I, too, am confused about what advantage this knowledge gives you over others? Knowing that your bets are just as good as others' doesn't give you better chances. Or what's the game? I remember Prezbo teaching that to the kids in The Wire's fourth season. I didn't understand it then. Not that I'm into rolling dice, and not that this thing would be important to the playlist's point, but still!
I don't really know the answer to your question, but I would point out that for any pair of six sided dice, snake eyes may have a 1/36 probability of turning up, but having the number seven (regardless of how it's added up on the pips) has significantly higher probability. You could have the dice roll 1+6, 2+5, and 3+4, and there are two of each of those in combination on the dice so you have essentially the same probability of 7 on a roll as you do of having ANY pairs, which is 1/6 probability.
Remember, this was a time when the concept of probability didn't exist. So if your opponent thought 6 or snake eyes was lucky for some divine reason then they'd be at a huge disadvantage!
I love the presentation!! It is slow enough for me to grasp the idea but fast enough to keep the message interesting and engaging! Good work and keep it coming Brit and Khan!!!!!!!!!!!!!!
I still don't understand how did this help Cardano beat his friends at rolling dice. I get that Cardano calculated that the probability of rolling "snake eyes" .. but then what ? So the probability of getting "snake eyes" is 1/36. But then so is the probability of getting any other unique combination!
If you bet based on a criteria, you're choosing a subset of probabilities, not just one. If said criteria encompasses a larger number of probabilities than your opponent's, your chances of winning would increase. An example of a criteria: Betting for pairs, betting for a total sum of 'x', etc.
there are 1 out of 36 ways to get a 6 and a 6. there are 2 out of 36 ways to get a 5 and a 6 though. thats a simple example, but using more complicated forms like what numbers add up to 9 or 4 or 3 (and they DO have different probabilities) he can bet on the most numerous of the 36.
he picks numbers with higher probabilities, like rolling a 3 and a 2 is more likely then rolling a pair because theirs more then one combo out of 36 that cause it. it is partially luck, but it's calculated luck that he can assure he has a higher chance of winning.
I really don't see how this would help you that much... sure you know the probability of rolling a pair of threes, but even if you bet accordingly there's always the possibility of the three threes coming, or not coming up... so it still all boils down to luck... i think?
I think people are confused by the narrator's choice of words: he said Cardano's opponents relied on "hunches and lucky numbers." Now, "lucky numbers" makes sense; like you said, it's easy to imagine Cardano modifying his game to exploit his opponents' tendency to choose certain numbers. But to me a "hunch" is a random guess; unexploitable. So maybe by "hunch" he meant Cardano's opponents reliably played as if they believed something like the gambler's fallacy to be true- that you could exploit.
Other than making dice and probability a field of study, I'm pretty sure that in Italy during the 1500's they already figured out how dice rolls work a long time ago. The Romans invented the bloody things, you would think the rules and the commonly known strategies involving the games were already sophisticated. I think his friends were just suckers. Spoiled and snobbish brats who were never exposed to gambling while Cardano spend a lot of his spare time at the docs and in the taverns. :-)
I assume he would bet high on likely outcomes and bet low on unlikely outcomes, but his friends would bet high on outcomes that worked out well for them in the past ("lucky numbers") regardless of the actual probability of them.
Only if they played the game with one die. 1 through 6 are equally likely in that case. But if you play with multiple dice, certain sums are more likely than others. Think of rolling two dice. There's only one way to add them and get 2 (roll a 1 on both dice), but there six ways to add up and get a 7 (roll 1 and 6, 2 and 5, 3 and 4, and the reverse of these). That makes 7 six times more likely than 2. They might have used different rules but there's always a way to play strategically.
I think he meant that by staying a consistent path, Cardano hedged his bets against people who would constantly change their choices and therefore increase the odds against their favored event. Another way to conceptualize this is if you have a multiple choice test and you know jack about it, stick to one letter (commonly C :) as moving around choices will inherently mess with your set odds for eg 1/6
Of course it's luck. Probability only gives you a reasonable expectation; it is reasonable to think that you would roll a pair of 3s about 1/36th of the time, since all possibilities are equally likely. But it's still entirely possible to roll a million pairs of 3 in a row; very unlikely, but entirely possible.
Unfortunately the Cardano metaphor distracts from the purpose of this video. How did this help Cardano win? Did he roll the dice multiple times and never change the outcome he bet on? Aren't his chances the same as his opponents? Did they really have plaid flannel shirts in 16th century Italy? Why are they gambling with Spanish money from the Central Bank of Peru? How come they're drinking O'Keefe Ale? Holy shi* what's that video that says "Don't Shoot The Puppy!!" and has 700,000 views?!?!?!?
![Lil Uzi Vert - We Good [Official Audio]](http://i.ytimg.com/vi/DrSfBULAsek/mqdefault.jpg)
I watched this about 5 times. The probability hypothesis was brilliant.
I, too, am confused about what advantage this knowledge gives you over others? Knowing that your bets are just as good as others' doesn't give you better chances. Or what's the game?
I remember Prezbo teaching that to the kids in The Wire's fourth season. I didn't understand it then.
Not that I'm into rolling dice, and not that this thing would be important to the playlist's point, but still!
I don't really know the answer to your question, but I would point out that for any pair of six sided dice, snake eyes may have a 1/36 probability of turning up, but having the number seven (regardless of how it's added up on the pips) has significantly higher probability. You could have the dice roll 1+6, 2+5, and 3+4, and there are two of each of those in combination on the dice so you have essentially the same probability of 7 on a roll as you do of having ANY pairs, which is 1/6 probability.
I LOVE this. PLEASE do more videos like this!
Remember, this was a time when the concept of probability didn't exist. So if your opponent thought 6 or snake eyes was lucky for some divine reason then they'd be at a huge disadvantage!
I love the presentation!! It is slow enough for me to grasp the idea but fast enough to keep the message interesting and engaging! Good work and keep it coming Brit and Khan!!!!!!!!!!!!!!
They are expanding and improving what they do. This seems to be a new type of video they are trying out. And imo it works out just great!
khan academy = great education - peer pressure
Very well done, these new additions are fantastic. Thank you!
this makes statistics cool
Exactly what i'm wondering, probably just bet that a pair would show up each time and won more often than not because of it
That guy just increased our freaking maths syllabus for money
Good Video. I love the Editing. So much better.
Highschool math. Interesting nonetheless. If videos like this were shown in classes, more students might pay attention
He was a mathemagician
I still don't understand how did this help Cardano beat his friends at rolling dice. I get that Cardano calculated that the probability of rolling "snake eyes" .. but then what ? So the probability of getting "snake eyes" is 1/36. But then so is the probability of getting any other unique combination!
nice animation=) this is actually probability in general (that become Space with the animation xD)
I swear, probability is such a basic thing to conceptualize. But higher probability is one of the hardest math branches to master. -_-
If you bet based on a criteria, you're choosing a subset of probabilities, not just one. If said criteria encompasses a larger number of probabilities than your opponent's, your chances of winning would increase.
An example of a criteria: Betting for pairs, betting for a total sum of 'x', etc.
there are 1 out of 36 ways to get a 6 and a 6. there are 2 out of 36 ways to get a 5 and a 6 though. thats a simple example, but using more complicated forms like what numbers add up to 9 or 4 or 3 (and they DO have different probabilities) he can bet on the most numerous of the 36.
he picks numbers with higher probabilities, like rolling a 3 and a 2 is more likely then rolling a pair because theirs more then one combo out of 36 that cause it. it is partially luck, but it's calculated luck that he can assure he has a higher chance of winning.
I really don't see how this would help you that much... sure you know the probability of rolling a pair of threes, but even if you bet accordingly there's always the possibility of the three threes coming, or not coming up... so it still all boils down to luck... i think?
I think people are confused by the narrator's choice of words: he said Cardano's opponents relied on "hunches and lucky numbers." Now, "lucky numbers" makes sense; like you said, it's easy to imagine Cardano modifying his game to exploit his opponents' tendency to choose certain numbers. But to me a "hunch" is a random guess; unexploitable. So maybe by "hunch" he meant Cardano's opponents reliably played as if they believed something like the gambler's fallacy to be true- that you could exploit.
Peru! The currency shown in the beginning part of the vid is my home country! 3
Vegas here I come!
Let us go to four dices and have a tesseract!
But how it helped him in dice games ?
can u do a video on the math behind counting cards?
Other than making dice and probability a field of study, I'm pretty sure that in Italy during the 1500's they already figured out how dice rolls work a long time ago. The Romans invented the bloody things, you would think the rules and the commonly known strategies involving the games were already sophisticated.
I think his friends were just suckers. Spoiled and snobbish brats who were never exposed to gambling while Cardano spend a lot of his spare time at the docs and in the taverns. :-)
i miss the occasional sneeze/cough
bro LMAO
I still don't understand how did this help Cardano beat his friends at rolling dice.
I assume he would bet high on likely outcomes and bet low on unlikely outcomes, but his friends would bet high on outcomes that worked out well for them in the past ("lucky numbers") regardless of the actual probability of them.
@@sliver170 but don't they all have the same probability in this case?
Only if they played the game with one die. 1 through 6 are equally likely in that case. But if you play with multiple dice, certain sums are more likely than others.
Think of rolling two dice. There's only one way to add them and get 2 (roll a 1 on both dice), but there six ways to add up and get a 7 (roll 1 and 6, 2 and 5, 3 and 4, and the reverse of these). That makes 7 six times more likely than 2. They might have used different rules but there's always a way to play strategically.
Thanks a lot
I know that dictators are bad, but if Khan became a dictator for all schools I would go for it.
I think he meant that by staying a consistent path, Cardano hedged his bets against people who would constantly change their choices and therefore increase the odds against their favored event. Another way to conceptualize this is if you have a multiple choice test and you know jack about it, stick to one letter (commonly C :) as moving around choices will inherently mess with your set odds for eg 1/6
Measure theory ftw!
Of course it's luck. Probability only gives you a reasonable expectation; it is reasonable to think that you would roll a pair of 3s about 1/36th of the time, since all possibilities are equally likely. But it's still entirely possible to roll a million pairs of 3 in a row; very unlikely, but entirely possible.
i mis worded that, rolling a 3 and a 2 is more likely then rolling a 3 and a 3. not ALL pairs accumulative.
haha! just watched the next video and realized you are the narrator. so is that what you meant? :) also great vids.
what about doubles? would not the chances increase if the pairs are = and occur again when rolling 2 dice?
Is Probability space=sample space??
…Filmed in Peru?
What is the use in this context?
Who says gambling doesn't help?
Too real
2+2=4.1..........
thought the video was on quantum mechanics lol
Watching in 2024
What is the name of the guitar track ?
En el vídeo aparece el billete de 10 nuevos soles del Perú xD!
i dont get it
so how could he win more than just by luck?
if for both the probability is 1/6..?
lucky 7!!!!!!!
por qué está usando nuevos soles?
Hello, I have a request ... You could subtitle videos in Portuguese?
why?
So 6th grade?
what ?
THIS ISNT BY SALMAN KHAN?! WTF
Unfortunately the Cardano metaphor distracts from the purpose of this video.
How did this help Cardano win? Did he roll the dice multiple times and never change the outcome he bet on? Aren't his chances the same as his opponents? Did they really have plaid flannel shirts in 16th century Italy? Why are they gambling with Spanish money from the Central Bank of Peru? How come they're drinking O'Keefe Ale?
Holy shi* what's that video that says "Don't Shoot The Puppy!!" and has 700,000 views?!?!?!?