The Bingo Paradox: 3× more likely to win
ฝัง
- เผยแพร่เมื่อ 11 ก.ย. 2024
- Details on where you can buy Love Triangle in the USA: bit.ly/3wCTesR
Or if you just want it from Amazon, this is my affiliate link: amzn.to/4fy30Ph
For people in Europe, signed UK copies are still available on Maths Gear: mathsgear.co.u...
The box set you should not buy:
achievefulfilm...
Paul Catherall shop:
www.paulcather...
And now for some actual links that pertain to the video itself.
The Bingo Paradox by Arthur Benjamin, Joseph Kisenwether & Ben Weiss
www.tandfonlin...
Also here: digitaleditions...
10,000 Stand-up Maths bingo cards: www.dropbox.co...
10,000 Love Triangle bingo cards: www.dropbox.co...
I heard a rumour you should listen to the podcast A Problem Squared. open.spotify.c...
Huge thanks to my Patreon supporters. They took very little convincing to make fun of me via the medium of bingo card suggestions. / standupmaths
CORRECTIONS
- None yet, let me know if you spot anything!
Filming and editing by Alex Genn-Bash
Written and performed by Matt Parker
Additional performance by Skylab the Dog
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson
Dice on loan from the Bec Hill collection
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinran...
UK book: mathsgear.co.u...
5:22 not the first time Matt has ignored the diagonals in a square grid like this
Lfmao
Wah wah wah
@@deleted-something Lfmao?
A diagonal acts the same as a horizontal
😂
He totally forgot to mention the paradox:
For each individual bingo-sheet, the chance for a horizontal line is the same as for a vertical one.
But if you play against other people, the chance of someone's horizontal row winning first increases. Up to 73% when you play against all the other existing bingo cards.
Yeah exactly - people are saying it's entirely intuitive when you know the distribution, but it's incredibly dependent on the parameters of the paper. As they themselves state, their simulation of 1,000 cards only got to 2:1. Intuition takes us in two different-but-similarly-wrong directions here, very cool.
Thanks for this comment, the video made no sense at all to me
now *that* is a cool fact
After being given the premise I thought about this for like 3 minutes said oh it's not the odds of your bingo card getting a horizontal versus vertical first it's the odds of whoever gets done first having that and that person can make anyone and then I unpause the video and he says that immediately
It's strange how P(H) and P(V) change with n. Intuitively I'd expect that if 1000 cards are playing, the probability of a vertical win becomes higher than horizontal.
Tested this by playing bingo with my 75! closest friends and its true
Reminds me of a mol of moles in the what if comics by Randall Monroe.
You only needed a quadrillion or so friends.
@@OriginalPiMan Yeah but he's not an introvert
You mean your [(15 choose 5)⁴ × (15 choose 4)]−1 friends. (according to Matt[note1])
75! is the number of possible drawing sequences for the 75 numbers; the max number of bingo cards is less.[note1]
note1: Actually, would it not be (15 choose 5)⁴ × (15 choose 4) × (5!)⁴ × 4!, because once you choose x numbers for a column, you can then order the numbers in the column x! ways to get Bingo card that are different? Am I wrong?
Wolfram Alpha reports 552 septillion, which is still less than 75!.
imagine being someone's 75!th best friend
This video has taught me that I had absolutely no idea how bingo cards are actually constructed.
Same, but I wouldn't (or I should say don't) worry, cause "proof by turning it over" teaches us that even Matt thought the same way lol
yeah as soon as he said that the bingo card is oriented I knew what the proof would be.
Matt sitting down to crank out some jpegs:
✋Number the bingo cards 0000 - 9999
👉Number the bingo cards 00001 - 10000
"Proof by turning it over" is the best math proof I've heard.
Proof by… just… 🔄
Also how to prove a car starts.
Everyone forgets that the sciences were essentially considered magic until fairly recently, math included.
And SunPup, it was invented by the machine -- not by the humans who programmed the machine.
Yet here Joe2501 is trying to tell us the sciences are not magic... Sheesh!
@@TheDavidlloydjones I don't consider there to be a distinction, honestly.
Fun fact about bestseller lists, they're based on the *number of books sold to bookstores* not the number of books bought by individuals, so a lot of it comes down to the publishers convincing bookstores that a given book will sell well so they should buy more of them. Really a truly bizarre system.
Edit: Note, I'm not saying the book isn't good, just highlighting one of the many ways companies lie and deceive by omission
So I guess we should only pay attention to books which stay bestsellers for multiple weeks, because that at least demonstrates that the booksellers did sell enough of them to justify buying the same amount the next week.
Much like the analysis in this video, it is simplified for practical reasons.
They are also pretty easily gamed. Some books, particularly books by celebrities or political people are commonly bought by the author's agents etc to pump them up the best sellers list and then often given away.
Interesting, cuz he did say he committed to a large amount of first editions so I wonder how that effected his placement on this list
@@LeoMRogersnah, this would work only if everyone knows how "best selling" works. There always will be people who think "bestsellers are about how many people bought"
Just don't bother if you see a bestseller on the cover, buy things you potentially might like instead
I'm just going to point out that the third book on the list (under Matt's) is simply called "MILF"
Glad to see people are actually getting Bingos on this video. I wouldn't have put it past Matt Parker to generate 10,000 "random" bingo cards and plan this video out in such a way that you are always JUST one square shy of a Bingo.
Ah yes, a Parker bingo.
That would be a great prank for a bingo game. You could choose 5 numbers to remove from the tumbler. Then print cards where the 5 numbers block every row, column, and diagonal. There are a lot of ways to arrange it, so it wouldn't even be very obvious.
Then everyone would win at the same time on the 71st draw if they didn't start a riot already.
I was expecting him to have either done that *or* to have found a way to include all seventy-five things in this one video.
694 is one off in 3 places :3 (interestingly one is vertical which is what you would expect w/ a 1:2.8 ratio i guess?)
I got two parker bingos on my card :c
(card# 04750)
2nd collumn, just missing "Matt catches something" - I need to rewatch for just this but I didn't notice it
and 4th row, just missing "Special remix of the theme music" - there's a couple bits of different music but they don't seem related to the theme.
Bingo on 1296 at 22:49. Diagonal consisting of “Instructed to write something in a comment,” “Printed Research Paper Appears As Prop,” Null, “Spreadsheets,” and “Number larger than 10^10”. I’m counting the table as a spreadsheet.
Diagonal is described in this video as not being a win condition.
@@Sinoxa2 No, they said they're not including in the calculations for simplicity's sake. It's still a win condition.
Bingo! I got all the earliest possible wins already at 01:39.
I won simultaneously with the following 4 plates:
1935 at row 1, with 01, 06, 09, 12, 13
2635 at row 3, with 01, 03, 08, 10, 13
6277 at row 0, with 00, 03, 08, 11, 13
9628 at row 2, with 01, 11, 12, 13
These are the assumed matches:
00: 'Matt's books in the background' at 00:00
01: 'Regular polygon visible in video' at 00:00
02: 'New object on the shelves in the studio' at 00:00
03: 'Matt is wearing a blue t-shirt' at 00:00
04: 'Matt's coffee mug isn't facing branding-side out' at 00:00
05: 'Sports-related video' at 00:00 (Questionable)
06: 'Stock video effect' at 00:03
07: 'Matt interacts with on-screen graphics' at 00:05
08: 'Shout out to patreon supporters' at 00:11
09: 'Matt credits a viewer for doing something better than he can' at 00:11
10: 'More detail included in description' at 00:21
11: 'Instruction to write something in a comment' at 00:42
12: '"Ridiculous"' at 01:14
13: 'Matt mentions his book' at 01:39
14: 'Prop appears from under table' at 01:40
15: 'Unboxing or unpackaging an object' at 02:23 (Questionable)
16: 'Multiple Matts on-screen' at 02:30
17: 'Matt catches something' at 04:03 (Questionable)
18: 'Whiteboard' at 04:58
19: 'Time lapse' at 05:01
20: 'Printed research paper used as a prop' at 06:54
21: 'Terrible python code' at 07:34
22: 'Number larger than 10^10 used in video' at 09:53
23: '"Maths!"' at 11:00
24: 'Future matt' at 14:55
25: 'Past matt' at 15:08
26: 'Matt has a drink of coffee' at 15:50
27: 'Spreadsheets' at 22:48
28: 'Skylab appears on camera' at 22:58
29: 'Bad pun' at 25:13
30: 'Matt is standing up' at 27:30
31: 'Camera person Alex mentioned' at 30:05
32: 'Producer Nicole mentioned' at 30:06
33: 'A problem squared mentioned' at 30:12
I did also get all the other 1070 possible non-questionable wins. These are the first 100 of them, with horizontal or vertical matches (matches do not appear in the order on the plate)
1935: row 1, with 01, 06, 09, 12, 13
2635: row 3, with 01, 03, 08, 10, 13
6277: row 0, with 00, 03, 08, 11, 13
9628: row 2, with 01, 11, 12, 13
0633: row 2, with 00, 09, 13, 14
1764: row 2, with 00, 11, 13, 14
3072: row 3, with 00, 04, 08, 13, 14
0197: row 2, with 10, 12, 13, 16
2500: row 2, with 10, 12, 13, 16
5247: row 2, with 07, 11, 13, 16
5838: row 2, with 11, 12, 13, 16
6180: row 2, with 07, 09, 13, 16
7827: row 4, with 06, 10, 12, 13, 16
8406: row 3, with 07, 08, 10, 13, 16
0052: row 2, with 01, 07, 13, 18
1108: col 0, with 04, 09, 10, 11, 18
1236: col 0, with 04, 09, 10, 11, 18
1368: col 0, with 04, 09, 10, 11, 18
6178: col 0, with 04, 09, 10, 11, 18
8736: row 1, with 01, 07, 08, 13, 18
9917: col 0, with 04, 09, 10, 11, 18
0196: row 0, with 02, 07, 16, 18, 19
1435: row 4, with 08, 12, 16, 18, 19
2116: row 2, with 00, 03, 18, 19
2364: row 2, with 00, 07, 18, 19
2674: row 4, with 01, 03, 06, 18, 19
3296: row 4, with 02, 03, 04, 16, 19
3438: row 0, with 01, 06, 11, 14, 19
3609: row 2, with 00, 12, 18, 19
4193: row 2, with 01, 07, 09, 19
4257: row 2, with 01, 04, 14, 19
4502: row 2, with 14, 16, 18, 19
4576: row 0, with 01, 03, 04, 06, 19
5214: row 2, with 10, 14, 16, 19
5375: row 4, with 00, 02, 04, 14, 19
5387: row 3, with 02, 11, 14, 16, 19
5687: row 4, with 02, 11, 12, 16, 19
6217: row 2, with 01, 03, 10, 19
7173: row 2, with 03, 10, 16, 19
7555: row 1, with 01, 03, 06, 11, 19
8344: row 3, with 00, 06, 10, 12, 19
8985: row 2, with 01, 03, 11, 19
9440: row 3, with 00, 08, 09, 12, 19
0162: row 2, with 07, 09, 19, 20
6159: row 4, with 08, 12, 13, 18, 20
6771: row 2, with 12, 18, 19, 20
7422: row 0, with 02, 10, 14, 19, 20
8057: row 4, with 02, 03, 04, 13, 20
8177: row 3, with 04, 06, 07, 19, 20
8304: row 1, with 08, 14, 18, 19, 20
0662: row 1, with 01, 06, 11, 12, 21
0690: row 3, with 06, 12, 16, 18, 21
1029: row 2, with 00, 07, 10, 21
1050: row 2, with 00, 07, 18, 21
1280: row 0, with 00, 03, 06, 11, 21
1513: row 1, with 01, 08, 14, 18, 21
1567: row 2, with 01, 09, 12, 21
1805: row 2, with 10, 14, 16, 21
1903: row 2, with 04, 12, 16, 21
2170: row 2, with 03, 11, 20, 21
2171: row 2, with 01, 04, 12, 21
2346: row 2, with 01, 09, 14, 21
2903: row 2, with 07, 11, 16, 21
3358: row 2, with 09, 14, 20, 21
3465: row 2, with 10, 14, 20, 21
3608: row 2, with 03, 04, 16, 21
4031: row 2, with 00, 11, 14, 21
4616: row 2, with 03, 04, 20, 21
4758: row 1, with 01, 06, 07, 10, 21
5198: row 0, with 00, 02, 07, 18, 21
5868: row 2, with 01, 10, 12, 21
6003: row 3, with 00, 07, 08, 11, 21
6624: row 2, with 09, 14, 16, 21
6665: row 1, with 03, 06, 11, 20, 21
7497: row 3, with 00, 06, 11, 12, 21
9362: row 0, with 08, 11, 14, 16, 21
9665: row 0, with 07, 08, 18, 20, 21
9684: row 2, with 00, 09, 12, 21
9893: row 2, with 03, 10, 16, 21
0095: row 2, with 01, 04, 14, 22
0541: row 2, with 04, 07, 16, 22
1083: row 2, with 07, 16, 18, 22
1213: row 4, with 06, 14, 16, 18, 22
1763: row 1, with 02, 03, 11, 20, 22
2515: row 2, with 07, 10, 16, 22
2695: row 2, with 01, 12, 18, 22
2919: row 4, with 00, 04, 08, 14, 22
3850: row 2, with 03, 16, 18, 22
4118: row 2, with 03, 11, 20, 22
4555: row 4, with 06, 12, 18, 20, 22
5204: row 3, with 00, 02, 10, 12, 22
5307: row 2, with 04, 12, 16, 22
5538: row 4, with 03, 06, 11, 20, 22
5917: row 2, with 07, 11, 20, 22
6108: row 2, with 01, 04, 12, 22
6313: row 1, with 03, 08, 09, 20, 22
6478: row 1, with 00, 02, 03, 10, 22
7410: row 3, with 04, 07, 08, 16, 22
7411: row 0, with 03, 08, 09, 16, 22
7412: row 2, with 00, 09, 14, 22
The column/row ratio is as follows - 294 : 776
Here are the first 50 wins, if you include the questionable matches
1935: row 1, with 01, 06, 09, 12, 13
2635: row 3, with 01, 03, 08, 10, 13
6277: row 0, with 00, 03, 08, 11, 13
6900: row 2, with (Q)05, 07, 11, 13
8794: row 1, with 02, (Q)05, 07, 09, 13
8963: row 4, with 02, 03, (Q)05, 10, 13
9628: row 2, with 01, 11, 12, 13
0078: row 3, with 02, 04, (Q)05, 13, 14
0633: row 2, with 00, 09, 13, 14
1764: row 2, with 00, 11, 13, 14
3072: row 3, with 00, 04, 08, 13, 14
4084: row 2, with (Q)05, 10, 13, 14
0013: row 0, with 01, 08, 10, 14, (Q)15
0075: row 1, with 00, 08, 09, 12, (Q)15
1415: row 2, with (Q)05, 07, 09, (Q)15
1636: row 2, with 01, 03, 10, (Q)15
3699: row 2, with (Q)05, 07, 10, (Q)15
4665: row 2, with 03, (Q)05, 09, (Q)15
5228: row 3, with 02, 04, (Q)05, 14, (Q)15
5963: row 2, with 01, 11, 14, (Q)15
6050: row 0, with 04, (Q)05, 08, 14, (Q)15
6198: row 3, with 01, 08, 11, 14, (Q)15
7062: row 1, with 00, 02, 10, 12, (Q)15
7544: row 1, with 03, (Q)05, 06, 09, (Q)15
8253: row 2, with 01, 03, 04, (Q)15
8829: row 2, with 00, 04, 12, (Q)15
0197: row 2, with 10, 12, 13, 16
0781: row 4, with 02, 03, 09, (Q)15, 16
2151: row 4, with 02, 03, 09, (Q)15, 16
2320: row 2, with 03, 11, (Q)15, 16
2500: row 2, with 10, 12, 13, 16
5247: row 2, with 07, 11, 13, 16
5838: row 2, with 11, 12, 13, 16
5931: row 2, with 03, 04, (Q)15, 16
6180: row 2, with 07, 09, 13, 16
7827: row 4, with 06, 10, 12, 13, 16
8406: row 3, with 07, 08, 10, 13, 16
8800: row 0, with 03, 04, 08, (Q)15, 16
1024: row 0, with 02, 04, 14, (Q)15, (Q)17
1223: row 2, with 09, 12, (Q)15, (Q)17
2073: row 2, with 03, 04, 13, (Q)17
2825: col 1, with 00, 01, (Q)05, 16, (Q)17
3004: row 2, with 03, 11, (Q)15, (Q)17
3579: col 1, with 00, 01, (Q)05, 16, (Q)17
3895: row 2, with 11, 12, 13, (Q)17
4890: row 2, with 03, 04, (Q)15, (Q)17
5171: row 2, with 03, 11, (Q)15, (Q)17
6966: row 2, with 09, 13, 14, (Q)17
7257: row 2, with 09, 13, 14, (Q)17
7385: row 4, with 08, 10, 13, 14, (Q)17
Including the questionable wins, there are 1964 bingo plates with a full row or column
If there are any matches i missed, please do tell!
(Yes i gave it a go and wrote some terrible python code!)
Wow! Impressed by this data! The speed of which you gathered the cards, identified the timestamps, and produced the results is simply amazing! Respect!
The bingo cards that stands out to me would be any of them with bingo on rows or columns in 3 or 4 using your index. (Bingo sheets 643, 3473, 3988) What do these sheets have in common? Timestamp 5:00.
I believe Matt & team intentionally sandbagged the “G” and “O” columns and also the last two rows to not bingo. Why? Maybe to more quickly identify those false positives.
What you identified as a “stock video effect” at timestamp 5:00 (maybe something the term overlooked- time lapse) I’m guessing it was not a stock feature on their mind. If we exclude that, I believe it is an impossibility to bingo in column or row 3 or 4.
Nice work!
@@bradwilliamson6053 Thanks!
Edit: DISCLAIMER - this is with old data (fewer matches)
Also, quite an interestering theory.
Yes, if i remove "stock video effect" i do indeed only get results in rows and columns 0-2. Interestingly this also changes the ratio to column/row - 51 : 36, which is even more opposite to what's taught in the video.
I'm though not sure if Matt would do that on purpose. It seems very specific, and could just be chance? But of course you never know with Matt.
But there are also other stock video effects, I've changed to now use the "image sliding in" effect at 00:03.
would it be possible for you to also include diagonal bingos?
@@lazy_gamer Sure. I can't make my post that long though (10000 character limit it appears?), so here are diagonal wins sorted by completion time:
2632: diagonal from top left times: 00:00, 00:42, 01:40, 01:40
4841: diagonal from top left times: 00:00, 00:11, 01:40, 01:40
1952: diagonal from top left times: 00:42, 01:40, 01:40, 06:54
415: diagonal from top left times: 00:11, 01:40, 02:30, 07:34
4377: diagonal from top left times: 01:40, 02:30, 04:58, 07:34
5544: diagonal from top right times: 01:40, 04:58, 06:54, 07:34
6825: diagonal from top left times: 00:00, 00:42, 01:40, 07:34
8555: diagonal from top left times: 00:00, 00:42, 01:40, 07:34
9785: diagonal from top right times: 00:00, 00:42, 01:40, 07:34
2088: diagonal from top right times: 00:11, 01:40, 06:54, 10:58
2190: diagonal from top right times: 00:00, 00:42, 01:40, 10:58
6532: diagonal from top right times: 00:42, 01:40, 06:54, 10:58
6856: diagonal from top right times: 00:00, 01:40, 04:58, 10:58
2122: diagonal from top left times: 01:40, 01:40, 02:30, 14:55
3460: diagonal from top right times: 01:40, 06:54, 10:58, 14:55
8210: diagonal from top left times: 01:40, 01:40, 06:54, 14:55
563: diagonal from top right times: 01:40, 06:54, 10:58, 15:00
1365: diagonal from top right times: 01:40, 02:30, 10:58, 15:00
1462: diagonal from top right times: 00:00, 01:40, 10:58, 15:00
3684: diagonal from top left times: 00:00, 01:40, 07:34, 15:00
5530: diagonal from top right times: 01:40, 01:40, 06:54, 15:00
8092: diagonal from top left times: 00:00, 01:40, 07:34, 15:00
9651: diagonal from top right times: 00:00, 01:40, 01:40, 15:00
3280: diagonal from top left times: 01:40, 07:34, 15:00, 15:08
4327: diagonal from top left times: 00:42, 01:40, 10:58, 15:08
8317: diagonal from top left times: 00:11, 01:40, 10:58, 15:08
933: diagonal from top right times: 01:40, 04:58, 07:34, 15:50
2574: diagonal from top right times: 01:40, 04:58, 10:58, 15:50
4510: diagonal from top right times: 00:11, 01:40, 07:34, 15:50
5602: diagonal from top left times: 00:42, 01:40, 01:40, 15:50
8859: diagonal from top left times: 00:11, 01:40, 10:58, 15:50
9751: diagonal from top left times: 01:40, 10:58, 14:55, 15:50
1907: diagonal from top right times: 01:40, 02:30, 15:00, 16:03
2058: diagonal from top right times: 00:00, 00:11, 01:40, 16:03
2279: diagonal from top right times: 01:40, 14:55, 15:08, 16:03
2333: diagonal from top right times: 01:40, 02:30, 04:58, 16:03
2422: diagonal from top right times: 01:40, 14:55, 15:50, 16:03
3450: diagonal from top right times: 01:40, 04:58, 06:54, 16:03
4037: diagonal from top left times: 00:42, 01:40, 15:50, 16:03
5010: diagonal from top left times: 00:00, 01:40, 04:58, 16:03
5146: diagonal from top left times: 00:42, 01:40, 06:54, 16:03
5409: diagonal from top left times: 01:40, 04:58, 06:54, 16:03
5713: diagonal from top left times: 00:42, 01:40, 02:30, 16:03
8420: diagonal from top right times: 00:11, 01:40, 15:50, 16:03
9848: diagonal from top left times: 00:00, 01:40, 04:58, 16:03
1368: diagonal from top left times: 01:40, 04:58, 07:34, 30:06
1990: diagonal from top left times: 00:11, 01:40, 16:03, 30:06
2771: diagonal from top left times: 00:42, 01:40, 10:58, 30:06
3947: diagonal from top right times: 01:40, 01:40, 15:00, 30:06
46: diagonal from top right times: 01:40, 02:30, 10:58, 30:12
242: diagonal from top right times: 00:00, 01:40, 07:34, 30:12
1580: diagonal from top right times: 01:40, 10:58, 15:50, 30:12
2121: diagonal from top right times: 01:40, 01:40, 15:50, 30:12
3042: diagonal from top right times: 01:40, 01:40, 15:08, 30:12
4280: diagonal from top right times: 01:40, 15:08, 16:03, 30:12
4330: diagonal from top right times: 01:40, 06:54, 07:34, 30:12
4332: diagonal from top right times: 01:40, 10:58, 15:08, 30:12
5664: diagonal from top left times: 01:40, 07:34, 30:06, 30:12
6060: diagonal from top left times: 01:40, 02:30, 16:03, 30:12
6348: diagonal from top left times: 01:40, 07:34, 15:50, 30:12
6731: diagonal from top left times: 01:40, 01:40, 15:08, 30:12
7341: diagonal from top right times: 00:00, 01:40, 07:34, 30:12
7428: diagonal from top right times: 01:40, 15:08, 16:03, 30:12
7558: diagonal from top right times: 01:40, 02:30, 16:03, 30:12
8485: diagonal from top right times: 01:40, 10:58, 30:06, 30:12
8939: diagonal from top left times: 00:00, 01:40, 07:34, 30:12
9177: diagonal from top right times: 01:40, 15:50, 16:03, 30:12
That's a total of 67 possible diagonal wins.
Props on this data!
Helped me check off another one on my card, but still no bingo haha
Next up, Matt pulls out the numbers 1 through 75 in order in one continuous take.
Sounds more like Derren Brown.
This isn't v sauce
Dream could do this, and claim it was all skill with a bit of luck.
And then he releases the full footage of him spending 2.480914e+109 times the length of a number pull in order to create that perfect sequence 😂
@@emilyrln That's not actually guaranteed to happen at all in that time. Could be that he gets the same, invalid sequence infinitely many times and never hits it. Could be he hits it on the first. That's the number of choices. The probability of hitting is 1/N, so basically 10⁻¹⁰⁹, and the mean is 1/p, so N, so the number you said. Therefore on average he would hit it on the 75!th time, but the variance is so insanely high that it's entirely realistic to even get that. There's a 50% chance within the first 10¹⁰⁹, roughly speaking. If you grabbed more universes than there are atoms in the universe, turned every atom into Matt and made him keep doing this for more times than there are atoms in the universe on average each Matt would finish around 10¹⁰⁹, with roughly 50% finishing before that and 50% after. Only 10% would have finished before the first 10¹⁰⁸ attempts. If you had to bet on the exact number of attempts that our Matt would get it at, you should still bet on the first one. Of all the individual attempts, it's always most likely that he gets it on the next one that happens. Obviously you should only bet that if you're getting a lot of money, more bills probably than there are atoms in the universe.
"How can that be?" "Oh they're not uniformly distributed."
I've never played actually bingo before, so I was really confused until I looked it up and found that this is how people, at least a considerable amount, actually play bingo
@@Thomas-uc4sg3 row of 10 number is the true bingo
Yeah, the moment I discovered vertical was pulling from a pool of 15 while horizontal was pulling from a pool of 75 this one became intuitively obvious
Yes. Not an interesting problem
It still is quite interesting. If I give you a bingo card and start drawing random numbers, it is equally likely for your first bingo to be horizontal as it is to be vertical. Yet in a tournament, it is more likely for the winner's bingo to be horizontal. I don't know if I missed it or if he just didn't mention this intriguing fact.
As our good friend Pythagoras used to say, "every triangle is a Love Triangle, when you love triangles"
Death comes to us all
Do the tooth's teeth have teeth too?
Or is it??
Or was it "Oh god, not beans"?
Bingo card number 2492 wins at the last possible moment, as at the very end of the video cameraperson Alex and A Problem Squared are both mentioned. Honestly, that outro felt like it was placed there specifically to make this precise bingo card win at the very end, kind of incredible.
Never seen this version of bingo before. The game I'm familiar with goes up to 90. Each ticket is 3 rows of 9 columns with 5 numbers and 4 blanks on each row. The columns are 1-9, 10-19 etc. You get a horizontal line and then a full ticket (house). You would usually play 6 tickets at a time which gives you all the possible numbers. There's no vertical win.
This video is American bingo rather than UK bingo. I'm surprised he didn't mention the difference in the video.
Bingo Card number 118:
0:00 NULL
1:40 Matt mentions his book
1:50 Prop appears from under table
11:00 "Maths!" (I decided "It's Maths!" is also acceptable.)
14:55 Future Matt
26:47 Timelapse
30:06 Cameraperson Alex mentioned
No bingo.
Full receipts!!! Well documented!!
what about coffee?
@@daveslamjamone imagines not on they card
16:03 There was an earlier timelapse
@@miladv6 There was an even earlier one than this where he drew the bingo card on the whiteboard but I don't want to go back and find it and I know it's earlier as I have only seen 10 minutes
Missed opportunity to call the center space the Parker Square; it wouldn't change anything, either, because one can guarantee there will be a Parker Square phenomenon in every video, thereby giving you a free space anyway.
By the way, the "someone wins as soon as possible" simplification also eliminates the diagonals completely, since if someone COULD win by a diagonal, they also could win via a horizontal line. So it doesn't matter which it is.
Ah, but you can win two ways diagonally with only four numbers but only one vertically and one horizontally, which does in fact change the maths.
Diagonal also has two different paths that only require 4, while horizontal or vertical only have 1 path each. So 50% of the possible ways to win @ 4 draws is by diagonal
Right, whenever a group wins horizontally, another group wins diagonally. Sometimes, these groups even overlap. Like, if numbers were drawn in order from B, B, I, I, N, G, G, O, then some people will get a double horizontal/diagonal win.
22:57 Dog loses interest once he’s got the math down, gets up and leaves 😂
British bingo cards are very different: nine columns and three rows, with five numbers and four spaces in each row. Columns are by ten. The pool of numbers goes from "Kelly's Eye" number 1 to "Top of the Shop" number 90.
This is only surprising because I didnt know that numbers on a bingo card aren't completely random. Knowing that each column is value limited makes this much less interesting.
Hey, I enjoy remembering combinatorics…don’t judge me
i wonder if there's a specific reason why it's ordered like that instead of just having it be random?
@@7oxytronI'd assume that because bingo is a game with a primary audience of older individuals it is made in a way in which it's easier for them to find numbers on their sheets. By putting lower numbers on the left and higher numbers on the right they then learn where they need to look subconsciously which makes the gameplay faster.
That's just my guess though.
@@7oxytron Ease of play. When the announcer announces "G53", you know to look in the G column to see if you got it. Having it completely random would make you look all over the card.
I guess it works this way to be able to scan for the numbers quickly, by knowning in wich column they can appear. At leas for the "pro" BINGO players 😅
16:50 Aren't you forgetting that any of those other pulls can be from column O, but not contributing to the specific row which wins? After all, exactly 5 of the 10 pulls do not contribute in this case. There's no special reason 3 of them can't also be from column O, unless I have missed something terribly obvious. To summarize, I believe the statement, "That has to be the first O that appears, because it's completing that row." Is false, because other O's can appear which do not complete that row before the winning one does. That said, since your distributions aren't ordered by specific column when you lay them out, I see no reason to believe this actually affects the maths proceeding it.
You forgot the early assumption that every possible bingo card is in play. As soon as there is a number from each set picked, a bingo is possible somewhere.
@@MGSchmahlI was wondering the same thing that seems to make sense
If every sheet is in place, then we would never reach 75 draws. So the rest of the math would be wrong.
You would only be able to 'shade' a 16 squares before you have to pick a winning square on the grid.
Ah haha that's literally mentioned right after I posted this
@@MGSchmahlI kept becoming confused, remembering this, forgetting it and becoming confused again. Like four cycles of the same realisation.
The square bingo card with B-I-N-G-O and 1-75 tends to be known as "American" bingo. "English" bingo uses 1-90, and the cards are a 3x9 grid with 1-10, 11-20, 21-30 etc. Wins only for horizontal, or a "full house" - all numbers on a card.
Further to that, the single "cards" are in "sheets" of several of the 3x9 cards (it's 5 or 6 from memory) - and EVERY number is on the whole sheet once - so if you bought a "sheet" for a game, you would always check off EVERY number. Of course, you'd only WIN if you matched a horizontal line.
So there you go - obviously somewhat of a different game - and mathematically TOTALLY different!!
If I remember correctly, the game Matt is playing is called Pongo.
There use to be rows of machines in seaside arcades,
6 cards on a sheet. 15 numbers per card. 3 rows as you said, with 5 per row.
Used to call bingo in australia, and we used this style. Each sheet had all 90 numbers in 6 groups of 15, each group of 15 in 3x5. Minor prize for first to get a line of 5, major prize for first to get a set of 15. Usually 30 rounds over 2-2.5 hours, a book of 25 + 5 individual rounds with larger prizes. 5 regular book games, then the special called at a slower pace, then 5 more book games, etc. With the final special round being very slowly called and for the large jackpot prize. usually around 50-60 numbers called before someone had a set of 15.
The two 'paradoxes' involved were first, that there were only 1000 distributions printed, the special sheets came in blocks of 1000. So if it was very busy, there might be more than 1000 sheets sold for the jackpot round, and those buying at the very end got the same sheets as those buying at the very start. Which meant that very occasionally, 2 people with an identical sheet would win.
And second, unlike most gambling, if you played long enough you'd almost certainly end up ahead, as the payout was normally more than 100%. Sometimes close to 200% if really quiet. Because this was in a club, and everything the club did, from regular bingo to restaurant specials, was run to encourage people to enter the club and use the poker machines. The 15-minute half time break and 30-45 minutes between sessions would see a big chunk of the bingo winnings poured straight back into the pokies. More than enough to offset the direct losses of a payout above 100%, plus to pay the staff to run it.
I've just commented that the traditional game I've always played is 3 rows with 5 numbers per row. And yes, we also play with a set of 6 cards that has the whole set of 90 numbers and we play to make first a line and then a 15 numbers card.
ca.wikipedia.org/wiki/Quinto_(joc)#/media/Fitxer:Jugadors_de_Quintu.jpg
Edit: Hell! I've just counted the holes on his own Bingo «machine» and it has NINETY holes!!!! So, he knows the real game has 90 numbers! He's been lying to us and he knows it!
Yes, this is Bingo as I know it here in Denmark (although we call it Banko). This 5x5 and 1-75 system is completely unknown to me. I was not even aware that alternative Bingo systems existed.
One slight difference here from what you describe: You can win on both a single row, two rows (on the same card), or a full card. When the game begins, numbers are drawn until someone gets a single row. The row is checked, and if valid the player gets a prize. Then the game continues until someone gets two rows (on a single card), and the same thing happens again, with a bigger prize. Then the game continues until someone gets a whole card, and the winner gets a big prize, often a gift basket of some sort. Then everyone clears their cards, and the game starts over. We don't usually use markers to make permanent marks on the cards, but use small semi-transparent plastic tokens to put on the numbers instead. This means that the numbers can be checked without removing the tokens, and that the cards can be reused. Sometimes in fancier Bingo games there are also "side prizes", which are smaller prizes for the people who happen to sit next to the winner on either side.
Thank God you finally re-enabled subtitles/closed captions. I can finally watch your videos again without trouble.
25:18 I got a diagonal bingo using card 699, with "Instruction to write something in a comment", "printed research paper used as prop", "Null", "Bad pun", and "Mat mentions his book".
I never thought I'd live to see the day but here it is
The Parker Square 2: Bingo Bogaloo
We are all of us blessed!
Well, you had a go at spelling "boogaloo" I guess
I love how Matt smiles when he is doing things mentioned on Bingo cards.
The important factor here is not only the groupings of numbers - it's also that we're looking for the first occurrence of a BINGO among many boards. If you instead ask the question "what are the odds that this particular board will give a horizontal or vertical BINGO?" then it's still an even chance of getting a horizontal or vertical BINGO, even though the numbers are separated into categories.
Indeed. And actually the number of boards needs to be so big that many boards start sharing the same sets of numbers in some rows or columns. That is where the difference comes from: the chance of a column winning is smaller than the chance of a row winning, but when a column wins, you have more winners simultaneously.
You need thousands of cards for this to become a substantial effect; that is rather unrealistic imho.
Yeah to me this is the more interesting aspect of the question that I wish the video goes into more. In particular, let's say you have a friend entering a Bingo tournament, and you are placing a side bet on whether your friend will win in a row, or win in a column. How should that side bet's payouts work? A naive interpretation of this video's result is that you should bet on your friend winning in a row as more likely, but in fact it's equally likely your friend will win in a row or column.
@@BrotherCheng Although the competition aspect complicates that scenario because they would likely stop playing once someone else won in a round, right? (Genuine question, I’ve never been to a bingo hall.) So the competition might need to, for example, work by playing until everyone gets bingo and score people by ranking how soon they got bingo in that round.
@@BrotherCheng Although the competition aspect complicates that scenario because they would likely stop playing once someone else won in a round, right? (Genuine question, I’ve never been to a bingo hall.) So the competition might need to, for example, work by playing until everyone gets bingo and score people by ranking how soon they got bingo in that round.
@@thenefariousnerd7910 No. What we were saying is that for large number of players, there will be simultaneous winners. You can have different Bingo cards and still win at the same time because you happen to have the same numbers on a row / column. You get more than one winners. But once someone won you don't keep playing.
The book was great. Honestly a fantastic intro to the practical applications of math, something I could have used when I was in school. Once my sons are a bit older I’m hoping they will enjoy it and find a love of math earlier than I did.
24:08 bingo. I waited for Matt to interact with a graphic for somewhere between ten and fifteen minutes. My bingo card is 00162.
1. Matt said the research paper simulated bingo with better code than he can make;
2. he used a printed research paper as a prop;
3. free space
4. Matt pointed at the bingo probability results; and
5. there were several timelapses but the first one was drawing the bingo card on the whiteboard.
My bingo was horizontal, appropriate but actually random, unlike number bingo.
i dont agree that there's a 'paradox.' the only reason its initially counter-intuitive is that people assume bingo cards are constructed randomly (as in the nth column is not restricted to numbers from 15(n-1)+1 to 15n). the moment it was revealed that not every number can appear anywhere the 'paradox' vanishes
Presh Talwalkar has a recent video where xe shouts at people who comment "But it's not a paradox if it is merely counter-intuitive at first blush!" about veridical paradoxes also counting as paradoxes.
@@JdeBP but this is not even counter-intuitive. It's completely intuitive, as long as you actually have all of the information.
@@JdeBP It's like someone calling something an Apple Orange Paradox and saying "how does this apple taste like an orange?!" only to reveal the apple was an orange all along. There's nothing paradoxical about it, they just gave the audience misleading information at the start.
I'd love to know the reason why bingo uses sets of numbers for each column up to 75 rather than randomnly distributing say, 99 numbers. 🤔
@@kentslocumIt makes it easier to check if you have a number, since you only have to check one column.
The number of possible bingo cards presented at ~10:30 is *incorrect* since the choose function does not count different orderings of the same subset as different. The correct number is 552,446,474,061,128,648,601,600,000 (~552 septillion / 5.52×10^26) given by the formula (15P5)^4×15P4 (the P is like C but it counts different orderings as different).
I was looking for this comment
I wonder if you also divide by 2 since every bingo card can be flipped vertically
I noticed the same thing
For anyone interested, the C means "choose" (unordered) and the P means "permute" (ordered)
The numbers in every bingo card I’ve ever seen are written lowest to highest, descending down each column. So Matt’s formula is correct here but this causes him to be incorrect later on when computing the probability of a horizontal win
@@maxmackie349 I think you are mistaken. Not only is the bingo card that Matt himself shows in this video not ordered numerically. And if you do a quick google search for images you'll see that virtually none of the results are ordered as you describe.
The french Bingo is very different.
3 rows, 9 collumns
15 numbers on (5 on each row, ranging from 1 to 90), the remaining 12 cells are black/null.
You then have 3 ways to win :
- complete 1 row, you then shout "quine" (5)
- complete 2 rows = "double quine"
- complete full card = bingo
Much more easier to figure out if rows are more likely than collumns with this setup :D
British bingo is identical. (9×3, five per row)
Congratulations on the sales! Thank you for all your hard work advocating mathematics
Before clicking on this I was thinking of UK bingo cards "well yeah there's going to be more horizontal line wins because you cannot win with a vertical line"
It immediately makes sense after you drew the bingo board and gave the number categories.
Having never played bingo with numbers, I was utterly baffled at how this could be true until that exact moment lol
yeah, after learning they were grouped like that the intuitive understanding makes sense. rows get to explore the more full probability which has more options each time, and columns have to stay in their lane.
So you're saying that the rest of the video is pointless?!
How dare you!
@@davidfinch7418 without the rest of the video we wouldn't get BBBBIIING
That plus the fact that it's about the winner from a group of multiple people playing. For any individual however the probability for horizontal and vertical are still the same.
True story - several years ago at a school PTO function there were t enough bingo cards so my wife made around 10 copies of one card and handed it out. I had a bad feeling about it but I got overruled. And as you’ve figured out, near the end of that last blackout game, when I called out the last number, 10 people all called out bingo.
They figured out prizes but it was a math lesson learned by all that night. Do not stack the decks against yourself hoping the random event never happens. Everything is random.
Like when I pocketed the money my wife gave me to bet on a rank outsider.
That cost me dear when it romped home by 5 lengths
This is such a funny random story!
@@David-xp7sr Oh man, couch for weeks?
Why would't you just make up cards with "random" numbers off the top of your head?
@@janTasita I assume because they needed to look actually printed out and not hand drawn on a blank paper. Much faster to run a copier than load up some software program and create 10 different pages.
"this is so silly" i say as i open the description to get my bingo card
I didnt get a bingo :( if only this was an ouside video
No bingo here either 2 ways missing only one though needed "Bad Pun" there was a bad joke but not a pun as far as i noticed, or the multiple Matts on screen which i could say happened during the lo-fi TV paused sections of explanation, but there was only ever one part of any particular Matt on the screen at a time. Fun game tough should we all start a tradition to play bingo for any future videos? Then if you win post BINGO!! with the time stamp and the number of the card you used.
@@robertmcmurry5489 Yes we should!
I needed him to use an unconventional measurement technique :(
I didn't get a bingo either, sadly. But I will keep my Bingo sheet for future Videos!
@@robertmcmurry5489I think the joke about putting numbers on the bingo was a pun
What is the probability that this entire video was a stealth subliminal advertisement for Microsoft BING?
Back in my day, paradoxes contained logical contradictions. Now, any math that takes more than one calculation to solve is a paradox.
11:00 🤣🤣🤣🤣🤣
"You can do it precisely, or rather, Wolfram|Alpha can"
🤣🤣🤣🤣🤣🤣
Wolfram Alpha knows...
The irony that the number Wolfram|Alpha gave him is wrong (not because W|A was wrong, but because Matt fed it the wrong formula)
BINGO! Card 6318 @13:47
How were you able to access a card more than 1000 away from the end of the list?
I my top-level comment: I mentioned getting stuck at card 00001 using reverse ordered list view.
Hmm maybe I should have tried scrolling up after reversing the order.
Edit: after reversing the order it starts adding extra items to the *top* of the list. no scrolling necessary.
Not any faster though.
@@jamesphillips2285 Dropbox is such a pain to deal with. I ended up installing the android app because I reeeeeaaaaally wanted to use a random number and not something higher up in the list. Turns out you simply can not search for files in shared folders on dropbox. The android app loaded all the files at once which eliminated the lag the website had lazy loading them and the scroll wheel that made it easier to navigate to the file I wanted. But then it took several tries just to export a file that wasn't 0 bytes. 🙃
It took me like ten minutes just to download a file - and I couldn't even get a bingo in the end (no. 4176) 😢
@jamesphillips2285 can't you just CTRL+F?
@@jamesphillips2285 I just scrolled down as quickly as I could to "about the halfway" mark and picked one.
@@lastchance1036 Nope Link to bingo card I want does not load in.
10:59 Matt: "It's Math's, you can do it precisely"
Me: glances at the equation for the perimeter of an ellipse. starts crying.
As someone who occasionally needs to calculate elliptical cross-sections for work.
Ouch, just ouch.
At least I've learned not to do it by hand these days.
Maths*
@@evanbasnawIsn't the perimeter of the elipse a multiple of a special trascendental number, just like pi is to circles?
@@leiferikson2210 Except every "eccentricity" (i.e. how squished the ellipse is) has its own special transcendental number that doesn't have any nice expression. For example, for an ellipse that's 4 by 5 the circumference is 10·E(3/5), but E(3/5) can't be rewritten as anything more familiar, all you can do is numerically approximate it.
@@leiferikson2210 (where E() is the "complete elliptic integral of the second kind")
29:25 Noo, it's the Mr Beast-trap. Random chance to get a unique prize, only if one purchases the box set. That's the lethal combination that turns this into an illegal lottery.
I was thinking the exact same thing.
Interestingly, no such law where matt is.
@@kingdweeb5065 the Gambling Act 2005 which prohibits lotteries without license?
@@kingdweeb5065 I'm not a lawyer, but I'm pretty sure it doesn't matter where the lottery is run; if it allows participation from the United States, it's subject to US gambling laws.
The don't look anything like bingo cards, at least not the ones I'm familiar with here in the U.K.
They are usually 9x3 and the numbers are _always_ sequential.
I know you live in the U.K. but is this based on U.S. bingo cards for an American audience?
#888 Vertical Bingo
0:06 - Regular Polygon Visible in Video (I figured a square bingo card counts??)
15:15 - Multiple Matts on-screen
4:04 - Matt catches something (Bit of a stretch but he did catch that ball from rolling off the table)
15:51 - Matt has a drink of coffee (I'm counting it as coffee)
27:31 - Matt is standing up
I wonder how many people buying "Love Triangle" don't look too closely at the thumbnail and just assume from the title that it's a romance novel.
Strategically titled indeed.
Soon to be a major motion picture, with Meryl Streep playing the part of the hypotenuse.
clickbait for books
@@_invencible_ more like advertisement, which is fine.
@@iteerrex8166 nah more like clickbait
are you sure it was a random 10,000 and not the first 10,000? we don’t want another happy little house.
Nice reference!
Find the happy house was an amazing bit of "figured everything out but overlooked that one detail". It's like a bit if code that compiles and runs without a crash first time but you don't find out until much later there's an off-by-one counting error in your algorithm.
About 10 minutes in. And I couldn't wait until the end :D.
If I get this right. It's essentially a bag of 75 items. Sorting them by color, we can say there are 5 colors, 15 of each.
We want to show that it's more probable that one of each color is picked, before 5 of the same color (or 4 of the middle one)
I guess the middle one isn't needed for all possible boards...
The verticals would be 2 more cases of 1 of each except middle color.
Edit: I mean diagonals... not the verticals. It's hard to type while trying to listen. :D
The moment I learned, that the numbers are grouped into the columns, I thought human intuition already tells the result of the paper.
Therefore I wouldn't call it a paradox.
It pains me that you kept not spining the bingo ball thing correctly. 😭 You are supposed to keep spinning it towards the back so it gets caught in that trough then it rolls to the front instead of falling out and rolling wherever
You can see he begins with rotating it correctly, but after lots of spinning fails to get a ball, so resorts to spinning it the other way
I think it's assembled the wrong way. The ball picker part only opens when rotated in one direction. So you can mix in one direction and then select the ball in other
Arthur Benjamin!! I had him as a professor and advisor. He's amazing! Best math professor ever. I took his class on special topics in combinatorics (which he said he would have called Benjamin 101 if the department had let him, since the class was just a survey of all his research). He had a section on this bingo paradox and the final exam asked us to derive generalized formulas for n×n bingo cards. One of the best classes I've ever taken!
I took discrete math with him, was a blast. Looking forward to intermediate probability next semester
Joseph Kisenwether (co-author) was a suitemate of mine in college, I love when these small world things happen. 😃
Came to the comments to look for other mudd students gushing about prof Benjamin! Class of 2015 here, loved discrete with prof Benjamin.
It's more than 15 choose five because the order matters, it's a different card if it has a different order of the same numbers.
yeah its actually 5.5245x10^26 different bingo cards.
EDIT: just realized that includes vertically flipped bingo cards which are actually the same when it comes to normal bingo. so its actually 2.7622x10^26 different bingo cards.
Also, just getting a number in each column isn't necessarily bingo, whereas getting five numbers in the same column is by definition bingo, so the probabilities are slightly closer together than Matt originally calculated.
@@samuelfitzgerald2025 I think he was assuming that, even though some people wouldn't have the numbers in the right column, there would be so many people playing that somebody would have a card that would have them all in the right column or row, as soon as the first opportunity of that arose. Actually, now that I think about it, that's probably the reason why he used choose rather than what's the other one called? He did it that way to factor out the existence of all possible combinations of numbers in each column under the assumption, there'd be one of each playing the game.
@@TedToal_TedToal yeah i think analysis is for the limit as n >>> the number of all possible bingo cards
The calculation is for the first possible win. Not all win possible
1:56 "hardback general, that's me"
*salutes* o7
Hardback General Parker, Sir!
00117
00:00 Null
1:43 book
5:00 Whiteboard AND special remix of the theme music (I think)
6:54 Printed research paper used as a prop
Maybe not the fastest, but probably the fastest diagonal one
It's not the theme song, I don't know what it's called but I'd consider it a very popular piece of music
Honestly the fastest is almost always going to be a diagonal, because there's only 4 lines that only need 4 items, and half of them are diagonal, with one being a much less likely vertical.
For the bingo cards created by Matt, how does the horizontal bias get introduced? In the actual number board it's because each column is chosen from small specific sets, so it seems feasible that it could be done in a similar way but wasn't explicitly mentioned in the video and easily could have. If everything was uniform then the intro was incorrect and people shouldn't ve winning one direction more than the other.
My guess is that each activity was assigned an arbitrary column, but I agree he didn't make that clear.
It's clickbait, nothing he talked about had anything to do with that bingo card.
There isn't an actual bias towards horizontal vs. vertical. What you're seeing is that there are more possible combinations on the rows than the columns - on any given bingo card you're just as likely to win on a vertical as a horizontal.. but when you have a *very* large number of bingo cards, the first one to win is more likely to be on a horizontal than a vertical (but if a vertical did win, it would win on more different cards at the same time). The columns have a lot more repeated bingos (for instance, you can have 1, 2, 3, 4, 5 and 1, 3, 2, 4, 5 both getting a bingo at the same time, whereas the horizontal lines don't have the same kind of equivalent).
I’ve never seen this style of bingo card before. According to Wikipedia, that’s the US 75 ball version.
I’m more familiar with the 90 ball version where tickets have 3 rows, 5 numbers per row, and the numbers are arranged into 9 columns, such each column has numbers from the sets 1-9, then 10-19, 20-29,…, and 80-90 in the last column.
I fancy my chances of getting a column before a row on the UK cards
Wait…what…then which column is the B column? The I column? Or the N,G, O columns? Or you don’t have that in your version?
@@VinTheDirector Correct, the UK Bingo card doesn't have letters at the top. It has 15 numbers from 1-90 placed in a 3x9 grid, spread across the 9 columns with 1-3 numbers per column pseudo-randomly (there may be some algorithm but I've never looked into it). It still "groups" numbers available to the columns (in groups of ten rather than 15), and each line has 5 numbers exactly. Columns do not score anything in UK bingo.
eg: (X = a number, o = empty)
X o X o X o X o X
X X o X o o o X X
X o o X o X X X o
Matt, being based in the UK but not actually native, may not have come across our version of bingo!
I was going through the comments, becoming more and more surprised that no-one had mentioned "real" bingo. I wonder how different it makes the chances.
I'm from Europe and I've never seen this. Apparently this is from the UK, but it seems less beautiful on its design, so I can't say I approve
I'm a bingo caller and also really like math and when I started my job at the bingo hall I quickly realized that the mathematics involved in bingo can get complicated - I wish people would make more videos about bingo math... for example, given a certain shape, how do you calculate the average number of balls being called in order for that shape to be completed - this problem takes into account both the likelihood of a ball coming out and the likelihood the number is in the right position on the card.
In your experience, how many balls do you pick before a bingo is called? Just on average. Presumably you want quite a fast turnover to keep the money rolling in.
I have questions as well. How likely is it for a game to go to the 17th ball under these assumptions. Assuming a hundred cards, how long would a game go? How long can it go? Under what conditions could you get to the 75th ball, and under what conditions is this no longer possible?
@@mb-3faze so it's obviously different for each pattern, but for a 1 line, on average I'd say between 8 and 11 calls, for a 2 line almost always between 20 and 25 calls. We do want them to be as fast as possible so that we can move on to the next game but that's mostly because we wanna leave on time, lmao
@@LlywellynOBrien I'll start with getting to the 75th ball - at the hall I work at this is nearly impossible as we have strips that have 3 cards and all 75 numbers appear once and only once per strip - we call these "perfect" or "dab-all" strips. Therefore, if we are going for a full card and even 1 of these strips are sold then there is a guaranteed full card on that strip on the 73rd call. In practice that will never happen already. Now, we also sell "random" strips and so if we somehow sold only random strips and by some coincidence every card within those strips had the same number on it, then it would be technically possible for that number to be the last one to come up, under those "dream luck" circumstances then it's possible to go to the 75th number - if that happened every single person would have a bingo on all of thier cards, lol that would be chaos
@@LlywellynOBrien I've seen a 1 line go to 15 or 16 but that's not very likely at all, it's tricky to try and work the odds on that though - tricky for me at least. I've also seen someone get a 2 line in 11 calls tho soo... questions like these are why I'd like more bingo math videos.
Most people will have 9 to 24 cards each so 100 is actually quite low
A short explanation:
Bingo numbers cards categorize the 75 numbers into 5 bins of 15. So in order to win with a vertical line, there needs to be at least 5 balls pulled from a single category (or 4 balls for the middle column). E.g. 5 balls from the B 1-15 category.
In order to win with a horizontal line, there only needs to be one ball pulled from each category.
This is a much more likely scenario.
Imagine an infinitely large bingo center with infinitely many senior citizens playing bingo, to the point where every possible bingo card is present.
In this scenario, then the win condition doesn't depend on the cards, it depends on the draws and whether a win is possible with the drawn numbers. A BINGO will occur as soon as 5 compatible numbers are drawn.
E.g. As soon as 5 B's, 5 I's, 4 N's, 5 G's, or 5 O's are called, there will be a vertical bingo. As soon as a single B, I, N, G, and O are called, there will be a bingo. OR as soon as a B, I, G, O are called, there will be a horizontal or diagonal bingo.
So the question becomes, is it more likely to draw 5 from any single column, or is it more likely to draw one from each column?
I swear to god I'd better not see that signed box on ebay in two months
Thank you so much for uploading at half one in the morning matt
It allows me to delude myself that I’m not up this late due to a lack of self control, rather I was able to predict an important upload
... I get to do this often. As an Aussie, 1am Monday morning has some of the freshest videos ever, it's a really healthy way to start the week
Ah, the classic drawing of a target after the arrow hits the ground
All 75K bingo cards have “because that’s just a mathematical fact” as the winning square
Card #00312 gets a horizontal win across the top at 10:06
dang, if i had picked 312 instead of 315 i could have had a bingo xD
I’m sorry, but I have to say this… as much as I love Matt Parker, he ain’t got nothing on Future Matt. Future Matt is just so much better at everything. he’s way more knowledgable and cooler, AND he’s from the future, which is just so hot imo
So, a non uniform distribution of the numbers, leads to different probabilities.
As beautiful as this is, I wouldn't call the fairly obvious a paradox.
This feels like it's missing some very important aspects of real bingo. Most importantly, this is simply figuring out whether it's more likely to draw 5 balls from any single column or 1 from each column. That's not how the game works though, so we have to assume that literally every possible card is being played. But for any given card, the order of the horizontal numbers on that card matter while the order of the verticals do not, which will favor verticals to some degree.
It works because we're taking the limit as the number of players grows to infinity, so we can assume that every possible bingo card is in play.
@@MGSchmahl but what if only 50 people are in the room playing? Is it still 75% chance a player wins via horizontal?
This paragraph from the introduction in the bingo paradox paper answered my question. Kind of wish Matt spoke to the spectrum of odds. It clears it up for me.
“.. when playing with a large number of Bingo cards, horizontal bingos are about three times more likely than vertical bingos.
By comparison, when playing with a single card, horizontal and vertical bingos are equally likely (and more likely than a diagonal bingo). But even with just ten cards in play, it’s still the case that the winning card is more likely to be horizontal than vertical, and that edge grows as the number of cards increases.”
So Matt spoke of the extreme case of all possible cards in play. And odds go down to 50/50 in the other extreme case of only 1 card in play. It would be nice to see graph of number of cards vs odds of horizontal win.
So in this video we find out how likely it is that a bingo game is finished by having a horizontal match on at least one card, compared to a vertical match on at least one card. On the other hand, there is no consideration on how many cards will have that match.
If my approach to calculation is correct: There are 15C5 significantly different versions of a column, so the chance of a bingo card containing the vertical row that can win is 1/(15C5) = 3.3^10^(-4). On the other hand, there are more variations for horizontal bingos. In the most simple case of a 5-number game, the chance of having the five numbers can be calculated like this: The likelyhood that the one-out-of-15 "B" number is on your card that contains 5 B numbers is 1/3. If there is no NULL square in the center, the chance of having a possible horizontal match on a card is (1/3)^5 = 4.11*10^(-3).
So if you have just one of the infinitely many cards, and a horizontal match is possible, the chance of *you* having a winning card is 0.411%. On the other hand, for a vertical match, the chance of *you* having a winning card is just 0.033%. Multiplied with the likelyhood of getting the possibility of horizontal or vertical bingo, this increases the disparity from 1:50 to 1:623 for your card to win with a vertical bingo compared to your card winning with a horizontal bingo after five balls. You might want to continue this evaluation for games not finished after 5 balls, as the ration between the chance for a single card to win horizontally vs. vertically will surely differ depending on the ball count.
Furthermore note that even this way of looking at bingo chances for a game with infinitely many players is not comparable with a game with only a few players, as in a game with infinitely many players, you won't ever have 6 or 7 digits from the same column in the set of drawn numbers, as one player will have a bingo as soon as 5 are drawn. With only a few players, the chance of a card with those five numbers being in play is quite low, so games with 6 or 7 balls from one column get relevant. This demonstrates the skew shown in this video is partly due to the fact that with infinitely many cards, the game is over as soon as a potential hit exists, no matter how unlikely it is, whereas in games with only a couple of cards in play, you have to consider the probability of a winning card being in play at all.
@@edwurtle Thank you. This felt like it would be the result but I had neither the time nor the confidence in my probability calculations to figure it out for sure.
#3391, the video was almost over and I just needed "It's so good", then you started talking about the box set and I thought, "he's gonna say it, I'm going to get a bingo right at the end."
28:40 he says "It's so nice!"
It would have been horizontal too.
I wish Matt showed a graph on number of bingo cards in play vs odds of horizontal win. This would make it more practical than assuming a winner as soon as possible.
This paragraph from the introduction in the bingo paradox paper answered my question. Kind of wish Matt spoke to the spectrum of odds. It clears it up for me.
“.. when playing with a large number of Bingo cards, horizontal bingos are about three times more likely than vertical bingos.
By comparison, when playing with a single card, horizontal and vertical bingos are equally likely (and more likely than a diagonal bingo). But even with just ten cards in play, it’s still the case that the winning card is more likely to be horizontal than vertical, and that edge grows as the number of cards increases.”
So Matt spoke of the extreme case of all possible cards in play. And odds go down to 50/50 in the other extreme case of only 1 card in play. It would be nice to see graph of number of cards vs odds of horizontal win.
would be pretty easy to model via monte carlo
100% agree!! This is what MAKES the paradox. Like the birthday paradox isn't impressive because if you get 367 people in a room, two people share the same birthday. That's obvious and boring. The paradox is that with just 23 people, it's more likely than not that two of them share a birthday!
The 'paradox' is the SPEED at which it goes 1-1 to 3-1 is unintuitive. This was such a bad delivery of this paradox - I'm not even sure he understood that the odds are 1-1 on an individual bingo card lol
Wait, what, how, when, why, where, how, wait, what, why would you write X as a backwards C connected to a C, when you can just draw two straight diagonal lines connecting one another on the middle like a normal person? I'm a simple man, this hurts my brain.
This is common among mathematicians. My understanding is that it's done to distinguish more easily between x and × (multiplication symbol) in handwriting.
@@ahlpym Oh, yeah that makes sense, i guess I've never considered that since i was taught to write the multiplication sign as a dot, for example 4 ⋅ 3 = 12, thanks for clearing that up =)
You are winning. My son had a 1 in 2m to survive and he is now 4 and doing AMAZING!
17:09 @Matt, it doesn't have to be the first 'O' that appeared, there could have been other 'O's called that appear on other rows that didn't complete the bingo. The "This must be the first O" only applies in your x5 system.
I noticed this invalid assumption for calculating X10 as well.
@@RobbBrock You're both forgetting that the if an O was already pulled, then the game wouldn't have won on an O being pulled since one of the other columns would be the last column to get their first number. Also that you can just relabel the columns in order that they get their first number pulled, since they're mathematically the same.
@@RobbBrockno, Matt is right. If O was already pulled, then the game wouldve been alresdy won at that point. The calculations are for the FIRST POSSIBLE bingo win.
Bingo card 7846 did not bingo even if you include questionable cases
0:00 Regular polygon visible in video
0:00 Matt's books in the background
0:00 Sports related video (questionable)
0:00 Matt's coffee mug isn't facing branding-side out (questionable)
1:40 Unboxing or unpackaging an object (questionable)
5:01 Stock video effect; transition
7:34 Terrible python code (questionable)
11:00 Maths!
14:54 Jump cut to condense long maths (questionable)
15:08 Past Matt
25:44 Matt credits a viewer for doing something better than he can (questionable (unclear if these people are also viewers)))
25:13 Bad pun
30:06 Producer Nicole mentioned
30:13 Problem squared mentioned
Even if you count the questionable scores (total 14), the card 7846 wouldn't have win a bingo.
8 scores, 6 questionable scores (Excluding free NULL)
**Extra stuff**
5:15 is really stretching "Unconventional measurement technique". I wouldn't count this.
Technically Matt is measuring the different probabilities but diagonals are being ignored.
I'm not good enough to understanding English semantics whether this is "unconventional measurement technique".
But if you count it as a score, that'd be a horizontal bingo at 30:06.
Otherwise 7846 is not a bingo winning card.
These were not mentioned in the video, but if any of them were, I would have had a Bingo
**orientation | missing case | Would've been a bingo at time stamp**
diagonal | Matt's facial hair changes mid-video | 11:00
vertical | Live show mentioned | 15:08
horizontal | It's so good | 25:13
diagonal | Video relating to a date in the calendar | 25:44
I guess one way to look at it is that horizontal wins are mostly independent across the entire population of players, while vertical wins are highly correlated. This is a theme that's come up in other videos on the channel as well.
Indeed.
It only starts playing a role for enormous numbers of bingocards, since you'll have three times as many winners that all have the same column when a column wins, and how many do you need for rows and columns to occur identically on many cards...; his 10,000 won't show the effect much.
A bit misleading. I hope for a follow-up.
@@landsgevaerIs it possible to work out the math to understand how the answer "2.8:1" depends on the number of cards, n, say? If n=1, as you say, the ratio "row : column wins" equals 1. If n is infinite, we get the ratio from the video. What about for other n, assuming those n cards are drawn uniformly from all possible cards? For what n does the effect become "noticeable"? I think Matt mentioned a simulation in the paper. They must have used a small n (compared to 75!).
Thank you, this made the idea of a single card having even odds but a bunch of cards having skewed odds finally intuitive to me.
@@xyzx1234 Yeah, I later noticed that there are 3003 possible sets of numbers for the first column, so 10000 should indeed be enough. I overestimated that. Still, even a bingohall with thousands of participants is not something I've ever seen. ;-)
The easiest way to conceptualize WHY horizontal wins are more likely is that: to win vertically, you need to pull from the same 15 numbers out of the pool every time. The more you pull those 15 numbers, the less likely it is that they come up in the future. Whereas horizontal wins are the exact opposite. Pulling from 1-15 first means it's less likely to pull those numbers again which is exactly what you want. The more you pull from columns you already have pulled from, the more likely the numbers from other columns will show up.
Yes, that's what I think. Let me see if I've got this right: the vertical lines can only be completed by a limited set of 15 numbers, but the horizontal lines are completed from the full set of all 75 numbers. For either to be complete, the numbers available in each set decrease by 1 as each ball appears, so clearly there's more chance of a number appearing from the larger set to complete a horizontal line. That would be true on many cards, or just one card, wouldn't it?
small detail: quickly explain what bingo is in the beginning of the video. i didn't know the game.
I do not wish to cause any harm by my comment but i must ask, for your comment it is too weird. How old are you? One must be quite young not to know what bingo is. Tis the game for the elderly, in many tv shows it is repreaented as that. Much like bridge, but for even older people.
@@witekki its ok. no probs.
i am 33 years old. i don't consider myself old, yet.
maybe its something locally played or i havent been too much in contact with it.
i dont see it played by elderly people around here. i do see rummikub. but thats not a game played in a big group.
@@witekkiyour comment is a bit strange, after all you yourself also arent a kid anymore i assume and should understand that people all around the world speak english and use youtube and theres probably a lot of places that dont play or know bingo at all
8:39 X's are made with two opposing diagonal lines that cross in the middle, NOT with a backward C and a normal C, you weirdo! 😂
That is the standard way to write x in mathematics in the UK, because the 2 diagonal lines are used as the multiplication symbol
What's the point of making 10,000 bingo cards when it takes forever to scroll to the bottom ones?
You probably should have made them in batches of 100 and put them in 100 folders and distribute those in packs of 10 between 10 folders
100% this. I can't even load past 766. A simple html file directory would have been better
I randomly generated a number, got 8632.
I've been scrolling forever, is now down to 2200. I give up.
Should've made a website that generates a random bingo card locally when you load it.
@@fatsquirrel75 My randomly generated number was 64246 and I didn't make it to 03000 before settling on a particular favorite number I had already passed.
A random card should be automatically assigned to each person who clicks the link. Dropbox probably doesn't support that functionality, so the 10,000 cards should have been uploaded to a site or app that does support it.
That green marker is hard to see
I found the first mistake in Matt's math -- The bingo game space is not 75! because that would imply we haven't found a winner by the 75th pull.
The maximum number of pulls without a bingo is 70 meaning the game space is 75C71.
At first it seems counterintuitive, but it makes sense:
For the first ball, there is 15/75 chance if getting a ball in the first column and 60/75 from another column.
For the second ball, there is 14/74 chance of getting a ball from the first column and 60/74 from another column.
For the third ball, there is 13/73 for the first column and 60/73 of the other column...
So it becomes more unlikely to get numbers from the comumns whose numbers have already came out.
If you think about it, 3 is the perfect number of copies to own of a book... One to read, one to lend out, and one to collect
Three is the perfect number because you can make a triangle with them
@@reinerzufall1292 But 3 is not a perfect number.
Jokes on you, I’ve been playing bingo on your videos for a long time ;)
You should now try playing TH-cam-comments-section bingo. I already have "Parker Square", "maths with an 's'" and "Wolfram Alpha" crossed off. (-:
Won at 5 seconds, every single square was filled at exactly the same time
What card?
you randomly rolled the exact card on screen? lmao
18:29 BIIIINGGG - the sound you get when you hold a ruler at the edge of a table so that half of its length is sticking out, then give the protruding bit a good thwack.
Neatly expressed! I think you'd enjoy the book 'The Meaning of Liff' by Douglas Adams.
Bingo at 10:00
Bingo card 1293 Randomly generated
Bingo from:
Free space, whiteboard, regular polygon visible, ridiculous, matt mentions his book
As a Canadian, i purposely ordered the uk version. Personally, like the cover better as well as the spelling of a lot of words are more aligned with UK
Bingo card #645 with a vertical win at 15:14 (if you count that as multiple Matts on-screen)
Technically there are multiple Matt's onscreen at 2:30, the photo from the dust cover of his book is very briefly visible
There should be as many cards with vertical filled columns as with horizontal filled rows actually.
And no, that does not contradict the video... 😉
@@landsgevaer Yep, I also watched the video believe it or not 👍
Question: At 17:23, why does the 10th ball have to be the first one from set 'O'? Could not a previous ball have been called from set 'O' that was not involved in a winning solution?
The assumption is that the crowd is large enough that if there is a chance of bingo happening it will happen. By this logic when a number from the fifth category *first* appears, someone with the correct arrangement of numbers on their bingo card will win with a horizontal line.
I think a more intuitive way to think about this question is to assume that the audience can freely choose their numbers within the rules. How can us, the host, maliciously arrange the bingo sequence so that the bingo happens at the 10th ball. (and by the same logic prove that a bingo will happen no later than ball 17th)
I worked part time at a bingo club for 5 years whilst at uni in the 90s, and it's today that I discover that in the UK, our game and card layout is totally different to the US!
Run simulations on all 10,000 bingo cards to find out which one's the unluckiest 😂
Technically, there aren't 75! possible ways for the numbers to be called. If you had only one person playing, you'd have a maximum of 9 numbers left before a BINGO would be called. 4 in a column, 4 in a row and the one shared space in the column and row. So, the most possible ways for BINGO numbers to come out would be 66!.
Sub folders at even base1000 would have been incredibly helpful for finding your favorite ciphered-number bingo card. Middle name NOVA, tried getting to 06682. Me and my mobile gave up after scrolling thru the first 3000 and things were slowing down
Diagonals feel like Horizontals by other means.
I don't think the Horizontal rule applies to Matt's cards, unless they've been arranged in subsets as well.
The examples shown on screen imply that they have been.
Yeah with all cards in play, if there's a diagonal win there's always gonna be some horizontal wins at the same time (and vice versa).
Great comment from Matt about finding it pleasing to need to manipulate factorials whose value are so large and yet not really need to deal with their huge size because they end up canceling each other out to a great degree.
When I took electrical theory and started to need to use complex numbers (i.e.: i) it seemed daunting (there’s no imaginary amounts of current, voltage, or electrical components - they are all quite physical and real), until I realized that for all practical applicable cases, after you carried through with the maths they just cancelled each other out in the end leaving you with actual non-imaginary values to use for real.
Fascinating!
I absolutely love making up incorrect calls for numbers, but it really annoys bingo players. Which makes me like it even more of course.
"4 and 3....*give everyone time to mark off 43*... 7!"
Damn I won 38 seconds into the video. Crazy.
I’m going to need to see some receipts.
You gotta call the Bingo, and your card number
@@standupmaths Does "trust me bro" count? >.>
@@DaxSkrai Not when death is on the line.
Shilling a book so hard that Matt is trying to sell a box set of 3 copies of the *same* book is taking the mickey...
19:00 What about the families that include the O column? In the first nine rolls we can have a sequence of (4,2,1,1,1) without getting a BINGO, with the 10th number being also in the O column and getting a horizontal bingo.
The assumption is that there are an infinite number of players so as soon as someone *can* win, they do.
So once all 5 columns have been called, that's it.
The calculated probability is assuming every single possible bingo card is being played at the same time.
If not all cards are played the probability changes and the math would be more complicated. Like he mentioned they simulated 1000 cards in play and got a ratio closer to 2:1, not 2.8:1.
@@BL3446 I don't understand why that is an assumption that was made, it kind of changes everything.
Drawing 3 from the O set and then assuming that the Xth draw is the final draw to give you a bingo seems more correct.
Obviously changing the stats but I feel like in a way that's more correct? Idk, I'm just also really hung up on why this assumption was made when it sort of throws everything off
@@BL3446 Thanks for the clarification, I got confused about this too
The assumption that somebody wins as soon as it is possible is kind of necessary. Without this assumption, every single calculation needs to have a parameter for the number of unique bingo cards, causing the math to be just incomprehensibly complicated.
Wow, those Love Triangle bingo sheets are really coooooool! Props to the illustrator!!
i watched this vid lying down. so I definitely won bingo horizontal instead of vertical.