03:00 Yet all three are equally likely to win in his example! (he should try aosme simple pmaths to prove this, tho that seems to be bond his ability!) Even if this imaginary disadvantage existed the 60-80 balls removes it!
I was a bingo caller for a couple of years. I can tell you that it didn't take me long to realize that certain numbers come up more often than others. I don't know what the exact reason is. It could be the weight of the black ink.
@@billcape9405 "that certain numbers come up more often than others. I don't know what the exact reason is. It could be the weight of the black ink." Not not ink. The question is why do expect random numbers to all come exqactly the same mount amount? Offcourse you never recorded this so its clearly biased memory!
@@danquaylesitsspeltpotatoe8307 Assuming a professionally run raffle is using quality bingo balls, blower or cage, manufactured to the specified standard, then operated and maintained in the mandated manner, then the result for the bingo players has to random and fair. 🎰
@@danquaylesitsspeltpotatoe8307 Exactly. Confirmation Bias comes to mind also. The human brain wants to find patterns, even in pure random white-noise.
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.
You also buy a card then are given the next one on the stack with no choice other than how many you buy so the randomness of distribution is what makes it fair. When he mentioned seeing the same people win repeatedly it's because some people will buy multiple sheets each round to increase their chances.
@@KOZMOuvBORGthe free space has nothing to do with the numbers you get. The free space just limits the numbers you get under the "N", which is 31-45. Since everyone gets the free space in the same place in the card, it doesn't affect your odds off winning. I personally feel like this kids logic is wrong. His example doesn't scale up properly. Besides, it's the calling of the numbers that would matter, not the numbers on the card.
@@KOZMOuvBORGActually, after giving it some thought, I believe you're correct, the free space would change the outcome, but not in the way you think. It makes it so, in theory, a person can get bingo after 4 numbers instead of 5. That would definitely change the outcome of hours proposed theory. I think, to do this theory properly, he should to an example with 9 spaces; a 3 by 3 grid with a free space in the middle. Though a factorial of 9 leaves over 362,000 combinations. He's gonna need a bigger board!
I don’t think the free space changes the odds. You can think of it as a number that everyone is given and is always called in the beginning. Say number X, then all possible combinations. The number of combinations will stay the same, and the winning card can still be predicted for each combination.
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.
If you are running the game, then you can make it be true. Especially since not all squares are equal, you can give just your friends the 1-5 in a corner, everyone else gets those numbers only on the spots one away from the corners, and the ones with those numbers in the middle get set aside for next week. Or if you just get there early, and make sure that the cards you play all have your lucky number in a good spot, you can thin out the combinations enough that you'll win more often than average.
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
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
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.
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.
@@indigotidebeeblebrox9978 Exactly - but in standard Bingo, if you have all half octillion cards in play, all games end in a four-way tie after 4 balls. Once 4 numbers are drawn, there is a card with the positive slope diagonal filled, a card with the negative slope diagonal filled, a card with the horizontal center line filled, and a card with the vertical center line filled. If you're ever playing Bingo with a half octillion people and the first draw is not on your card or not on one of the free space lines, just go home. You lose.
@@markdavis7397 I fully agree. What I was saying is we shouldn't draw too close a comparison between this simplified game and the real one. In the simplified game the odds disparity is much greater than in the real game. However, given the titular premise "Bingo isn't fair" I simply countered that at the scale of the real game the probabilities are less delicate. This does not explain why we see some cards win more than others in a real game. The short-term effects of randomization explain that fully. If you, along with all players, are offered a random card to play, there is no bias to the game because, even if the subset of cards means some cards are going to win more, you have an equal chance at playing those cards.
@@Qermaqthe numbers go up to 90 in the Uk ...,they print billions of cards at a time ...it may work in a maths solution you want to present as correct . His statistic doesn't account for anything random or having a base point to prove it .only way to do it is play the same cards thousands upon thousands of times ,but then still it is not difinitive just chance . Repeating it the following day would give different results again. Nice to see that you are clued up ..Waste of 6 mins of my life ..😂😂
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.
I am wondering if you could rig a bingo game, have a set of cards whose numbers are more likely to win than others and rig it? I think that the Ohio Lottery is rigged as most of the folks who win scratch off are from the North. I think that the pwoers that be send the wining cards more up to the north of the state than to the south. probably corrupt rigged people related to the mob.
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 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.
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.
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.
You can't do that. Bingo cards are played on pre-printed sheets, and each sheet must be played in order. You may only buy sheets for the upcoming session, then you must re-buy for the following session. There is no way to "stockpile" or arrange your cards a certain way. It's complete luck of the draw.
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 made the same mistake as you. The way he drew the chart immediately made us both think we were looking at Bingo cards, but that's not the case. Listen closely at 1:23 and it'll make sense.
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.
Re: fun fact My college Prob/Stat professor spent one lecture showing us that buying 2 (fair) lotto tickets was no more likely to win than just buying 1. The key: rounding and significant figures. There were simply so many outcomes that 1 and 2 are equally small as a fraction of the number of possibilities.
@@jasonfullerton7763 That sounds like a stupid argument. Then, 0 or 1 ticket is also equal, and all he is proving is that your chance of winning is very small whether you buy a ticket or not.
@@landsgevaer For sure. Hard to believe a professor would say such a thing. And hard to believe Jason the college student would believe it. The prof must have used a "four banger" calculator that only has 8 digits and no exponential notation. It reminds me of a video I saw earlier this week where a father said his son's teacher taught him that 1 / 0 = 1. This enraged the father and he went to the school to discuss it, and the principal agreed with the teacher!
@@Hyxtryx Yep, black pen red pen did a video on that, indeed. It does show that teachers with silly nonsensical opinions exist, and certainly there are students who believe them. (Churches are great examples too.)
@@poa2.0surface77 In case you're actually serious and not trying to be funny, 1/0 does not mean there is nothing to divide 1 with. It does NOT mean you can skip the divide operation because the denominator is 0. That works for subtraction: If you are subtracting 0 then you can "skip the subtract operation" if you want to think of it that way. It does not work for divide. How many times does 2 go into 6? Let's see... 2 + 2 + 2 = 6. So the answer is 3. How many times does 0 go into 1? 0 + 0 + 0 + 0 + 0 + 0 + 0 + ... How many times do you have to add 0 to itself before it totals up to 1? Also, tell me this: What is 1 times 0? I suppose you'll say that's also 1 because there is nothing to multiply with.
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.
6 cards. 1.3 and 2, 4 are also missing. In real world bingo not all cards will be equal, as there are far more combinations than cards, so in that sense the point of the video is fine, but as others say it evens out if cards are randomly distributed. Some games though you keep the same board for each game (e.g. using sliders to cover) and then some boards WILL be better than others - but not by much, and depending on the number of palyers it may be possible to have each player having the same number of duplicates on their boards. .
Yeah, but... First, you might only have three players. Second, with the full 75 numbers and 24 numbers per card, I doubt (but haven't checked) that the universe could contain a complete set of those!
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.
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.
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
@@aaroncapo6175 no its because they buy more cards then us, its nothing to do with math, unless you have the ability to examine every card. We but 2 cards and get 2 out of 3 but the other person buys 10 cards her odds gets a like 10/3 chances
Family, big sponsor, and close friends get their cards for free. How to win Bingo: 1) Be related, befriend or simply be a big sponsor like a corporation. 2) If you are: A) Family - You beg a family member to give you the luck card. B) Friend - Remain on the person running it's good side and they'll give you 12 lucky cards. C) Sponsor - Privately meet with the person running the casino and give them a fat stack of cash. That will instantly give you the winning card. To add more, you can find dirt on them and bl4ckm4il them or guilt trip them into giving the card. 3) Enjoy and ruin everyone's game. **Maniacal laughter intensifies**
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
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
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.
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?
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.
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 depends on the ruleset. Where I live, some people have their own "lucky card set" that they can keep or select and use every week, and certainly everybody uses the same cards the whole evening.
@@landsgevaer you and I play different games... every game a new card, color coded so you can't use them for a different game, all cards discarded after the game is completed.
@@greatbigguy Yeah, that is why I mentioned the ruleset. I presume that you are in the US, but the world doesn't all play that type of bingo. We don't write on our cards but cover the numbers with tokens, just to name one difference.
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.
Easy. Buy a giant stack of bingo cards. Ask everyone at the bingo hall to show you every one of their cards. Then tabulate the numbers to find out the variance. Finally, grab the cards out of your giant stack that have the best chance to beat that variance. Voila.
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.
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.
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.
Sure, if this was a big effect it would have been noticed. The point of the video is that the mere fact that the numbers are drawn randomly and fairly doesn't make the winner random or fair, as one might intuitively think, and that is a good take home message.
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.
Good job making content. You should have showed how the win distributions are actually equal when all 4 cards or only 2 cards are played. You could have then calculated the number of possible real bingo cards (an absurdly huge number), and realized while there could be incredibly rare edge case cards among a cards relatively close groupings, manufacturers are producing such a small pool of actual cards and could control variability. Why, I bet you could even make an algorithm that could figure out a fair number of appearances by each digit based on the number of unique cards that you want to include in a print run (or digital set). Another fun problem would be figuring out the odds of 1 digit that is completely unique to a given card when producing n cards.
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.
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
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.
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.
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
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.
If you repeat your simple example but the cards contain [1,2], [2,3], and [3,1], and the only numbers to choose from are 1, 2, and 3, there is no advantage. One could design a perfectly fair SET of bingo cards in this way, but of course not every game will be played with a complete set, so there may still be some small bias.
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.
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
I feel like you’re saying that cards that have unique numbers will be advantageous and bingo and that would definitely be true if in fact, there were actually cards with unique numbers and bingo, if they just made a set of bingo cards with the same number of each of the different numbers distributed across all of the different cards and then it would immediately get rid of the issue as you’re describing it, assuming every bingo card is distributed. If every bingo card isn’t distributed, then you would still have no way of knowing which of those bingo cards has been granted rare numbers, numbers not shared by other bingo cards that were distributed, and which of those bingo cards have been granted common numbers. You could also go totally random with it, every number on every bingo card could be independently chosen with the caveat that it simply can’t be a number that was already used on that board; then you really wouldn’t have any way of knowing the probability.
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
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!).
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.
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.
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...❤
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.)
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.
The odds that a card, chosen at random, has no numbers in common with another card chosen at random are quite small. Let's look at just the B column where the numbers are constrained to be between 1 and 15. Card A has 5 of those. So, if the numbers on card B are random, each number has about a 2/3 chance of not being one of the 5 numbers in A. (2/3)^5 is about 13%. In reality it's worse than that, because the odds are 10/15 (2/3) only for the first number in B. After that the odds are 9/14, then 8/13, then 7/12, then 6/11, because a number can't appear twice on the same card, so the pool of possible numbers and the pool of "safe" numbers remaining decreases by 1 each time. That means the odds that B has no numbers in common with A in the B column are only about 8.3%. And then the same thing is true of I, N, G, and O columns. The odds are 0.083^5, or a little over 4 in a million, that A and B have no numbers at all in common.
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.
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
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 🍀 🧐😇
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.
I think you should do this a bit bigger. Like monte-carloing larger sets. I did not play bingo often. But when I did, I ususally picked my own numbers.
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.
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.
I think you’re right but, other than your explanation, I don’t know why. Have you noticed that ‘big’ bingo prizes are won late in the week? A once-upon-a-time friend who worked at a bingo hall (he was related to the owner) told me how that is arranged. Unfortunately, I can’t remember. But it happens. Can you explain it???
When my family was taking the bus to Disneyland 1974, a tour guide held bingo games for passangers to help pass the time (with reusable cards). Noticed over a few days, that some players found that particular cards were "luckier" than others, and would covet (by surrepticiously marking) them. Don't think the ball machine they used were as rigorously maintained or calibrated as the ones used in lotteries starting a decade or two later.
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.
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.
I dont think this can be considered as competive or advantageous in anyway. The only way to take advantage of this is if you had perfect information, the time to actually calculate which card in the pool of cards that get used in whatever bingo "event" you are going to has the best probabilty of winning, and do all that before anyone else starts gettinf cards...which is obviously impossible. All cards are not equal but the card you get is still completely random which nullifies this bringing it back to the game of chance....and no, you cant just see who keeps winning and try to trade cards...bingo cards are one time use, you stamp each number when it gets called, to prevent ppl from reusing them, so more cards get sold
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).
This is a very good question. To be honest I'm not sure I have a great solution. I suppose whenever you come across a word or phrase you're not familiar with, you could google that phrase with "math" next to it and see what comes up. I will say that learning math is a journey in probably any language and this is how I've learned quite a lot myself (just looking up things I've seen pop up on the internet) I'm sorry I couldn't be of more help, but I wish you the best of luck!
@@BriTheMathGuy You got degrees in maths? go back to school and ask someone to explain basic probabilty to you as you have got confused! They should be taking your degree back!
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.
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
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.)
If a machine that blows the balls around with air is used, then certain balls are more statistically likely to be called earlier than others, based on weight. At least that's my theory. At the campground where I live, I plan on recording every last bingo game (full card) and transcribing to text later. Then take a look and see which numbers are called early most often.
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?
The same people win over and over again, because they are the people buying like 10 boards per game lol. What you're explaining here has no actual statistical relevance when the boards are the size of typical bingo boards. And your conclusion to 'trade' cards with people who always win -- have you given up science completely in favor for superstitions? This would be funny if you weren't actually trying to make some type of valid point.
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.
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?
Help me out. I see your logic, but it still seems fair because cards are handed out at random. So, wouldn't you have just as much chance of getting a good card vs a bad one? And, like you mentioned, even IF you were given a choice, it would be extremely difficult to down right impossible to find one with an advantage. Am I wrong? Thanks. Great vid. More of these please!
For sure you have just as good a chance of getting a “good” card as a bad one. In that sense, the game is fair. On the other hand, as everyone is playing, it sure seems as though you’re just as likely to get a bingo as everyone else. (Though we now know this is not necessarily the case) Probably more and more people playing the same game would make the cards more “fair” to one another, as no one would have exclusive numbers anymore. To me, bingo is fair, but not an even game.
I feel as though the workers have a winning stack that they grab from for there regular players and a bad stack for the casual players just my thoughts.
If the cards are handed out randomly, that is as fair as handing out the prizes randomly and just skipping the whole bingo. Indeed. But can you be sure the cards are handed out randomly? Ever been to see a magician? I could design a set of "bad" cards, distribute those randomly to my visitors, and then use some trick to hand the only "good" card to a planted player. In principle. (Not an accusation, but don't think it cannot be done.)
Having work bingo at my fire company for years I've seen many looking for the "best" bingo card but we rarely have a night where any one person won a lot of games maybe 5 times in 10 years. So while your small test shows a slight advantage to a certain card when scaled up, I don't see it still having much if any effect on the game
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.
In 1988 I had been out in the sun all day so I decided to play bingo with the old folks on the cruise ship I was on. The room was pretty full with maybe 75 or 100 people playing, each with multiple cards (usually three). I played with three cards and won the first two games of four outright and then tied on the "blackout" fifth game (and I should have won but I was too slow with the previous number). And the crazy thing is that all three wins were on the *same* bingo card! Obviously the card shuffle had resulted in me having one card that didn't share numbers with most of the other cards out there even though there were maybe 2 or 3 hundred cards in play. I can tell you that I won enough money to buy a nice watch at the next port and that the other players were wondering if I was somehow cheating!
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03:00 Yet all three are equally likely to win in his example! (he should try aosme simple pmaths to prove this, tho that seems to be bond his ability!) Even if this imaginary disadvantage existed the 60-80 balls removes it!
I was a bingo caller for a couple of years. I can tell you that it didn't take me long to realize that certain numbers come up more often than others. I don't know what the exact reason is. It could be the weight of the black ink.
@@billcape9405 "that certain numbers come up more often than others. I don't know what the exact reason is. It could be the weight of the black ink."
Not not ink.
The question is why do expect random numbers to all come exqactly the same mount amount?
Offcourse you never recorded this so its clearly biased memory!
@@danquaylesitsspeltpotatoe8307 Assuming a professionally run raffle is using quality bingo balls, blower or cage, manufactured to the specified standard, then operated and maintained in the mandated manner, then the result for the bingo players has to random and fair. 🎰
@@danquaylesitsspeltpotatoe8307 Exactly. Confirmation Bias comes to mind also. The human brain wants to find patterns, even in pure random white-noise.
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.
You also buy a card then are given the next one on the stack with no choice other than how many you buy so the randomness of distribution is what makes it fair. When he mentioned seeing the same people win repeatedly it's because some people will buy multiple sheets each round to increase their chances.
wouldn't the "free" square that's usually in the middle of cards affect the factorial (74 out of a pool of 75 numbers)?
@@KOZMOuvBORGthe free space has nothing to do with the numbers you get. The free space just limits the numbers you get under the "N", which is 31-45. Since everyone gets the free space in the same place in the card, it doesn't affect your odds off winning. I personally feel like this kids logic is wrong. His example doesn't scale up properly. Besides, it's the calling of the numbers that would matter, not the numbers on the card.
@@KOZMOuvBORGActually, after giving it some thought, I believe you're correct, the free space would change the outcome, but not in the way you think. It makes it so, in theory, a person can get bingo after 4 numbers instead of 5. That would definitely change the outcome of hours proposed theory. I think, to do this theory properly, he should to an example with 9 spaces; a 3 by 3 grid with a free space in the middle. Though a factorial of 9 leaves over 362,000 combinations. He's gonna need a bigger board!
I don’t think the free space changes the odds. You can think of it as a number that everyone is given and is always called in the beginning. Say number X, then all possible combinations. The number of combinations will stay the same, and the winning card can still be predicted for each combination.
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.
The frequent winners are probably buying more cards!
@@tobyfitzpatrick3914 Yes but not so many that they lose accuracy on finding every number called on every card.
NOL its all equal! Theres no bias in the random picked numbers!
@@danquaylesitsspeltpotatoe8307 did you not even watch the video?
Sometimes people lose because they aren't paying attention or make mistakes on their cards too.
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.
Read my mind.
If you are running the game, then you can make it be true. Especially since not all squares are equal, you can give just your friends the 1-5 in a corner, everyone else gets those numbers only on the spots one away from the corners, and the ones with those numbers in the middle get set aside for next week. Or if you just get there early, and make sure that the cards you play all have your lucky number in a good spot, you can thin out the combinations enough that you'll win more often than average.
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
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
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.
thats called Keno in Nevada!😂😂😂
In what Bingo game do you have every permutation of Bingo Cards present? Just doesn't happen, therefore the point of the video remains correct.
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.
And with all six possible bingo cards with 2 numbers in play there could be no ties.
@@indigotidebeeblebrox9978 Exactly - but in standard Bingo, if you have all half octillion cards in play, all games end in a four-way tie after 4 balls. Once 4 numbers are drawn, there is a card with the positive slope diagonal filled, a card with the negative slope diagonal filled, a card with the horizontal center line filled, and a card with the vertical center line filled. If you're ever playing Bingo with a half octillion people and the first draw is not on your card or not on one of the free space lines, just go home. You lose.
@@markdavis7397 I fully agree. What I was saying is we shouldn't draw too close a comparison between this simplified game and the real one. In the simplified game the odds disparity is much greater than in the real game. However, given the titular premise "Bingo isn't fair" I simply countered that at the scale of the real game the probabilities are less delicate. This does not explain why we see some cards win more than others in a real game. The short-term effects of randomization explain that fully. If you, along with all players, are offered a random card to play, there is no bias to the game because, even if the subset of cards means some cards are going to win more, you have an equal chance at playing those cards.
@@Qermaqthe numbers go up to 90 in the Uk ...,they print billions of cards at a time ...it may work in a maths solution you want to present as correct . His statistic doesn't account for anything random or having a base point to prove it .only way to do it is play the same cards thousands upon thousands of times ,but then still it is not difinitive just chance . Repeating it the following day would give different results again. Nice to see that you are clued up ..Waste of 6 mins of my life ..😂😂
@@harmoniefaerielove What a sweet thing to say.
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.
I am wondering if you could rig a bingo game, have a set of cards whose numbers are more likely to win than others and rig it? I think that the Ohio Lottery is rigged as most of the folks who win scratch off are from the North. I think that the pwoers that be send the wining cards more up to the north of the state than to the south. probably corrupt rigged people related to the mob.
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 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.
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.
That very much depends on the type of bingo game, apparently.
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.
You can't do that. Bingo cards are played on pre-printed sheets, and each sheet must be played in order. You may only buy sheets for the upcoming session, then you must re-buy for the following session. There is no way to "stockpile" or arrange your cards a certain way. It's complete luck of the draw.
@@gregoryschmidt1233 Sounds like you got the wrong cave to play in. Find a better group.
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 made the same mistake as you. The way he drew the chart immediately made us both think we were looking at Bingo cards, but that's not the case. Listen closely at 1:23 and it'll make sense.
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.
Re: fun fact
My college Prob/Stat professor spent one lecture showing us that buying 2 (fair) lotto tickets was no more likely to win than just buying 1.
The key: rounding and significant figures. There were simply so many outcomes that 1 and 2 are equally small as a fraction of the number of possibilities.
@@jasonfullerton7763 That sounds like a stupid argument. Then, 0 or 1 ticket is also equal, and all he is proving is that your chance of winning is very small whether you buy a ticket or not.
@@landsgevaer For sure. Hard to believe a professor would say such a thing. And hard to believe Jason the college student would believe it. The prof must have used a "four banger" calculator that only has 8 digits and no exponential notation. It reminds me of a video I saw earlier this week where a father said his son's teacher taught him that 1 / 0 = 1. This enraged the father and he went to the school to discuss it, and the principal agreed with the teacher!
@@Hyxtryx Yep, black pen red pen did a video on that, indeed.
It does show that teachers with silly nonsensical opinions exist, and certainly there are students who believe them. (Churches are great examples too.)
@@poa2.0surface77 In case you're actually serious and not trying to be funny, 1/0 does not mean there is nothing to divide 1 with. It does NOT mean you can skip the divide operation because the denominator is 0. That works for subtraction: If you are subtracting 0 then you can "skip the subtract operation" if you want to think of it that way. It does not work for divide.
How many times does 2 go into 6? Let's see... 2 + 2 + 2 = 6. So the answer is 3. How many times does 0 go into 1? 0 + 0 + 0 + 0 + 0 + 0 + 0 + ... How many times do you have to add 0 to itself before it totals up to 1?
Also, tell me this: What is 1 times 0? I suppose you'll say that's also 1 because there is nothing to multiply with.
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.
6 cards. 1.3 and 2, 4 are also missing. In real world bingo not all cards will be equal, as there are far more combinations than cards, so in that sense the point of the video is fine, but as others say it evens out if cards are randomly distributed. Some games though you keep the same board for each game (e.g. using sliders to cover) and then some boards WILL be better than others - but not by much, and depending on the number of palyers it may be possible to have each player having the same number of duplicates on their boards. .
So what you're saying is that in real life 75! people always play bingo at the same time, so it's always fair?
Yeah, but... First, you might only have three players. Second, with the full 75 numbers and 24 numbers per card, I doubt (but haven't checked) that the universe could contain a complete set of those!
Only works if you didn't print a card with 1/4...
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.
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.
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.
Yep! Also,there are a LOT of people who here who are offended on behalf of the game. It's kind of fun to read :)
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
they are rigged i know
@@aaroncapo6175 no its because they buy more cards then us, its nothing to do with math, unless you have the ability to examine every card. We but 2 cards and get 2 out of 3 but the other person buys 10 cards her odds gets a like 10/3 chances
Family, big sponsor, and close friends get their cards for free.
How to win Bingo:
1) Be related, befriend or simply be a big sponsor like a corporation.
2) If you are:
A) Family - You beg a family member to give you the luck card.
B) Friend - Remain on the person running it's good side and they'll give you 12 lucky cards.
C) Sponsor - Privately meet with the person running the casino and give them a fat stack of cash. That will instantly give you the winning card. To add more, you can find dirt on them and bl4ckm4il them or guilt trip them into giving the card.
3) Enjoy and ruin everyone's game. **Maniacal laughter intensifies**
And thats what people dont get more spent more wins 🤣
Not rigged.. I believe
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
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
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.
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This assumes the picking of numbers stops after a winner. Some Bingo games continue drawing balls until a pre-determined number of winners surface.
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?
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.
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?
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.
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 depends on the ruleset.
Where I live, some people have their own "lucky card set" that they can keep or select and use every week, and certainly everybody uses the same cards the whole evening.
@@landsgevaer you and I play different games... every game a new card, color coded so you can't use them for a different game, all cards discarded after the game is completed.
@@greatbigguy Yeah, that is why I mentioned the ruleset. I presume that you are in the US, but the world doesn't all play that type of bingo. We don't write on our cards but cover the numbers with tokens, just to name one difference.
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.
Easy. Buy a giant stack of bingo cards. Ask everyone at the bingo hall to show you every one of their cards. Then tabulate the numbers to find out the variance. Finally, grab the cards out of your giant stack that have the best chance to beat that variance. Voila.
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
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.
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.
I used to go with my grandmother to play Bingo some of those little old ladies would have 10 + cards.
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.
Sure, if this was a big effect it would have been noticed. The point of the video is that the mere fact that the numbers are drawn randomly and fairly doesn't make the winner random or fair, as one might intuitively think, and that is a good take home message.
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.
Good job making content. You should have showed how the win distributions are actually equal when all 4 cards or only 2 cards are played.
You could have then calculated the number of possible real bingo cards (an absurdly huge number), and realized while there could be incredibly rare edge case cards among a cards relatively close groupings, manufacturers are producing such a small pool of actual cards and could control variability. Why, I bet you could even make an algorithm that could figure out a fair number of appearances by each digit based on the number of unique cards that you want to include in a print run (or digital set).
Another fun problem would be figuring out the odds of 1 digit that is completely unique to a given card when producing n cards.
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.
Thanks for explaining this fact. You are very smart
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
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.
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.
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
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.
Cool analysis and surprising outcome. I definitely would have bet a lunch that the odds were exactly even!
If you repeat your simple example but the cards contain [1,2], [2,3], and [3,1], and the only numbers to choose from are 1, 2, and 3, there is no advantage. One could design a perfectly fair SET of bingo cards in this way, but of course not every game will be played with a complete set, so there may still be some small bias.
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.
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
I feel like you’re saying that cards that have unique numbers will be advantageous and bingo and that would definitely be true if in fact, there were actually cards with unique numbers and bingo, if they just made a set of bingo cards with the same number of each of the different numbers distributed across all of the different cards and then it would immediately get rid of the issue as you’re describing it, assuming every bingo card is distributed. If every bingo card isn’t distributed, then you would still have no way of knowing which of those bingo cards has been granted rare numbers, numbers not shared by other bingo cards that were distributed, and which of those bingo cards have been granted common numbers. You could also go totally random with it, every number on every bingo card could be independently chosen with the caveat that it simply can’t be a number that was already used on that board; then you really wouldn’t have any way of knowing the probability.
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
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!).
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.
People who win a lot are probably buying more cards than the others. The "good cards" would be distributed randomly each time. Semi-silly video.
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.
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...❤
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.)
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.
The odds that a card, chosen at random, has no numbers in common with another card chosen at random are quite small. Let's look at just the B column where the numbers are constrained to be between 1 and 15. Card A has 5 of those. So, if the numbers on card B are random, each number has about a 2/3 chance of not being one of the 5 numbers in A. (2/3)^5 is about 13%. In reality it's worse than that, because the odds are 10/15 (2/3) only for the first number in B. After that the odds are 9/14, then 8/13, then 7/12, then 6/11, because a number can't appear twice on the same card, so the pool of possible numbers and the pool of "safe" numbers remaining decreases by 1 each time. That means the odds that B has no numbers in common with A in the B column are only about 8.3%. And then the same thing is true of I, N, G, and O columns. The odds are 0.083^5, or a little over 4 in a million, that A and B have no numbers at all in common.
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.
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
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)?
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 🍀 🧐😇
This claims bingo has a competitive advantage and isnt fair while ignoring that everyone is given random cards, making it fair
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.
I think you should do this a bit bigger. Like monte-carloing larger sets.
I did not play bingo often. But when I did, I ususally picked my own numbers.
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.
What bingo hall let's people pick their cards?
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.
Bingo is just a humble farmer’s dog. Why you gotta pick on him?
I think you’re right but, other than your explanation, I don’t know why.
Have you noticed that ‘big’ bingo prizes are won late in the week? A once-upon-a-time friend who worked at a bingo hall (he was related to the owner) told me how that is arranged. Unfortunately, I can’t remember. But it happens. Can you explain it???
When my family was taking the bus to Disneyland 1974, a tour guide held bingo games for passangers to help pass the time (with reusable cards).
Noticed over a few days, that some players found that particular cards were "luckier" than others, and would covet (by surrepticiously marking) them.
Don't think the ball machine they used were as rigorously maintained or calibrated as the ones used in lotteries starting a decade or two later.
Hello can we be friends
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.
A good thing to learn before you go to live at the old folks home.
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.
All those quarters at the apple harvest bingo table....wasted...
And we were none the wiser
I dont think this can be considered as competive or advantageous in anyway. The only way to take advantage of this is if you had perfect information, the time to actually calculate which card in the pool of cards that get used in whatever bingo "event" you are going to has the best probabilty of winning, and do all that before anyone else starts gettinf cards...which is obviously impossible. All cards are not equal but the card you get is still completely random which nullifies this bringing it back to the game of chance....and no, you cant just see who keeps winning and try to trade cards...bingo cards are one time use, you stamp each number when it gets called, to prevent ppl from reusing them, so more cards get sold
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).
This is a very good question. To be honest I'm not sure I have a great solution. I suppose whenever you come across a word or phrase you're not familiar with, you could google that phrase with "math" next to it and see what comes up. I will say that learning math is a journey in probably any language and this is how I've learned quite a lot myself (just looking up things I've seen pop up on the internet) I'm sorry I couldn't be of more help, but I wish you the best of luck!
@@BriTheMathGuy You got degrees in maths? go back to school and ask someone to explain basic probabilty to you as you have got confused! They should be taking your degree back!
The BIGGER mystery is why people insist on a lucky seat and how that factors in to their win...
it's like a roulette wheel !! ... the more numbers there are - the lesser chance of winning !! ... your betting on dumb luck !!
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.
Good luck with the strategy of trying to trade bingo cards with someone who's winning. LOL.
The caller keeps certain balls after the first game.
Everyone criticizing this guy, but here in Panama you actually get to pick the card you want. And now I have a strategy.
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
You really should weight ties properly,so for instance a two way tie each winner only gets half.
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.)
I came for the Step Function and now Im watching how Bingo works. Lol, thanks man, you have an interesting channel! 😎👌🏼
If a machine that blows the balls around with air is used, then certain balls are more statistically likely to be called earlier than others, based on weight. At least that's my theory. At the campground where I live, I plan on recording every last bingo game (full card) and transcribing to text later. Then take a look and see which numbers are called early most often.
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?
The same people win over and over again, because they are the people buying like 10 boards per game lol. What you're explaining here has no actual statistical relevance when the boards are the size of typical bingo boards. And your conclusion to 'trade' cards with people who always win -- have you given up science completely in favor for superstitions? This would be funny if you weren't actually trying to make some type of valid point.
Every 85 year old in the nursing home playing to win "Moon Pies" secretly knows this
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.
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?
If a ball machine was used to draw numbers, how were the tollerances of weight and roundness of the balls were produced or maintained?
Help me out. I see your logic, but it still seems fair because cards are handed out at random. So, wouldn't you have just as much chance of getting a good card vs a bad one? And, like you mentioned, even IF you were given a choice, it would be extremely difficult to down right impossible to find one with an advantage. Am I wrong? Thanks. Great vid. More of these please!
For sure you have just as good a chance of getting a “good” card as a bad one. In that sense, the game is fair. On the other hand, as everyone is playing, it sure seems as though you’re just as likely to get a bingo as everyone else. (Though we now know this is not necessarily the case) Probably more and more people playing the same game would make the cards more “fair” to one another, as no one would have exclusive numbers anymore. To me, bingo is fair, but not an even game.
@@BriTheMathGuy "Fair, but not an even game". Well said. Thanks.
I feel as though the workers have a winning stack that they grab from for there regular players and a bad stack for the casual players just my thoughts.
@@edwardrodriguez4159 I feel you on that and the same people keep winning where I go smh I guess they tip good so they win alot
If the cards are handed out randomly, that is as fair as handing out the prizes randomly and just skipping the whole bingo. Indeed.
But can you be sure the cards are handed out randomly? Ever been to see a magician? I could design a set of "bad" cards, distribute those randomly to my visitors, and then use some trick to hand the only "good" card to a planted player. In principle. (Not an accusation, but don't think it cannot be done.)
Having work bingo at my fire company for years I've seen many looking for the "best" bingo card but we rarely have a night where any one person won a lot of games maybe 5 times in 10 years. So while your small test shows a slight advantage to a certain card when scaled up, I don't see it still having much if any effect on the game
For me, the message is the game can be easily fixed if the organizers want it to be.
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.
In 1988 I had been out in the sun all day so I decided to play bingo with the old folks on the cruise ship I was on. The room was pretty full with maybe 75 or 100 people playing, each with multiple cards (usually three). I played with three cards and won the first two games of four outright and then tied on the "blackout" fifth game (and I should have won but I was too slow with the previous number). And the crazy thing is that all three wins were on the *same* bingo card! Obviously the card shuffle had resulted in me having one card that didn't share numbers with most of the other cards out there even though there were maybe 2 or 3 hundred cards in play. I can tell you that I won enough money to buy a nice watch at the next port and that the other players were wondering if I was somehow cheating!