Do socialists play the lottery?

  • At around 10:10 he says the European lottery has a 0.40 expected value so its worse than the Mass lottey, but 0.79 cents on a 2$ ticket is also 0.40 expected return… Not very good math for a math guy (still enjoyed the video)

  • great stuff but where´s the q and a ?

  • Great story about Abraham Wald, and great video.

  • An interesting talk.
    I wonder what would be the shape of the connected lottery number geometry be capable of being represented in 2d?
    Always been fascinated by geometry and the nature of geometry. It's good to know new insights in geometry are being made all the time.

  • Yah I wish to be as smart as U

  • Just confirms the saying that lottery money transfers money from the poor to the rich, not vice versa.

  • Being right all the time sucks.

  • To Ask, Is the Riemann Hypothesis true? Is akin to asking, is the Prime N2, the only even Prime out to Infinity?! Of course the answer to both questions is YES! And we prove it by Intuition, Logic & Common Sence. -1+0^0/2+1. Qed.RH.TM PROVEN!!!

  • Lovely stories. Making logic and math interesting. He knows and loves his subject. The negative comments must be some form of jealousy….

  • what's the definition of parallel?

  • This is exactly how I think
    I don't let others set up the question

  • lol you may not download academic articles on a guest account, but we don't mind that you scam people out of millions of dollars of lottery investments
    mit logic

  • 28:11 those are permutations, no?

  • google is the same thing. fist they put their friends at the top.. so your business gets cheated., then the monopolynsotes rais prices everywhere so you pay AGAIN.. then they demand everybody do SEO optomization, whichngets passed on to YOU again..
    but heres the mathematical insight.. youre not just paying thee times..
    THE MARKET BELONGS TO THE PEOPLE.. somthat money should go,to the state.. so,younhave to pay again Three more times.. the missing taxes must be made up by you. Google is theft SIX times over. totally rapeing the u.s. marketplace. ..

  • WAIT!! So why does it make sense to fill in lots of tickets by hand and not automatically?? I missed that part. Did someone invent an algorithm to pick random numbers that is more likely to win a lottery than mere chance?

  • This needs to be made into a movie.

  • I love his book.

  • That moment at 24:25 … Made me laugh. "…You are the house!!"

  • Philosopher: Is it right to make weapons of mass destruction?
    Scientist: How can we make bigger bombs and cause maximal damage?

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