These 27 tickets guarantee a win on the Lottery 

Matt, congratulations for making the least depressing video on RU-vid that involves a middle aged, unshaven, man comparing lottery numbers on his couch in a dark room with his dog for company.

It would have been hilarious if 1,000 mathematicians all read the paper and bought the tickets; won the big prize; then had to split it...

You actually won two tickets. The ticket [8, 14, 18, 20, 40, 44] has 8 and 20 in it.

Back in the early 90's when NZ lotto was only 6 numbers from 40, I spent waaaay too long working out how to manually fill out tickets, to guarantee 3 numbers for $10. I mean, every combination was accounted for.... I filled it out to plan , and got 3 numbers.... I won $5... Half my spend, but I'll always remember how proud I was, that I worked it out! And now I watch your videos, because math is fun to work out 😂

@11:10 I thought that "random numbers live" is a proud tradition on this channel. If anything, compared to "Generating π from 1,000 random numbers", "2,000 throws of three-sided coins." and "Matt flips a coin 100 times.", these 7 numbers from a gravity pick lottery machine are nothing to write home about. By the way, I personally think that air mix machines are more fun to look at. But I'm not from the UK so I don't have much reason to complain about what the UK National Lottery does.

Actually, you won *two* lucky dips, on 12 22 32 33 56 57 and on 8 14 18 20 40 44. (Looks like you forgot to mark 8 on your tickets.)

Don't gamble is solid advice.

I remember when the lottery changed from 49 to 59 and it was marketed as more numbers to choose from. The odds went up considerably and there were many times when there were no wins.

The non-zero amount of Skylab content in this video pleases me! I love how elegant the maths is for making this work with 27 tickets.

“It’s okay, I have a system.”?? How many better opportunities could you have to say “It’s okay, I’m a standup mathematician.”?

Wow, almost 8 years since you covered the lottery on the main channel! Love when we advance the original plotlines like this.

Quite interesting! It does raise two questions though: (1) How many tickets will you need to be sure you have at least 3 matching digits? (2) And how do their likelihood of profits compare?

For what it's worth, Matt, a piece of paper with only tons of numbers is exactly how many many people do their lottery tickets. Sadly, most expect the clerk to input the numbers, so I'm happy to see those little scantrons in use :)

Imagine the universe in which he just happened to win the jackpot and had to figure out how to turn that much money back in to the channel

I remember when the 6/49 came to Canada. They ran a huge ad campaign on, "How are you going to choose your lucky numbers?". They had a Mom say its the ages of her children, a guy using the years his parents were born and the year of his first car. You get the picture. A year later, they ran a campaign in which people in the ads were congratulating their friends and family that "their lucky numbers" were drawn, and the friends and family hitting their heads on the table etc because they lapsed in buying a ticket. Evil

Matt, the first 20 seconds of your video is amazing. Thank you for making this video.

That was great! I was able to follow you! I went back and saw the pattern work!

I liked this video alot tbh, just seemed more down to earth. Truly highlights that you're just a nut job 24/7 haha (I mean that in a nice way) keep up the good work you inspire this 21 year old who had a mandatory understanding of maths throughout school to keep learning new things. I'm sure I'm not the only inspired one here either 👍

I think this was back in the 90s or early 00s, but I recall this competition where someone won the chance to do lottery for 50k, and now I recall that amount, it was almost certainly pre-euro (finnish marks, 1 was worth 17 cents in 2002 when we switched), and she won nothing. Or presumably she got like, a bunch of two number hits, but basically nothing compared to the time spent filling out 50k worth of lottery tickets. Which of course tracks because lottery is a waste of money.

This perfectly demonstrates why you don't do lottery. Even with math you buy 27 tickets and get 2 right to win basically nothing. In Finland it's otherwise the same but the numbers are 1...40, they roll 7+1 numbers and you have to get 3+1 to win anything (2 euros, which is twice the ticket price). You have to have 6 correct to win anything worth mentioning (I guess 40e is worth mentiong for 5 correct, but nobody bothers to say they won 40e on lottery, 6 correct is 1600e this week).

I did similar with a lottery in my state. I even wrote a tidy little spreadsheet program to semi randomly generate the number sets after spending multiple hundreds across 2 weeks (14 drawings), I only came up with one day that paid more than I spent that day. most of the time it was never more than 20% over spending

When trying to invite my dog on the couch when Matt asked his, he first was standing exactly between me and the screen, but now has settled next to me🐕🐾

Came for the maths, stayed for the dog.

bizarrely I did this math on fixed odd football betting back in the 90's. Worked it out on a psion, using some basic matrix calculations. Not the same approach but it put me off gambling ever after. Wish I'd had the platform and courage to show what I'd worked out. Unfortunately the psion has long since passed away. Used it to rewrite my employers annuity calculations as well. Which got me a disciplinary followed by an a award when they realised what could be done. Happy days!

You bought 27 tickets and won 1 extra ticket. Now that's what I like to call PROFIT!

Thanks, matt, your videos are like my guilty pleasure... i think some of my people would make fun of me for watching math videos for fun but ur videos are so good. lol

True story, when I was learning programming in uni I made a random number generator to guess lottery numbers for my state but there was a bug in my code and it would only pick numbers in the 20’s it was late and I missed the deadline for the drawing but I decided to watch the drawing even though I didn’t play and wouldn’t you know all the numbers picked were in the 20’s.

This video was super chilled and a great Sunday watch.

I imagine all of his video ideas start with him getting a notification and exclaiming "New maths!"

My dog went nuts during the walking in the street part. As soon as it ended he settled down. We tested it five times every time we rewound the video to that part, and it's any part of that part, the dog instantly reacts. All other parts of the video - no reaction. Totally weird. I wonder if there is a background sound that I cannot detect that the dog is detecting somehow?

Wow, your dog is a fantastic actor.

I was looking forward to you ticking the numbers off your tickets in real-time like a bingo pro!

Real gamblers know you only need one ticket to win big

My personal preference on lottery is to play with sets of rows which have minimal possible overlap between each possible pair of rows on these sets. One might argue that such play reduces "clumpiness" of winnings although it certainly doesn't improve chances of winning the jackpot or even getting even. Just that individually random rows don't really have statistical guarantees over a set of rows played.

Dude...I'm going and getting 30 tickets right NOW.

Moral of this story: Even if you're doing lots of fancy maths, the lottery is statistically a losing bet.

Thanks for making an awesome video!

The numbers went from 49 to 59 in the past few years, right? Off the top of my head, I believe there was no two ball prize, though, just £10 winnings for three. Would be interesting to see if and how this could have been exploited back before the change, and whether you're more likely to "win" before or after

40 years ago here in Ontario we had the 6/39 lottery. Match 3 numbers and you got a prize. My idea then was to cut a dowel into39 pieces, number them and draw them at random until our group had 10? different tickets. We won something almost every week but never a substantial prize.

Would be interesting to see how many twos there was in that week compared to other weeks

From a National Lottery email "In Saturday’s Lotto draw, match 3 main numbers and instead of winning the normal £30, your prize will be boosted to £60*. Double the celebrations!". That is for Saturday, 5 August 2023. So there is now about 1 in 4 chance of making a net £6. The £60 for three matches is a guaranteed amount and does not depend on the number of winning tickets. I wonder if the National Lottery people have read the paper and decided to up the ante.

I loved everything about this video!

Fascinated by the box of switches on the desk!

The true irony is if you had played the numbers on the paper you would have made 4 matches of two

Hi Matt, great video. Is there any chance of a diagram of 5 and or x6 number combo's? it would be a great help.

hey does anyone know the name of the song at 0:15? I tried searching it with Shazam but it leads to this weird title that is clearly not the actual song, can anyone help?

Its nice of skylab to remember your lead. Australians can be a real menace when not properly trained.

Congrats on the new book, Matt!

Love how eager Sky is in the intro. Reminds me of that old British kids' show _Come Outside_ with Pippin the dog

Oh man, that message notification got me TWICE!

I love the framed comma on the wall!

11:15 Random Numbers LIVE, my favorite tv show.

Imagine this was brought to you by DraftKings 🤣

The gimbal spin was super satisfying.

Are you shooting for an April 1 release of your new book?

My dogs went nuts from this video. They must be really excited about lottery numbers.

Are you going to record the audiobook yourself again? I absolutely loved listening to Humble Pi, and I’m sure whatever you’re cooking now is worth making an audiobook out of it!

0:20 seconds in and I’m already loving this video 😂

Your dog is very cute and clearly uninterested in becoming a youtube superstar. Her expression at 12:44 made me chuckle.

Matt Parker: You are such a nerd that you are mathematically the most satisfying kind of nerd for another nerd to watch.

I wish I was good enough at math to do this for the Australian Powerball 😂

That's cool! I know you said that the winnings would go to the channel. Does this mean that if you lose money, you will skip the next release? :( By the way, have you seen the Mathologer video on the pigeonhole principle? I thought it was pretty nice!

MindYourDecisions posted a video just like this like an hour before you uploaded that's wild

Hmm, times have changed. When I was a kid there were only 49 numbers and prizes started at 3 matches.

Well before watching, I think this must be related to some kind of 2-system or 3-system with blocks of size 6, such that any two blocks share at least 2 numbers in common. That would indicate a symmetric system, aka a projective plane if it's a 2-system, and the goal here would be to construct 27 blocks s.t. any possible block of size 6 would fall into some possible projective plane with at least one of the 27 selected blocks. So this should be an optimization/packing problem, and since I don't see an immediate combinatoric relationship between 27 and 59, (the number of numbers in the UK national lottery, which I assume is the lottery in question), I'm going to guess that it isn't a perfect packing problem, and there's some "wasted space", but that it is impossible with 26 tickets. I kinda hope that hadamard matrices, (which are directly isomorphic to incidence structures such as 2-systems, as it happens), play a role in determining the optimal packing algorithm. I am, however, too lazy to work out a solution before watching, so at this point I will just watch.

This is the same thing as the card game where you have to find the matching character

My biggest takeaway from this is actually "That looks like a Labrador" to which my brain immediately rebelled and stated "Ofcource it is a cozey wozey woofsey Labrador, the statistics for it not to be would boggle the mind!"

I honestly thought WHSmith was only in Airports around the world

Aha, I worked out something similar when I was younger. Back when it was a £1 a ticket in the UK, I used to buy a similar number of tickets once or twice a year and I always won something (often a few things at once).

What's the story behind the comma wall art?

so how many tickets for n matching numbers?

How would you adapt the generation process for the ticket for any size of pulls for example what if instead of 59 number in the pool the was 80 and what if instead of 6 ball pulled there was 5 I'd be interested if someone could explain it :)

There are many ways to pick your numbers , python scripts ,random number generators ,or manually picking numbers. Picking numbers manually isn't always the best option and people have bias against picking certain numbers .

I've seen a couple of mathematicians react to a certain video so far, but I've really been wanting to see you cover Animation vs Maths by Alan Becker. I think you'd get a kick out of it.

the first shot of the video was so cute! New Maths!

11:37 there you go, 21 and 37 appearing on the lottery, cheers from 🇵🇱

Wacthed the video, great by the way...but how did you come up with the list of 27 numbers?

Can your planer chart be expanded to hold 59 numbers in one chart? I image that doesn't work for some good math reason. Love your work.

I need Matt to make a bluesky account only to hear him say "skeet" out loud

Didn’t realise you had a second account, I’ve been following your main account for several years. Surely this topic merits being on the main account.

Any systems for thunder ball ?

More dogs and walks in town please! I don’t know where that is but its beautiful, and the pup is too

This video reminds me that I believe all the lotteries in my area don't let you pick anything. You just buy the tickets and get random numbers. To be fair though I don't look into lotteries very much and just get a ticket when one of the 2 big ones get up stupidly high because it's fun to think about it.

Hi Matt. Great video and explanation. I've got a similar math problem, and have been unable to calculate the answer. Perhaps you can lead me (or create a video) on the correct direction to get to the answer. The question is: How many tickets can be generated where no 2 numbers are repeated on any of the generated tickets? In Canada, we have 49 numbers and have to choose 6 numbers. At first, you would think ( 49 ! 2 ) / ( 6 ! 2) = 78.4 (or 78 tickets) But wait... not so fast. That's not possible because a single number cannot appear more than 9 times on the total of the tickets. Why is that? Let's take the number "1". On the first ticket "1" is with 2, 3, 4, 5 and 6. On the second ticket, "1" is with 7, 8, 9, 10, 11 and 12. (and so on and so on until...) On the ninth ticket, "1" is with 42, 43, 44, 45 and 46. This leaves only 47, 48 and 49. That's not enough to create a tenth ticket, and hence those combinations are wasted. So... A better limit would be (9 x 49) / 6 = 73.5 (or 73 tickets) But wait... not so fast. No matter how hard I try, I cannot get even near 73 tickets without hitting some kind of duplication. So, what is the real limit, and what do the results look like? Thanks, Edward.

9:39 "If I _happen_ to win any money." Me: mhm, yes, of course

teh intro alone makes this video worth watching

The system has the priorities all backwards. A 2-number win is the worst outcome: If you win big, then you are making more money than you spent on the 27 tickets. If you don't win at all, you can just stay at home. But if you win a 2-number prize you have to go back to the lottery place just to not let some loose change go to waste. In reality, I'd want a system that *minimizes* the chance of having a 2-number win, not one that guarantees it. Then again, it is nice to know that if you were planning to play exactly 26 tickets every week, the guaranteed won ticket means that the 27th ticket is essentially free - if you view it as decreasing your chances of low wins (which are now 2,3,... tickets with a 2-number combination instead of 1,2,... of those) while increasing your chances of high wins (for example a 27th chance at winning with 6 numbers).

Great video

Great Video. Now if you want to go super-nerd: try one of the US systems with a multiplier ball that has fewer numbers than the regulars (MegaMillions?). Yes, it happens to be high right now, and I'd love to win; but pure coincidence. And/or break the lottery system: combinations that would guarantee a profit.

Hey Matt, here in 🇩🇪 we luckily habe 6 out of 49 only, ok plus an extra number. How many tickets would I need for 6 out of 49? Or even generally n iut of m? 🤔

go to dog school to walk your well-mannered dog in a dignified manner

new title: How to go -26x in the UK lottery GUARANTEED

You may not have cashed in, but you’re very lucky to have that sweet dog.

I’m not particularly good at mathematics but I’m proud that I guessed that it uses the Dobble math

00:53 Though I think what's actually being said is, "Come on, let's go" -- I briefly heard & presumed your dog is named Scone. "Come on Scone!"

It would be cool to display the drawn numbers on the graphs and work out the winning tickets from there

Amazing that he tells people "I have a system" and not "I'm a mathematician"

I would like to know how many other tickets won with the bonus ball? Seeing its a perfectly valid ball to be used it surely counts as an additional point?

To increase your chances of winning more money, only play Lotto when there's a Jackpot Rolldown. This is roughly once a month when no one has won the jackpot. For example, on the 10th February 2024, all the lower tier cash prizes were boosted. The normal payout for 5 winning numbers on Lotto is £1,750, but boosted it was £4,323.

Is there a standardised way to do this? With that I mean: between a choice of X numbers, the amount of combinations needed to get at least Y numbers matching a selection of Z? The diagram method above appears good for two numbers from a selection of 6 from 60, but for a selection of 5 from 50 it seems not that practical.