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Actually, with 75 factorial combinations, there is a slight advantage for some cards. But it's going to be so minute as to not even be statistically significant. Also, in real bingo halls, they use different cards for every game, and the card is then unusable because of the ink dabs. So if anybody seems to win more than once, it's pure luck.

It's a competitive advantage, but given that it's dependent on the cards everyone else gets, it's effectively randomly assigned, meaning the game goes back to being pure luck.

question is: are bingo cards actually distributed this way? because your example could easily be solved by introducing a 4th card with the winning numbers 1 and 4. it is only through your limited sample size and uneven distribution of numbers that there is an advantage. in a situation where all numbers are equally common on bingo cards, the bingo cards are randomly picked and new ones are used every round (and the bingo cards being much bigger) there really isnt any real advantage left.

This is a very narrow look at the game and perfect for an example of getting a "bad" card among the set of cards handed out. But if you have every permutation of Bingo Card (12,13,14,23,24,34) instead of the three examples, every card wins 4 times with every possible draw order and there are no shared wins. Having fewer shared numbers with other cards in play is an advantage, but you are correct that it's nearly impossible to predict or calculate. I hate to burst the bubble, but Bingo is fair for all intents and purposes. You can influence the game by selectively removing certain cards to make other cards stronger, but that's manipulating the base game. Some Bingo sets might be unfair with less cards than the potential permutations if they don't have measures in place to make sure each card has the same number of shared numbers with other cards. But realistically, you could make blank Bingo cards and let everyone fill in their spaces before playing and it's 100% fair. I was hoping this math would discuss the N column having 4 numbers and a free space more than permutations.

He didn't really explain it, but it's the _absence_ of the cards that would make it completely fair that ends up with some cards then getting an advantage in that round. He also left out the idea of Expected Value (EV) which if you assume the winners have to split the pot, means that a tie in the used example is only worth 1/2 of a win. The score in that case is A=9, C=9, and B=6

At 3:50 you list the 24 permutations of 4 items. Although you only present three, there are 6 possible bingo cards in your game. (In a real bingo game there are 75 numbers and half an octillian possible unique cards. So your proportion of possible cards used is quite generous.) Each card has 4 orders of draws that will win in two draws. Therefore in a game with 6 players on unique cards everyone has an equal chance to win or lose 4/24 or 1/6 of the time. It's your distribution of three cards that is the flaw here. There are simply too few balls to offer an appropriate analogy. With small numbers of cards and options we expect the absence of half the cards to be very impactful, but when the quantity of numbers one can select increases, losing half the cards loses impact because the randomness remains smoother at those quantities. With 75 numbers, we're talking very small impact when a quarter of an octillan cards are used out of a possible half an octillian. But even with your 4-ball 3-card game, if you randomly generated the cards and distributed them randomly, the odds are still fair. There would still be some favored to win over others, but since there would be no gamesmanship one can employ to turn that to one's advantage, it would remain fair because the variously lucrative and less lucrative cards were all distributed by lot. Provided there is no mechanism to corrupt the purity of the randomness (and in today's world we ought not accept that assumption) the game of Bingo is as fair as any game of chance. As stupid as well. Put two dollars in a shoebox every day. Every month or two, open it and win. Pays better than the lottery on average.

You should have provided the simple conclusion: You want a bingo card with as few shared numbers with other cards as possible. The other fun fact is that any TWO cards, if there are only 2, have equal odds vs one another. These other issues only show up in higher #s of cards.

There’s definitely a way to take advantage of this knowledge. Example: in most bingo games a player can play more than one card. Now imagine if the game went really fast and you could only play 2 cards. This tells you which two to play. In real life you might buy a hundred pack to play all day. And play six at a time. So before just grabbing six and playing them you might want to regroup your cards into unlike sets.

i think it's an more of an implicit advantage. the randomness is two stages: the distribution of bingo cards and then the drawing of numbers. so he's really saying it's not all about the draws, and it's a mistake to ignore the cards as a key component of the game. thanks for the insight.

In real play, you not only have to get the winning numbers, but the numbers have to be arranged one of the winning patterns. You can have numbers B 1 - I 16 - N 32 - G 49 - O 70, but if they're not in a straight line you don't win.

I expect that the reason some people win more often is because they are better at finding the numbers that are called. The other people are occasionally missing an available number.

2:00 My quick intuition was B. My thought was that if I’m more likely to win when one of my opponents win I’d by more likely to get a bingo. That’s exactly wrong though. Xp. A better intuition is that when you share numbers with someone else, some of the sequences that would lead to a bingo for you will terminate prematurely as a bingo for them. So you want to share numbers with as few people as possible. (It will get more complicated in real bingo since different squares contribute to different numbers of bingos. Diagonals for example.) And incidentally you don’t block others when you share a bingo. Here follows a brute force count. (You only have to go up until the stopping condition.) 12: 2A 132: A+B 134: C 142: A 143: C 21: 2A 23: 2B 241: A 243: B+C 312: A+B 314: C 32: 2B 34: 2C 412: A 413: C 421: A 423: B+C 43: 2C Summary: A: 10 B: 8 C: 10 Comments about the counts. These are all the sequences leading to at least one bingo. I don’t actually know the rules of bingo so I just assume it ends when someone gets bingo. If that’s false my analysis is wrong. 1. The two ball sequences are twice as likely as the 3 ball sequences. So I count them twice. (4 choose 2):(4 choose 3) 2. Some sequences result in a simultaneous bingo. Those count as a win for both. Nice to correct myself my intuition here.

This is one of the difference between Bingo in the US and the UK. In the UK everyone plays with a strip of tickets all which contain all numbers 1 - 90. During a bingo session there will often be 'some' intermittent games where the Americn Style card games wil be played and these are usually given their own session names, such as 'The Yankee Flyer' or 'The Americana" .

I used to go with my grandmother to play Bingo some of those little old ladies would have 10 + cards.

Talk about using a crazy small number of permutations to try and extrapolate to a massive number of permutations is one of the most egregious examples of making up shit for clicks that I’ve ever seen.

I came for the Step Function and now Im watching how Bingo works. Lol, thanks man, you have an interesting channel! 😎👌🏼

I have played bingo over 40 years. Same damn people win frequently. There are sessions the same numbers come up and other not. We used to ask the caller "did you wash your balls today?" If a caller has sweaty hands or lotion and touches the balls, I think those have a minute amount of extra weight and won't come up the tube. Then the converse, a number has come up every game until I need it. LOL

I worked around a bingo hall and have family that go every weekend, it does seem the same person wins, but j know they can't pick their cards, and a slow bingo night have like 150 people and a busy night 400 and the same person seems to win, we had to investigate and prove the monster jackpot wasn't rigged, the reason why the same people win is because they invest in alot more cards

I'd like to see this video re-visited. Last I checked, BINGO cards don't share numbers across columns (i.e. 2 being in both A and B and 3 being in both B and C). I think a better video would be Cards A consisting of two numbers (1, 2, or 3), Cards B having 4, 5, or 6, and Cards C having 7, 8 or 9. Then set up a match of card A1 (1,2) vs. card A2 (2,3) vs. card B1 (4,5) vs. C1 (7,8). Then conclude how many times A1 wins outright, A2 wins outright, B1 wins outright and C1 wins outright and how many times A1 and A2 tie.

I realize this video is 4 years old but it just showed up in my feed so I watched it. The thing you missed in your analysis is that there are actually 4, not 3, ways to pick two of four numbers; if you include 1,4 as a card D, the winning percentages even out across all four cards because there isn’t any number only held by one card.

Holy shit the longer I watched this video the more enraged I became that it even exists. At the end you finally say that there are so many numbers on an actual card that even if you could hand pick your card it would be too hard to pick one with an advantage. Meaning, it’s random. Then after that you make a statement that leads me to believe you somehow mistakenly believe people get a card and just play it all night for every round. Which is dumb as hell. Cards are discarded after use.

Every 85 year old in the nursing home playing to win "Moon Pies" secretly knows this

This is a permutations problem since the placement of each number matters for alignment or the 4-squares win. So the formula is nPk = n!/(n-k)! for this problem. For the columns under the B, I, G, and O, we are looking at nPk(15,5) = 15!/10! = 360360. For the column under the N, we have nPk(15,4) = 32760. So multiplying each column's number of permutations, the final number is 5.52x10^26, or 552 septillion (using USA naming standards for large numbers). This is the number of possible different BINGO cards. It might be possible that some cards will have an advantage over other cards but to determine the fractional advantage you would need to run something like 2.4x10^13 runs (the square root of the number of permutations) to get a statistically significant result. Therefore, this video is probably technically true but the advantage diminishes as the number of possible cards grows.

This claims bingo has a competitive advantage and isnt fair while ignoring that everyone is given random cards, making it fair

This assumes the picking of numbers stops after a winner. Some Bingo games continue drawing balls until a pre-determined number of winners surface.

I love this because it starts out as a counter-intuitive problem (like Monty Hall) which then turns out to be completely intuitive once you get it.

You mention that players can win multiple times with the same card. I don't know where you play but I have never been able to use the same card in more than one game. That was stopped 50 years ago when they use to play with the cards that had the little slid window that covered called numbers.

The caller keeps certain balls after the first game.

A good thing to learn before you go to live at the old folks home.

The BIGGER mystery is why people insist on a lucky seat and how that factors in to their win...

If you had printed all possible different cards with 2 numbers on a card picked from 4 possible numbers.... Every cards would share both its numbers with two other cards. The card 1,2 : Would share its 1 with the cards 1,3 and 1,4 It would share its 2 with the cards 2,3 and 2,4

Bingo is just a humble farmer’s dog. Why you gotta pick on him?

Only works if you didn't print a card with 1/4...

This changes when you add the rest of the possible cards. A=1&2, B=2&3, C=3&4, D=1&4, E=1&3, F=2&4

Except that when you play bingo You actually discard each set of cards at the end of The Game and have a new set of cards with Different sets of numbers for each game so that still doesn't explain WHY the same person might WIN multiple games unless they are extremely extremely Lucky in getting cards with unique numbers All The Time

That's wrong or misleading for two reasons. 1. As the numbers get bigger (75 options instead of 4), the probability of numbers being significantly over-/underrepresented becomes negligible.* 2. The reason why the same people tend to win is because you can usually purchase additional cards. Obviously, more cards means a higher chance to win. * The best comparison would be to the lottery, where you would avoid numbers that others are likely to pick (dates, series, etc.). While it's technically better, it's mostly insignificant because the expected value is virtually identical.

Won a $1,000 tonight at Bingo so I’m here trying to figure out the odds of winning. 🤣 lady next to my table won 11k I don’t have that kind of luck 🍀 🧐😇

Ok, so you explained that not every card has an equal chance of winning but you didn’t explain how someone could realistically take advantage of that since bingo cards are randomly assigned to the players.

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That's not how bingo cards work though. Each letter row has a specific subset of numbers assigned to it. The numbers can't just be anywhere on the card. Have you played bingo?

Bingo is a game of chance. You can increase your chances of winning if you were able to pick your cards which you can't do in a bingo hall.

Hi, really enjoy your content Bri. So, I've been studying math in English for about a year now, but there are some stuff that I don't know the name of yet, and those tend to be really basic sort of stuff, do you have a way to sort information out quickly or something like that (it would really help international students out).

Calling a flat out win to be equivalent to a tied win is a significant error here making the delta look less pronounced than it actually is. Because you have to split winnings, a tied win should only be given a value of 0.5. If you do that, it's 9 vs 6 instead of 10 vs 8, Which is 50% better rather than 25% better.

I think a lot of people develop a gambling addiction thru bingo. The hook is, the game is played until there is a winner and someone always wins. It teases you into thinking you will win. I always have wondered what the average take is on a bingo game and what the minimum number of players needs to be for a bingo hall to operate profitably

Instinctively, my brain says that if you included all the possible cards (6) instead of just those three (why those particular 3?), every card would win four times and there'd be no shares with the draw used here (two ways of starting with 1-2, two of starting with 2-1, etc. etc.)

even though individual cards have better or worse odds, its still completely even for everyone playing because the cards are dealt out randomly. This argument is like saying the game of poker is unfair because everyone gets dealt different starting hands. yes, but that is part of the game.

I'm not particularly versed in formal math, so I'm not going to try and prove it, but I don't really think this works. With a 5x5 grid and numbers going up to the 50s or beyond (it's been a long time since I saw a bingo card, cut me some slack), any advantage a given card has is statistically insignificant.

Thanks for explaining this fact. You are very smart

Why is there no 1-4, 1-3, or 2-4 cards? Based on the randomness of BINGO cards, they should be there also, no?

This happened to me when I was 10. I won a ton of times at a charity event to the point that prople were booing me lol

That doesn't explain why the same people always win. Just because some of the odds are drawn before the game starts doesn't make it unfair. Players aren't checking every card for the game and choosing one.

Good luck with the strategy of trying to trade bingo cards with someone who's winning. LOL.

Note: Bingo is NOT a game - it's a competition you either win or lose based on a random draw, (which includes the cards you are given). (Games are activities that can be won or lost by the player's behaviour.)

This presumes that there aren't any "rigged" cards, rigged in the same way lotteries are rigged... for example, only one card in the whole stack has B4. This puts that card at a disadvantage if B4 isn't called, but at an advantage if it is.

The fewer people playing, the more likely you'll be the winner. So, wait for the blizzard...

Im hooked playing an online bingo and jm still trying to figure out how to increase my percentage on winning and i learn that jf you have diy cards yourself the odds of creating a pattern increases rather than random cards

It's clear this guy never played serious bingo.

There are so many cards in play in a given game at a bingo hall, I can't imagine there are any worthwhile distribution biases on any of them. I would say there's probably more "unfairness" in the way the numbers are drawn. Wouldn't shock me at all if some of the bingo balls have imperfections that make them either more or less likely to be drawn.

No he didn't teach himself how to write backwards. The writing would be backwards to us but he flips the video. You can see in the ending where he's no longer writing he didn't flip the video.

In the minimal example you'd have to consider games with all 12 possible cards in play to be thorough about it.

This is like tossing a coin then asking people if it's heads or tails. Normally we'd conclude there's a 50% chance of guessing correctly. However, if we use the logic in the video, this "isn't fair" because the people who guessed the right answer win 100% of the time. Likewise, if we guess the right bingo card (or get it randomly assigned to us) we have a mathematically greater probability of winning.

Interesting content. Lets go a step further. In a two-player game, neither player would have an advantage with any card at all. In a three-player games, the advantage of having unique numbers on your card is at the maximum so you should keep "good" cards. However, as the number of players increases, the chance of truly unique cards becomes diminished and also the value of a unique card becomes diminished due to the dumb luck of one of the many others winning before your unique numbers are drawn.

From a mathematical perspective this makes sense. I'm not a bingo player. I have played once at the county fair and once in a charity event, but in both cases we were given new cards for every round, and we weren't given the opportunity to select cards we wanted. This redistribution of cards every round would seem to make the game fair over multiple rounds.

Actually it's not nearly impossible to calculate your chances of winning a bingo game... it's simply how many cards are in play and how many catds you are playing with...all of the numbers have an equal chance of being drawn, and unlike lottery, the numbers continue being drawn until a player or multiple players achieve the preannounced pattern...❤

So... print the cards so that certain numbers only appear on your cards. Then you win a lot of the games where that number comes up.

If it's impossible to pick the winning card, even if you get to choose your card (5:56), then how do the same people win again and again (1:04)?

Considering you do not know what other bingo cards are in the game (I really doubt you are in a game where EVERY possible card is in play), also different games have different win conditions, there is not really a useful competitive advantage in Bingo. What I mean is that there is not anything that you can do to change the outcome. This is fun math exercise

You forgot to include car 1,4. In a vacuum, you could say that it isn't fair, but in reality, there are so many number combinations on a bingo card, that the statistical difference is tiny. Also, the more people that you have playing, the closer the odds are among players. Fewer people could have the same effect, as it would be similar to just having card A and C out there. While what you are saying is correct, it is also very flawed in the real world.

it's like a roulette wheel !! ... the more numbers there are - the lesser chance of winning !! ... your betting on dumb luck !!

When you say that bingo is rigged did you only use this over simplified example? Not accounting for the fact that bingo cards are 5x5 giving a mixture of 25 numbers, (the same card isn't used for more that one game in a paid game) and each letter in bingo has 15 numbers and 5 are picked for each column with the middle column has a free space that everyone gets to use. And on top of all that you picking from 75 numbers and not 4 so you get a lot more randomness from the whole game

This just pops up into my feed and is an interesting subject. However, in practical sense, once a bingo is called, assuming there will only be 1 winner, it would make sense to stop drawing numbers. In those cases, let's say the scenario of 1 2 3 4 or 1 2 4 3, wouldn't they be counted as 1 single scenario rather than 2? Even if not, I think it would be interesting to try to calculate off those scenarios as well, it would be impossible to continue the game after 1 and 2 are drawn first (same with 2 3 and 3 4) - in fact, I would exclude the 4th number as the number of scenarios, given that as soon as a third number is called, there will be a winner. Admittedly, I am no math expert.

I did not do good in my stats class. Interesting discussion about the “typical “ bingo game, but will the same apply for other winning patterns? Example create the letter “L”. Given that number of cards distributed is very large, at the hall I work at computers can have close to 200 cards. I wonder if it is more a function of the number of cards you have compared to the total number of cards sold?

I hated playing bingo in school. It felt so stupid.

This was actually incredibly interesting

Everyone criticizing this guy, but here in Panama you actually get to pick the card you want. And now I have a strategy.

All those quarters at the apple harvest bingo table....wasted...

Cool analysis and surprising outcome. I definitely would have bet a lunch that the odds were exactly even!

Thats why when you play bingo at a gaming hall you get a strip of 3 cards that contain all numbers that can be drawn randomly printed across all 3 cards. You can then purchase multiple strips, typically 3 strips per sheet for a total of 9 cards on a sheet. If you have only a single card, you are missing 1 third of the possible numbers to draw from

so a fair bingo game is possible, it just has to be designed on purpose; If you took that game and added a 4th crad that contianed 1 and 4, then every number appears on exactly two cards and the win ratios should become the same for all cards.

Off topic, but how do you write on the screen so that it's not backwards?

you have a better chance on getting a good coin (error, old, ect.) in the coin pusher, than winning at bingo. (i found silvers, errors, and old quarters for my collections!).

available bingo cards missing from your examples : the 4 and 1 card, the 3 and 1 card, the 2 and 4 card.

This is awesome! I still might keep playing though 🙃😉

Sounds like bingo IS fair but you just dont want to share numbers with other people. So you cant pick a specific card with better chances before other people have their cards

His logic is oversimplified. It misses that it’a not just the order the numbers are called in, but the shape they form on the card. Calling the numbers 1, 12, 3, 4, and 5 in that order does not mean every card with those numbers win. You’ve also to deal with the probability of getting one number from every column, and getting all the numbers from one column.

Would a solution be to require the winner to turn in the winning card and to select a new one. The cards are still "unfair" but the relative advantage of all the cards change slightly with each game.

Bingo is a form of gambling. Any form of gambling the odds are always with the house. The payout has to be less than what's taken in or they won't do it.

Cool video. Explained well.

Speaking purely mathematically, if you had every 1 copy of every single possible combination, would that not still be fair overall? Cards would have an advantage over certain combinations of other cards, but most of the time you don't get to pick your card anyways, reducing the game to pure chance.

There is an online game with 75 balls (1-75) available but only 49 balss are called. There are various patterns. There is a pattern that would let you wil 4 thousand pesos, the pattern is all outer edge are marked. You are allowed to make your own unque bingo card with the numbers of your choice. I am not a math genius and I am looking to get all the possible combination card. If you can help me with the combination for the pattern ( all outer edge marked ) then that would be great.

No wonder those old timers will chew your head off--- Sal

also, you should of play a real game of bingo with the of #1, 2, 3, and 4. put these #s into the basket and spin it, to prove your point. Without it, its just half of the illustration, it's like trying to prove if the glass is half full or half empty.

Good information 😮

Even here the house always wins.

So what would be the strategy exactly? How and why would some cards have numbers that are less likely to show up on other cards??? If you got to write out your own numbers on your card, then maybe this might work, but how would it work with randomly generated cards, since every number should have the same chance of existing as any other number? The reason you see some people consistently winning more than others is because they purchased more cards.

There's roughly an octillion unique bingo cards in a standard bingo game (75 numbers). How big is an octillion? Big enough that you could give everyone on the planet (assuming population = 8 billion) 8.6 million unique bingo cards and still have some unique cards left over.

Very interesting, but you're not telling the complete story. If player D has 4 and 1 on his card, every player wins 8 games. Also please explain how certain players can be 'frequent winners' when both the cards and the numbers are drawn randomly. You only explained why in a specific game a certain player can have an advantage, but we must assume that in the next game another player has better chances of winning.

I'm slightly confused as of which bingo rule it is that disallows for the outter numbers to be reused even though every other number is allowed to be reused? I feel like you've got to justify that part first before basing every following table on that principle. What makes it so my card cannot be 1&4? How does this tie into true bingo without these assumptions in place?

Not sure if this really applies because the few Bingo parlors I’ve played at, required you to use a different card on each game so trying to switch cards with someone shouldn’t be a good strategy. Sure, they had a good card for one game but there is no guarantee that they will in future games. If you at a place where you don’t have to use different cards for each game, then yeah. It could make a difference but not when you have to use different ones for each game.