@@standupmaths Your maths in this video is incorrect. Please see my comment for an explanation of why. You have assumed the probabilities across different tickets are independent, when they are not.
Though I like math jokes I love whiteboards (and maths). Please, do make more "Matt Parker explains..." because I found them (at least this one) quite enjoyable and interesting.
Thanks for making videos WITHOUT Brady. I prefer your simple and non-distracting shooting by leagues over his nauseating and idiotically, purposely, artificially clumsy camera style. As far as I am concerned, you two can be within any proximity in applicable dimensions as permitted by quantum physics all you want, but as soon as it becomes an n>2-some by means of adding his cameras and/or, sanity beware, Sean Riley and his cameras, for the love of all that provides reference points to human senses, please, please, please endeavour to rarefy yourself from such constellation.
A long time ago I heard someone say that the National Lottery is a tax on people that are bad at maths. I've always thought it was quite close to the truth.
+Symon Fobbester I guess people who are mediocre at maths think that it is quite close to the truth. But let's take this one notch up. You see, money does not have linear value compared to the amount. Losing the buy-in is almost always insignificant, but winning the jackpot is hugely influential in an average working/middle class person's life. Actually this is something about which Matt should plan an episode. The non-constant value of money with regards to amount, also time, also disastrous outcome.
Taurwathwylth the problem is the chances of winning the jackpot in your lifetime are very slim. losing the buy in once, twice, maybe even 10 times is insignificant, but if you do the math if there was a 1% chance of winning the jackpot (which the chances are actually significantly lower than but for sake of example lets just go with it) there is a decent chance that you could pay the buy in 100 times and not get a jackpot. in fact with the lotteries odds winning the jackpot could require paying the buy in thousands or tens of thousands of times and there is never a guarantee. if you pay for a lottery ticket once a week for the rest of your life and never win (which is the likely outcome) you have thrown a crap ton of money down the drain for nothing the jackpot is the only thing that could justify the cost and it is extremely improbable that you will ever get it..
+stalectos Hehe, that's true, but luckily the value of money is also non-constant with respect to time. You win the jackpot immediately, at one single moment, but you invest the money in small increments, it adds up only during the course of tens of years. These two things are not immediately comparable. Actually you can think about the lottery as something where you take damage in the expected value but accept to pay premium in order to gain variance. This is not much different from paying for insurance! Insurance is actually the opposite in one way, you take damage in the expected value but accept to pay premium in order to reduce variance. Both of these may be completely OK things to do even though they will have negative expected value.
That all assumes that the financial "investment" is the only benefit to playing the lottery. People also get pleasure from the excitement and anticipation of playing, whether they win or lose, and that pleasure has a value too.
I can't speak for anyone else but I quite enjoyed this. It got me thinking about other questions, like how much it affects your odds if you reinvest everything but the bonus ball winnings, because those are rare enough to not affect your odds very much and 50,000 pounds is presumably quite a lot. (Pounds are more than dollars, right?) Anyway, I would definitely watch more of these if they got made, but I think creators should make what they like making so the most important thing is whether you want to do this sometimes or you'd rather focus on the more jokey, goofy stuff. But you do this incredibly well. Also, on a technical note, look into your camera's light settings, they were kinda going all over the place. I don't know how noticeable that is to the average viewer, but as a fellow creator and video editor it was bugging me. I've definitely struggled with stuff like that on my own projects and I still haven't gotten it to fully stop, but figured I'd mention it.
Oh wow, that explanation of the hypergeometric distribution was astonishingly clear. I never learned it that way, but it makes so much sense if you think of it like that.
+SpySappingMyKeyboard You clearly didn't read my comment since I didn't mention series at all. Or you did read my comment, but are completely ignorant about distributions.
Please make more of these explanation videos. I always asked my professors during undergrad how what we were learning could be applied to real world situations, and too often I was told it couldn't yet, or that it was for engineers later to figure that out. Thus, naturally, videos like this satisfy that side of my intellectual curiosity.
Please keep doing this! I'm learning about this stuff in college and this makes so much sense. I totally understand whats going on with a geometric series now. It's nice to watch entertaining educational-like videos for once.
I love the full math explanations. In the scenario where we win enough to buy 25,000 more tickets, how do we pick our numbers? It seems like there should be a strategy to cover as many possibilities as we can to maximize how much we can win again.
Super entertaining to watch! That's exactly what I'm having in high school right now, and it's exciting seeing it applied to the real-world happenings. Math is so powerful as it can translate so many things to simple and clear representations, and then work with them! Hoping to see more of your videos.
Loved it. Yours is one of a few channels I watch with my 6 year old at bedtime. Please keep making videos, I love that my kids are digging math because of folks like you that make entertaining videos.
I'm a maths teacher in York and I talked about your first video with my year 11 class today as we started revision of probability for their mocks. keep it up! this was cool ;)
Watched right until the end and really enjoyed it! I think a lot of your subscribers are subscribed because of your personality and the fact that you are excellent at explaining things, so either format is great!
Big problem being that you still have a 9/10 chance of not winning anything from your first play, thereby canceling any additional winnings thereafter. Love your videos matt, keep it up, thanks for the maths themed entertainment.
i loved this video "matt parker explains" videos are generally more understandable for me compared to the others as i think this one went at a slower pace but i also love the other videos i just love every video you make you are awesome!
I actually quite like this video format as well. I learned some things from this one beyond just cute little anecdotes, and you're still very entertaining to watch! This problem seems quite similar to how one might go about calculating the odds in a roleplaying system with iterative rolling rules. Perhaps you could do a video about that sometime? You could start with a relatively simple system, like Shadowrun's, then maybe move up to White Wolf's (the most complicated I know of) for the advanced second half of the video. The latter is a question that has stumped every mathematician I've ever asked who's taken a crack at it. To state the problems reasonably formally... Shadowrun: -Roll a number of d6's based on the character's skill and attribute ratings summed, typically between 2 and 18, with a mean somewhere around 6. -A number of successes is required to accomplish a given task, typically anywhere from 1 for a near-trivial task, to perhaps 10 for an extremely difficult task. -A result on a given die of 4, 5, or 6, is a "hit". -A 6 (in the case I'm interested in, in which a point of "Edge" is spent to change the roll to the non-trivial open-ended version) adds another new die to the roll, which can then iterate infinitely. -If the roll succeeds, but with more than half of the dice showing a 1, the result is a "glitch"; the task succeeds, but with some little thing gone awry. (For example, the character hits his target with a gun, but the gun fails to eject the cartridge properly and thus jams). -If the roll fails, and more than half of the dice show a 1, it's a "critical glitch" and the gamemaster gets to have fun. ;) So, what is the probability of rolling a success of target number of hits H, and optionally (since it seems far more trivial), of rolling a glitch or critical clitch as well. White Wolf: -Roll a number of d10's based on the character's skill and attribute ratings summed, generally between 2 and 12. -A number of successes is again required to succeed, in a task, as determined by the game master. -The target number on each die that counts as a success is also determined by the game master in this case. -As before, a 10 results in a die added to the roll, which can interate infinitely. -This time though, a 1 actually subtracts from the number of successes. -If there are any 1's left over after a failure, it's a critical failure and something Very Bad (tm) happens. If there are 1's with no successes whatsoever, on any of the dice, it's even worse. So, what is the probability this time of rolling a success of target number of hits H and per-die threshold T, in this system which can iterate in both directions? It seems very similar to this new lottery system, and I'd be curious to see what you think of it.
i wish you were my maths teacher, i love hearing you explain al lthe fun parts of maths rather than just "heres what you need for the test because the school says so"
The tricks of math, the nomenclature, heck even the history of the symbolism which led to the deeper discoveries of abstraction. All good ideas to explain. Some people just like to solve problems, and they need real world applications to wrap their minds around what the math is used for. So, yes please do more of both.
That was well presented. You kept it moving, jargon free, and the matter didn't require too much domain knowledge. Also, the content was relevant to a current real-world situation - very important to allow viewers to see an application.
I've enjoyed this video so much, it's pretty fun to see explanations like this. You should continue doing the "Matt Explains" videos. (I'm not saying that your other videos are boring, I also enjoy them, so continue doing both kind of videos) :D
I frankly did not understand the vast majority of that, but nonetheless enjoyed it because I like Matt's voice, especially when enthusiastically solving huge complex mathematics.
I think a mixture of both types of videos are great, keep it up! You should do Matt Explains differentials and integrals and Matt Explains tensor maths next!
Hey Matt, huuuuge fan of yours, I love your book, your videos, your numberphile stuff, all that, and I absolutely loved this video. Keep this up, and obviously keep up all the other awesome videos you were already doing!
Excellent, more Matt Explains please. There are lots of maths videos that out there but few that capture the joy of mathematics as well as this. Thanks R
You should do more of these as they are very interesting. Coincidentally, this is a similar topic to the a level stats work I was doing earlier and your way of explaining it is very clear.
Just finished Humble Pi...it's really good. I knew probably half of the stories in there but love the character and pace of the writing. Unfortunately MP chickens out of giving a strat for lottery numbers. And I figured one out when I was in school. Surely go for a set that people choose the least frequently so that when it's a winner it's more more likely that you are not sharing the prize. So avoid all numbers under 32 (especially under 13) and avoid numbers in sequences (like squares, primes, cubes, Lost bunker sequence) and multiples of 5.
on a microbe level scale, the friction of the balls moving around in the pot affects the outcome by a very slight bit, and since when a ball is picked it experiences less friction when its fairly static on the table, we can assume that the other balls maintain higher contact amounts per second (basically they bounce around more). so if you choose ANY number the following lottery, avoid the numbers last picked because they will have more density by a miniscule amount because of the friction in the pot. this will change your odds by about 0.002% at the very least, given the size of the balls and how often they are used.
That is a good point! Don't worry: the joke-based videos will continue. I just wanted to check if people would like a parallel stream of more-mathsy ones.
Thanks for the video! You should definitely make more of those! You may poke a little bit into Brady's territory there, if you're not careful, but other than that I think it's pretty nice to have maths explained to you by a charismatic person for a change, instead of those boring old maths professors we have in Germany
+d3rrial Very true. Matt was my maths teacher when I was 15; and if it wasn't for him I never would have taken an interest in mathematics (and probably never gone to university). The teacher makes such a difference.
Although I missed the jokes, I think the appropriate answer to any question that starts with "Should Mat Parker make a video about" is "yes" so long as it's not illegal or non-math related.
This does not say that buying a lottery ticket is a bad decision. It is a "good" decision if 1. The jackpot is over 90 million pounds (or, if you're willing to do more work, the sum of the prizes times their probabilities is at least 1 times the cost of a ticket, but the easy way out is to ignore all the lesser prizes), or 2. You get at least 2 pounds of enjoyment out of a lottery ticket. (About 30 years ago [still in the days of print newspapers] Sally Forth berated her husband Ted for buying a lottery ticket. He replied that it was "cheap insurance". She said "insurance against what?" "Boring meetings." If you start working on finding odd perfect numbers, you tune out the meeting [been there, done that] and miss important stuff. [Yeah, importance is relative, but when someone signs your paycheck they have kind of a big say in that.] Daydreaming about jackpots eliminates that risk -- you're still there for the meeting. But the comic is not well indexed and I can't find the one I'm looking for.)
The last math class I ever took was statistics my first semester of college almost 35 years ago. There are 2 specific things I remember from that class. First, how to calculate a factorial. Second, my professor explaining "The lottery is a tax on stupid people." I'll admit I have occasionally paid that tax, usually during very large jackpots. But I never saw it as an investment, even for a very generous definition of invest. Rather, I looked at it in terms of a former slogan of the NY State Lottery, "a dollar and a dream." I think that was probably the most honest lottery slogan ever. People (well most of them) pay not out of a real expectation of winning, but so they can dream about what they would do with the jackpot. They are really paying for the dream because as another former NY State Lottery slogan said "you need to be in it to win it." That particular slogan was technically accurate (I believe Matt's favorite type of accurate) but a bit misleading given the odds.
Your presentation skills are just the right mix of crazy geek and warm human :) I followed this all the way I think because I like probability and knew the Lottery odds to be very off putting. However, human logic shows that someone will win and you "gotta be in it to win it" ........... but betting on a random horse in any race would probably mean more return, given no chance of millions of your local currency. Its enough to put me off. I am not a gambler, so the Lottery was just a Saturday morning thing while buying the weekend paper, when I used to do that Love your work and I have a few popular maths books including Simon Singh's and Adam Spencer
it was really good, especially because few videos seem to cover the maths behind interesting problems. either they show qualitatively a interesting topic. or their dryly going through 30 lines of proving the chainrule
I think a mix is good. Some very funny vids, with little thinking involved (for when our brain tired), some in the middle with a bit of humor and a bit of thinking, and some like this where you explain how things work out. Actually I'm glad you went into the mechanisms of how the numbers are selected. When I watched your first vid, 45 million seemed way too low, and I calculated 59^6 = 42 billion because I didn't realize numbers couldn't be repeated.
I thought I followed you pretty well throughout. Then came the summation. I noticed that both the Free Games and Buy Games odds ended in 99, when my inner Gump was suddenly seized by a brain cramp. Yup. That's the bit that got me. It was followed by a strong desire to retrace my maths history far into the past. ... I'm wondering if perhaps I never really gave thumb-sucking a proper go. !O.o! -Phill, Las Vegas (Pulling your leg, of course. You boggle the mind, Matt, but with such precision that my mind truly doesn't mind. Always a pleasure, sir. Carry on.)
35+ years ago my grandmother bought all her grandchildren 5 lottery tickets - one of mine won $5. I asked her to buy me 5 more (she lived in Ohio, I lived in Arizona). She said, "Oh, no one ever wins the lottery, just take the $5;" - and refused to do it!
Yes! Whiteboard teaching is great! While there are lots of other maths videos and presenters available, i still think that in a typical classroom of students, there are a wide range of ways that people learn best. This method is great because it's like a 1 on 1 tutoring, where it's easy to simply rewind and watch the part not understood. Although it's been a long time since I was in school, I sure hope that students today are going online to watch these videos. Especially when they don't understand what's going on in the classroom, since lessons are based on the previous classes work, making it so easy to fall behind. ... or loose interest because one gets so far behind. I failed math a few times, until i got it right as i didn't understand the core concepts behind it. If RU-vid was around back when i was in school, i would probably have done much better. Fortunately, i can now watch all of these videos, so to simply have a better understanding of how math is used in everyday things. Keep up the great work!
Learning about probability and infinite series is much more fun when you don't have to worry about a test coming up that could decide whether or not you'll finish your degree on time.
While I am certain these style videos will have less broad of an appeal, I think they can be great educational tools. You are far more entertaining even without jokes than my maths professors. I would totally say it is worth it to do more Matt Explains videos should you find the right subject. Thank you.
I once did the math to determine the odds of winning the lottery. What I discovered was that buying a ticket provided no significant improvement in my chances of winning vs not buying a ticket.
Good job. Its a great refresher on some of this for an old engineer that hasn't done combinations/permutations and factorials in over 20 years. Financial sanity, not worth it, - unless you write a book about "how I won the lottery and didn't let it screw up my life" and it becomes a best seller. But that's still not a good strategy as the odds there are terrible too. But yes, for the entertainment value its better than most forms of entertainment you can spend 2 pounds on, right? Here in the US its about $12 to see a movie in the cinema (9.21 pounds)... and a week of dreaming and planning and wishing may give you a better joy value than 90 minutes of unknown happiness in a dark room at 4.5x the cost.
Whoa, as a long time numberphile fan, my head just exploded a little. Thanks for responding. Just want to say I love your stuff and hope this channel keeps growing and becoming awesome. Also, your calculator unboxing videos were the best surprise I didn't know I wanted.
When you explained the geometric series, I recalled my Calculus III professor pounding into our heads the idea that you cannot claim that the series goes on forever and you cancel one with the other for each term; otherwise setting "r" to be anything larger than 1 will yield ridiculous results that are obviously not true but aren't very obvious as to why they aren't. It is a difference between two series with an equal number of terms, with the number of terms approaching infinity. There always remains one term not canceled, but that term approaches 0 as the number of terms approaches infinity.
I loved it...mainly because I like having my strategy confirmed... I choose a set of numbers, put the ticket price in a savings account and enjoy my weekly small winnings as the draw takes place. After around 20 years of doing this, I have sacrificed winnings of about $170 and have a savings balance of about $15,000
I'm not a math scholar but this seems to imply that if you're u were to specify a particular amount as a jackpot, I.e. $10,000, parlaying any winnings on a gaming table (ex. Roulette) slightly increases your odds of winning, perhaps even enough to overcome the house odds on casino games?
Two reasons why I don't play lotteries: 1. The average player loses money. 2. The more times you play, the greater your odds of becoming that average player. Your odds of making a profit basically start out low, then get worse over time, thus making the lottery an effective tax on the poor and elderly due to the demographics.
It was nice to get a refresher on the geometric series - something I haven't had to encounter since middle school. Also, not knowing how the British lottery system works, it sounds like the jackpot amount is really unfathomably small compared to the odds of actually winning it.
![Matt Explains: The Lottery [featuring: Choose Function, Infinite Geometric Series]](/img/logo.svg){kind=logo}
