The Easiest Problem Everyone Gets Wrong
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- čas přidán 26. 05. 2024
- We know how difficult the Monty Hall Problem is for so many people even after they’re shown all the math behind the best possible strategy. It’s basic probability, but it’s deceptive -- and it all started with the Bertrand’s Box Paradox.
In this video, I go back to the origins of a probability problem that continues to plague humanity. And it all started in 1889 when French mathematician Joseph Bertrand published his “Calcul des probabilités,” which included a simple scenario involving gold and silver coins.
70 years later, recreational math columnist Martin Gardner unveiled The Three Prisoners Problem involving the pardoning of one of three prisoners scheduled to be executed. The mathematical concept was the same as Bertrand’s Box, but The Three Prisoners continued to be a probability paradox that haunted everyone from the readers of Scientific American to professional mathematicians.
But the Monty Hall Problem is really what made this mathematical illusion explode. By the 1990s, there was an all-out argument about whether all of these problems -- Bertrand’s Box, Three Prisoners, and Monty Hall -- were paradoxes or simple 50/50 coin flips. It’s time to go back to the beginning… and show why there’s something even more important than solving this math problem.
** SOURCES **
Krauss and Wang, “The Psychology of the Monty Hall Problem: Discovering Psychological Mechanisms for Solving a Tenacious Brain Teaser”: www.researchgate.net/publicat...
“Why Humans Fail in Solving the Monty Hall Dilemma: A Systematic Review”: www.ncbi.nlm.nih.gov/pmc/arti...
Joseph Bertrand’s “Calcul des Probabilités”: archive.org/download/calculde...
Dan MacKinnon (mathrecreation), “Monty Hall and The Three Prisoners”: www.mathrecreation.com/2009/03...
Dan Jacob Wallace, “Bertrand’s Box Paradox (With and Without Bayes’ Theorem): www.untrammeledmind.com/2018/...
Eugene P. Northrop, “Riddles in Mathematics”: archive.org/details/RiddlesIn...
** LINKS **
Special thanks to Internet Historian: / @internethistorian
Vsauce2:
Twitter: / vsaucetwo
Facebook: / vsaucetwo
Talk Vsauce2 in the TCU Discord: / discord
Hosted and Produced by Kevin Lieber
Instagram: / kevlieber
Twitter: / kevinlieber
Podcast: / thecreateunknown
Research And Writing by Matthew Tabor
/ tabortcu
Editing by John Swan
/ @johnswanyt
Huge Thanks To Paula Lieber
www.etsy.com/shop/Craftality
Select Music By Jake Chudnow: / jakechudnow
Get Vsauce's favorite science and math toys delivered to your door!
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#education #vsauce2 #learning
"I'm about to stretch my winkey until it snaps."
Well I'm scared.
Winkey and Pudding torture
he's very elastic.
Oh no.
it seems like he knows what winkey means in the rest of the english speaking world, outside of the usa lol
he was subtly alluding to it for all of his foreign english speaking viewers, while still dodging the wrath of the american english based algorithm lol
And Jesus wept.
Kevin: Right?
Me: nods head
Kevin: *wRoNg*
*_Cries in corner_
he should really learn to be compassionate.
😭 I cry everytime
OK, I solved the problem AT 2:18 ! Orange said, "If I'm going to live, just choose which of the other two you'd like to name." So Orange lives! BUT, Kevin did not keep his word!
(I'm replying to Soumya so y'all can see my comment.)
@@allegrovivace6806 no actually that's a humrous part
purrfect, me too have learnt to do that, lol.
I once wrote a program that ran a long series of Monty Hall examples. I was sure it would prove the contestant who did not switch would win just as often as the one who did. When I ran the program, the contestant who switched won twice as often. It was fun having my own code tell me how wrong I was.
I would very much love to see an example of that program. Do you by chance have the source on GitHub or a similar means of sharing?
@@VizXRyRy Sadly, I wrote it many, many years ago in Hypertalk.
I want to believe you, I do, but everyone who tests out this problem one way or another claims they can’t share proof of their findings.
@@yellowpowr8455 you can see it is very clearly, when you switch, you win about 2/3rds of the time, and when you don't, you win about 1/3rd of the time. it is not 50/50.
I also wrote a program to run over 10,000 tries. It came up 50/50 for switching. This is, once you remove the flawed math of the actual problem setup -- the host/warden knows and may get to choose which is identified, which in itself is a choice.
My favourite way to explain the Monty Hall problem:
Imagine you're going into the game with the plan to switch. In that case, you want your first guess to be a losing door, so that the other losing door will be revealed and you get to switch to the winning door.
And since there 2 losing doors, you have a 2/3 chance of successfully doing this. So always switching gives you a 2/3 chance of ending up with the winning door.
I think it is an excellent way to look at it. It makes it easier to understand the logic but it still makes the result puzzling.
I try to explain it by exaggerating it to an extreme. Say I am thinking of a specific grain of sand on Earth, and you must pick the one I am thinking of. There are so many grains of sand you are pretty much gonna guess wrong. After you pick a grain of sand, I remove all other grains of sand except the one you picked and some other grain of sand, and one of those 2 grains is correct. It's so extreme that despite narrowing it down to 2 grains are you really gonna think that all of a sudden you had made the ultimate lucky guess all along? When you initially picked that grain you'd be thinking, "there's no way this is correct", so why would it be correct now? And I guess it is as you stated you go in expecting to pick a wrong choice since a wrong choice is more likely, making the other revealed choice more likely to be the correct one.
Not if you realize there is only (1) independent choice being made and that is the first one since the 2nd choice is dependent on a known outcome. @@Trip_mania
@@keylimepie3143 Yes this is also how I think of it, and it becomes very clear. If you think of the problem with 1000 doors instead of 3 suddenly it is trivial to most people. It's the same with the gold coin problem here, if you just imagine the first jar has 1000 gold coins and the second jar has 1 gold coin and 999 silver coins, after you pick the first gold coin you're either on the jar with 999 gold coins or on the jar with 999 silver coins, but it's pretty obvious that you're way more likely to have picked up a gold coin from the jar with 1000 gold coins.
It really feels like Kevin is training us for when he eventually takes over the world, and the only way to survive is through paradoxical games he set up.
He just got reminded of a puzzle
DUUUUUUUUDE UNDERRATED COMMENT
You know too much. I'll have to recalibrate my plans.
@@Vsauce2 Dude, we are three. Just do this one
But now there is 4
Everybody gangsta till Kevin starts stretching his winky until it snaps
WARNING I am the unprettiest human alive and I need YT to afford my house and the desires of my two girlfriends so please observe my highly stimulating videos, dear adel
DEMONITIZED
Why do I see this big foot with Internet access everywhere
😂
@@Agvazela_Vega *_cursed comment?_*
This didn’t make sense to me as a child when I heard it, but now that I’m older it makes complete sense. There’s a 1 in 3 chance that whatever your picking is the right choice. That means that there is a 2 in 3 chance that one of the other two is the right choice. If you eliminate a wrong option then there is still a 2 in 3 chance. If someone explained it like that to me when I was younger I would’ve gotten it easily.
I think the problem is the phrasing. Eliminated, Removed, Taken Away. When you see the "whole problem" even after the choice is made, you can get the correct answer. If you see the "remaining problem" your answer is wrong.
In your explanation you are considering the "whole" problem. There are 3 options, 1 is incorrect but 2 are correct. but all 3 were/are possible.
Orange Winkey is seeing the "remaining problem" There *were* 3 options but now there are 2, so he see's the choice is 1 of 2 possible.
That's why I feel the gold coin explanation is better.. It breaks the 3 options into 6 parts: 2 gold, 1silver 1gold, 2 silver. It "removes" the [2/6] option [silver/silver] while still showing that the remaining 3 coins you can choose 2 of them will be gold while one is silver [2/3 in golds favor.
The illusion is reducing the 2/3 chance of gold into a 1/2 chance because the choices are either gold or silver.
yeah, we get tunnel vision on what options have instead of what options are avaliable
one of the 2 in 3 chance got eliminated, therefore, you are back to 1 in 3
if there are 3 boxes and 1 has gold in it and other two are empty, you pick a random box and have 1/3 chance of being correct. Each other box also has a 1/3 chance, now one of the incorrect boxes is removed. Because there was a 2/3 chance that one of the boxes you didnt pick has the gold, the 1/3 chance from the removed box is effectively transferred into the other box.@@bobconnor692
No kidding! I had trouble with it when I first saw it, too. But over time, I came to understand it better- Monty Hall's reveal does not affect the correct answer nor does it affect your choice.
For the Monty hall a way to make it more intuitive IS imagining 1000 Doors you pick one door the présentator opens 998 Doors only the one you have picked and an other one Can be the right door, you know it's probably the other door still closed.
Me watching this alone: probability and such
Me when my mom walks in: I AM ABOUT TO STRETCH MY WINKY UNTIL IT SNAPS
XD
underrated
oh sorry mom my winky was talking to me
@@starlegends3092 hej
@@oliwia5877 hej! Jag alskar avenska! Men jag lara det.
That was probobly bad grammer XD
Kevin: Right?
Me: Yea-
Kevin: WRONG!
----------
Kevin: Right?
Me: N-
Kevin: Yes!
@RaptorM82 no!!!!
@RaptorM82 why would you think that lol ( I assume you are kidding but idk)
RaptorM82 no they were gonna say No not that
@@irenaveksler1935 yah I think that’s known lol :)
Petal Girl lol
I've watched many Monty hall paradox problems. About half of them have successfully made me understand. But Everytime I encounter it again I have to learn it all over again. It's a really counterintuitive problem.
This is the method that worked best for me: Cut the "reveal" out of the equation, and collapse all the remaining choices down into one.
Three doors, one has a prize. You pick a door, but before anything else happens, you get a choice: Keep your original pick, or swap and take BOTH of the remaining doors. If the prize is behind either one, you win.
In that case, it seems obvious that you should swap. So, when you have the host reveal that one of the two doors you get in the swap is empty, you don't actually have any new information: you know that at LEAST one of those doors is empty already, you still get to pick both doors.
Another good way to think about it: Bump it up to 100 doors, using the same method. You pick one, and then you can swap and keep the other 99 if you want. Monty will show you that 98 of those 99 doors are empty, but you still get to keep all 99 doors. So, which is more likely: That your 1/100 first pick was right, or that the 99/100 doors you didn't pick has the car, and Monty is showing you which 98 of those 99 doors are empty?
This is the most intuitive version of the Monty Hall problem I’ve ever seen
"You're watching this video because you're a smart, curious person"
Me: Nodding my head pretending I understand
I'm not even going to pretend that I understand.
Being stupid never felt so smart
it's actually a simple problem but i think he didn't explain it super well, if you think about it like having 3 groups of numbers like this:
1 1 they are the same
1 0 they are not the same
0 0 they are the same
2/3 times the other number in the group is the same number, i hope this helps.
The part that throws most people off is that this isn't a real paradox.
Skinnymarks Who are you to dictate what is and isn't a paradox? This is a veridical paradox.
I always had a feeling that Internet Historian was a little stretchy orange man.
I had to play it back several times - I guess it wasn't just me imagining things after all!
The world was finally ready... The face of a new dawn... *Orange winkey*
An unkillable stretchy orange man
A winkeyw
et Han of Astora But he was killed!!!
The biggest mistake of people who don't understand the Monty Hall Problem is that they accidentally see 2 empty boxes as one box. So when they choose a box, they think there are only TWO different scenarios in front of them: The chosen box is empty, or the box has prize in it. It's WRONG.
In fact, there are THREE different scenarios about chosen box: The prize box, the 1st empty box and the 2nd empty box. Remember, there are 2 empty boxes in the game, not one.
* Chosen 🤦♂️🤦♂️🤦♂️
One get eliminated, just like the blue toy... So it's empty and filled with prize. Still 50/50
I’m sorry sir, but that is pink, not purple
And red not orange
@@JoyfulJay08 it’s kind of both
@@JoyfulJay08nope
I swear Internet Historian sounds like he's about to laugh the whole time
Tbh i got so surprised when i heard him
Dont
I was so disappointed that when Kevin pulled out the second orange that Historian would have two voices
Not at all
He probably did.
Did I just watch 16 minutes of some dude playing with his winky and sticking it in pudding and acting like I understand
Lmao
I read this before he said what a winkey was and I was confused
You know you loved every minute of it.
Uh yeah
Correct
I'm laughing extremely hard. This is a thoroughly amusing way to learn about math paradoxes!
When I heard the Monty Hall version of the statement, it definitely seemed like it should be 50/50, but I think I found the coin version much clearer. Sure, 50% of the remaining possibilities are a gold coin, but if you had selected the gold/silver option, there would have been a 50% chance you drew the silver coin first.
But that then flips the problem to being a 1/3 you got the silver gold vs the 2/3 you grabbed silver silver
The Monty Hall version is indeed a 50/50, as you make a second choice.
Essentially your first pick is just there to confuse you but actually doesn't matter, the only door that really matter is the one you choose at the end, when there's only two doors...
But, in the three prisoners version, the warden doesn't draw a second time, so even after one of the three is executed, the odds doesn't really change.
So, the two "versions" are actually two different problems...
@@Sephiroth517 You are wrong about Monty Hall. When you make first choice, the odds are 1/3 that your choice is right and 2/3 that it's wrong. But when you choose the second time, the odds of your first choice still 1/3 but the odds that the other door is the right one are still 2/3. In other words, your first choice have really poor chances of picking the right door. So why would you want to stick with it?
@@MaxusR Since your first pick doesn't matter, the second pick is the only one you consider, hence a 50/50, the other door can't magically increase to 2/3 odds since there only 2 doors...
@@Sephiroth517 It does matter. Pretend that there are 100 doors instead of just 3. The odds that you've chosen the right one are 1%. Then another 98 doors are eliminated. Do you think that your first choice with 1% chance of winning still have the same odds with the other door? Your door can't magically increase to 50% odds since when you picked it there were 100 doors.
“Thank you for licking me clean, Kevin” must have been one of the weirdest things he ever said.
"your tongue is so smooth"
And that fact their names are called WINKYS it just sounds well... ( ͡° ͜ʖ ͡°)
@@kevinnguyen552 Nice :)
0:02
Or "my winkie is talking to me!"
Whenever Michael(Vsauce1) seems to arrive at a conclusion, he says, "Or is it?"
And when Kevin seem to arrive at it, he says, "WRONG!"
Harikishan Rakhade or does he?
@@alexsorgard2225 wrong!
Hand Grabbing Fruits WHAT IS WRONG?
I think the explanation with the coins was the most clear. I guess people treat all the gold coins as the same coin since they are all gold coins, but when you break it down and consider each coin a separate thing with equal chance to be picked initially then you can conclude the result you have explained.
The reason for this is clear (I'll use the coin scenario): If you pulled a gold coin initially, that improves the probability that the box from which you pulled had two gold coins because it was more likely that you pulled from that box (you had a 100% of pulling gold from that box vs only a 50% chance from that other box). To throw in Monty Hall, you can imagine boxes that contained either 100 gold coins or 1 gold coin and 99 silvers. If you pull a gold coin, you can pretty safely guess that it's from the box that contained 100 gold, though there is a small chance (less than 1%) that you are wrong.
“My winky is talking to me”
“I’m going to stretch my winky until it snaps”
“Welcome to the three prisoners paradox”
“I’m going to stick my winky in my pudding”
This is out of context gold.
All of the ones with winkie in them sound like sexual innuendos...
But the question is: what is the chance the other out of context coin will also be gold?
famous last words
"I got tricked be a winkey."
"My mom stickied winkys in my pudding"
Kevin: "I will stretch my winky till it breaks"
People in the UK: *demonic screaming*
People all over the world:
me: what is he found g
lol
I’m not in the UK and it still DEFINITELY sounds wrong
‘My winky is talking to me’
I think the part that really makes it harder to realize is that the part that tilts it is the odds of pulling a yellow with a silver vs the odds of pulling a yellow with a yellow. Basically, the illusion of equality is created by the thinking that simply getting rid of one of the possibilities leaves an equal chance, which would only be true if you knew one of the possibilities was eliminated without drawing a color yet. Once you draw the color, the odds are then tilted, but this is often overlooked because of the seemingly simple first answer you would think of. Basically, you first process the first piece of information, which is that one possibility has been eliminated, and then forget about how the color pulled affects the probabilty of what other color is pulled.
This is literally the first time I've actually understood this topic well done!
“Do I need to teach you college level statistics?”
“Do I need to teach you high school statistics?”
“Do I need to teach you 8th grade statistics?”
“Do I need to teach you kindergarten level statistics?”
BooOOoooOoOooOoOooOONnnNNNnnnnNnnnNEEEeE!!???????
I'm so glad I was not the only one who thought that the time I saw this
BOOOOONE!
This is youtube, so we're gonna need preschool level statistics.
Thing is, most people don’t understand statistics intuitively.
I find a branching graph to be the best way to represent statistics intuitively as it shows visually different versions of the world given a change.
I finally understood the Monty Hall's problem when a friend told me: "Imagine there are 100 doors. One of them has the money. You choose, say, number 10. Monty Hall says the money is in either door number 10 (the one you chose) or number 82. Would you switch to door 82?"
Yes
I watched this video but for me it's still a 50/50 chance. I still don't get it
@@davidkedra3001 think about it logically. You pick door 1 out of three. He then will decide to open a bad door, either 2 or 3. there is a 2/3 chance one of the two is the right door. he will always pick a bad one so if door 2 is the good one, he will purposefully pick door 3 and vice versa. Because of this the probability does not change. Door 1 has a 1/3 chance of being the right one and door 2 and 3 together have a 2/3 chance. Since he has already openedeither door 2 or 3, the one remaining has a 2/3 chance of being correct.
@@davidkedra3001 ok, let me explain this for the onrange one he had 100% chance to pick orange, but for the mixed he had 50%chance to pick orange, thus since he has orange he had 2/3 to pick the orange
@@stevenbowdich6716 Yeah, it's a simple probability change. For those who are still struggling. Look at this simple depiction. There are 3 options. Let's say you always pick the first door.
100
010
001
if you switch, you win in the second and third scenario thus your chance is bumped to 2/3 instead of 1/3. You can basically do the same for picking door 2 and 3 and always get the 2/3 winning chance. My only issue here is that there really is no paradox here. The second pick, switch or stay isn't a disconnected event. 50/50 is true only if after your initial pick and the false door being locked out you completely forget about what just happened and what are the rules and just pick a door randomly.
As soon as you started I was thinking _Monty Hall Problem.! Good work for bringing another perspective to a hard problem. :)
3:18 "Aaaand, just like that, your odds are now 0."
This "Monty Hall Problem" was featured already 3 times on vsauce... Looks like you really love it
It wasnt just me who thought about this
Running out of ideas
A good teacher knows when the majority doesn't understand something. This is why good teachers will teach a lesson more than once using several approaches. Take the time to notice the confusion around the topic and the need for more examples is clear. I honestly think it will take more than 3 videos on the topic for most people to comprehend this different way to mentally analyze their odds.
@@statikwolf69 It's possible this is because people were very confused in the other videos
Also repeating something will physically make a memory form better by strengthening the neural connection in your brain
Yeah, I could tell it was the "Monty Hall Problem" before he even posed the question and was hoping it would be something new... but it keeps getting the views and seems people keep not understanding, so it makes sense they would keep doing it with different approaches. Whenever I sense someone I'm trying to teach is not grasping something, I'll try a different approach or phrasing. For those that grasped it in previous iterations, it may sound the same or repetitive, but for others, it may just be the angle that cracks it for them.
That said, hope this is the last one of these.
So, my daughter was coloring when I started watching this and heard the "I'm gonna stretch my winkey" line and immediately (with the most confused/concerned face an 11 year old can make) asked me what I was watching. LMAO. Thanks Kevin....
Did she watch the rest of the video with you? And how much of it did she understand? :)
Also want to know
Yeah, I started the video over (a couple of times because we both started giggling) but then she watched the whole video with me. Afterwards, I got out a notebook and explained everything a bit more to her so she could understand it better.
@@presumedlivingston9384 Thank you for being a good parent and person. It helps change the world when we learn to co-operate and embrace curiosity.
I'm just happy that she wants to watch/learn stuff just like I do. She's addicted to Tier Zoo because of me. Lol
10:45 oh! I figured out why, this time. The coins weren't actually randomized, they were deliberately placed in this arrangement. Otherwise there would be a small chance (1/12 I think? Or, it is common enough to bridge the gap between 66% and 50% which is 1/12) for there to be three boxes of gold+silver. This averages out across all possibilities to make 50% of all coins after a gold coin also gold, and 50% of all coins found after a gold, silver. So, mapped out...
11 10 00
11 01 00
11 00 10
11 00 01
10 11 00
10 10 10
10 10 01
10 01 10
10 01 01
10 00 11
01 11 00
01 10 10
01 10 01
01 01 10
01 01 01
01 00 11
00 11 10
00 11 01
00 10 11
00 01 11
This is 20 possibilities, and a variation of 3 mixed boxes being presented to you is 8/20, or 40%. If we discard those, because we know they are impossible, we then instead get these 12 possibilities:
11 10 00
11 01 00
11 00 10
11 00 01
10 11 00
10 00 11
01 11 00
01 00 11
00 11 10
00 11 01
00 10 11
00 01 11
And also, if we eliminate the ones with a leading 0, where we found a silver coin first, we get these 6 possibilities:
11 10 00
11 01 00
11 00 10
11 00 01
10 11 00
10 00 11
Which simplifies down to 2/3 that the second coin in our box is gold, by process of elimination starting with a uniform distribution.
I was confused till I saw this comment
Having it all arranged in binary form has made it click
Thanks man
@@thatapollo7773 I was struggling to find all of them until I decided to sort them in descending form as binary numbers
Other commenters have given good explanations for understanding the coin problem, but another aspect is how the setup takes advantage of the shortcuts our brains take by obfuscating the fact that every single coin is unique. Our brain thinks, "Oh these are all gold coins, so they're equivalent," but as the video states, it matters that there are three unique gold coins you could have chosen at the beginning.
Imagine the coins are actually pairs of numbered cards in three separate stacks, the first pair labelled 1 and 2, the second pair labelled 3 and 4, and the third pair labelled 5 and 6. You draw a card but don't look at it, and show it to your friend instead. They say the card is either a 1, a 2, or a 3. Then they ask you what the odds are that the other card in the pair is a 1, a 2, or a 3. Well, the card can either be a 1 (if you first drew a 2), a 2 (if you first drew a 1), or a 4 (if you first drew a 3). So the odds are 2/3. The original coin problem basically imparts the same information without making you intuitively aware of it. The mathematical probability reflects all the information logically available to the perspective holder, but the setup hides the information from them in a practical sense until they've had the oversight explained.
Let me rephrase what he said in the video: "The Winkies are left to wonder, who lives, who dies, and who tells their story."
I WAS THINKING THIS
LMFAO
damn i got that reference
Glad to see my hami fans
And that's how you don't throw away your shot at a perfect pun!!!!!
This was so confusing until he drew arrows from coin to coin
Yes, when I originally tried to wrap my head around the Monty Hall problem, what did it for me was also the distinction of each individual choice option. What makes it difficult for us to understand is that we instinctively group together options that appear to be the same. As such, when a gold coin is drawn, our brains sort of refuse to consider the notion that it matters which SPECIFIC gold coin was drawn. Outlining the various choice scenarios with each separate coin (or door, in the case of Monty Hall) as the starting point is the explanation needed to make the logic snap into place in most people's minds, I think.
It's still not right because your first choice is 50/50 gold or silver and if gold is chosen the first choice is 1 in 3 between the gold coins. After the first coin is chosen there are only two gold coins left so the second choice is 50/50. He's just using semantic slight of hand.
@@WoodRabbitTaoist yeah I'm.. I'm not wrapping my mind around it. I think the coin demo is wrong. I feel like i understand the argument though:
Once you've chosen the first gold coin, you don't know which one you've chosen so there's 3 scenarios.
1. G1 then G2
2. G2 then G1
3. G3 then Silver.
Therefore 2/3 chance you're in a situation where you will pull a second Gold coin.
But... Because they're paired, there's really only two scenarios after you've picked a gold coin.
1. You picked the G1 & G2 pair
2. You picked the G3 & Silver pair.
Picking G1 vs picking G2 is the same scenario, not two different scenarios. Because order isn't important - the only question is whether the second coin is gold. At least, how it's presented here. Seems more like a "lol u r dumb" trick rather than a Paradox.
@@TheHigherFury Picking G1 and picking G2 are different scenarios though; once you've chosen a gold coin the scenarios are:
1. you picked the G1 and G2 pair by picking G1
2. you picked the G1 and G2 pair by picking G2
3. you picked the G3 and silver pair
Because of the fact that G1 and G2 are two different coins, the odds are that it's a 2/3 chance of picking G1 or G2.
@@benparsons4979 you would be right if the question was, which specific gold coin did you pick?
But the real scenerio is
1. Jar A
2. Jar B
And no matter how much you want to believe pulling a Gold coin gives you more of a chance in that specific jar to get another gold coin it will always run on to be 50/50.
Now if you pull a silver coin you can bet with 100% certainty the other coin is gold. Provided you are still dealing with just the two jars add the third jar and things get spicey.
I love how he does paradoxical games and math, but the humor that is in the videos is great
Blue winky here! Thanks for the beat down! I feel better now. Since I went to the hospital. But I’m glad I could still participate! Thanks! - blue winky
Vsauce: ... or is it?
Vsauce2: ... right? WRONG!
what about Vsauce 3 ?
Seems like Kevin hasnt taken his pills
He's talking with winkeys again.
But the winkeys be talking back man
@@azariah8675 you sure you're not high?
The winkeys even complimenting him lol
@@jennicornplayz8178 i sure am not high right..?
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
*His Normal Pills
You got a new sub, ur videos make me think A LOT (thats good)
8:00 we all know it's orange orange because you set it up and you did that so you'd have a 100% chance of pulling out an orange for the skit.
To everyone who still doesn't get the monty hall problem and doesn't want to be blinded by too much math try this variant out with a friend.
Get a deck of 52 cards and get your friend to point to a card which they think is the Ace of Spades (without them looking) and place their card face down, then while you can see the other cards remove 50 other cards and show that none of the 50 cards are the Ace of Spades. Now there are only 2 cards left, the one your friend chose and the remaining card in your hand.
Now ask them if they want to switch to the other card.
it's basically a choice of "a random guess" vs "something the host knows is the right answer" (this is the case even if you chose the correct answer, as the host will have to choose randomly if you choose the correct one)
@@shinydewott Exactly. This is a way to try to show the person that the host actually conveyed information by choosing which choices to remove.
Unfortunately, every time I've seen these paradoxes explained to people, this explanation never convinced them. It looks to me like an explanation than is only clear and intuitive to people who already know how conditional probabilities work.
For the monty hall problem I generally explain it with "bundle of doors" and assigning probabilities to these bundles. I'm under the impression that it works a little bit better, but it's far from a 100%. what's hard with counterintuitive stuff like that is that I've often talked with people who were following and agreeing with the reasoning, and yet couldn't believe it was not 50/50. And I don't blame them, it was kind of the same for me until I studied (conditional) probabilities.
I did math probability at university and still would not switch, not because i don't recognize the added chance by the extra info, but I dream to be lucky and have picked the right one from the beginning.
LoL
Yeah, the problem is just with the phrasing because if you ask, “what is the probability that the winky will be orange vs yellow.” That’s 50/50. But then, “what is the probability that out of three options consisting of orange/orange, yellow/yellow, and yellow/orange, after already finding an orange winky, that I will find an orange or a yellow winky?” It all lies within context. And I can’t get past that.
@@ApiolJoe The easiest way I've been able to get people to understand it is this way: instead of three slips of paper, there's six. Orange is written on two of them, so if you draw a slip, there's a 2/6 chance it will be Orange, while Blue + Purple will have 4 of the 6 slips. That won't change if Blue and Purple have two each, or Blue has one and Purple has 3, or Blue has 0 and Purple has 4. The combination of Blue + Purple always has 2/3 chance of winning.
The thing is that well to make this easier, imagine it like this, if you choose the correct door, the show runner will flip an unbaised coin and call out the door it landed on, but if the door you choose is incorrect, they will always call out the other incorrect option, now, if you don’t know what door it is, and they call out a specfic one, it could be a 100% chance they call it, cause you choose the incorrect door, or a 50% chance to call it, if you choose the correct door, thus why it is a 2/3 chance that you should swap, and 1/3 you should stay, since the probalities must equal 100%.
I love how I come out of your videos more confused than when I started them.
Short answer:
Orange had lower odds because he insulted the warden
Also nice glasses
You're probably on his good side when he takes over.
Yes.
If a simple problem can’t be solved by anyone then is it really a simple problem?
There is a difference between simple and easy. Easy is to difficult as simple is to complex. It is a simple problem, but it is difficult to solve.
It is simple haha
I was going to comment something similar, and then I saw your comment. Everyone would think I copied you. I had to delete my comment. :(
simple problem does not mean simple solution.
Yes, it’s just not easy
Monty Hall problem variations:
1) There are 1000 doors. The host does NOT know which door the prize is behind. The host opens a door at random until there are just 2 doors left. The prize has still not been found (what are the chances of that). Is it better to swap or does that make no difference?
2) There are 1000 doors. The host does know which door the prize is behind. 998 doors are opened. The prize still hasn't been revealed. Is it better to swap or does that make no difference?
Scenario 1 - odds are 50 / 50 as it's purely by chance the prize hasn't been found so the odds of winning have improved
Scenario 2 - odds of being right are 1 / 1000 as the host knows which door it's been found so there was no chance of it being shown to you.
(I tried demonstrating that to someone with cards and they still struggled)
I love how goofy yet serious these videos are
Let's make the right Monty Hall solution obvious and intuitive:
There are 1'000 doors with a prize behind one of them. Your are told to pick one and pick door 4, because why not? The chance of the prize being behind ANY door is 1/1'000. Monty then goes about opening all the doors EXCEPT two, one you picked and one you didn't. At first he just rushes along the doors, opening them wildly. But around door 300 he slows, looks at a piece of paper then very carefully doesn't open door 314. Then he rushes along and opens all the others before asking you if you want to switch doors.
Should you switch? What's the chance of your door having the prize behind it? 50-50? Of course not! You picked it randomly, meanwhile door 314 looks awfully suspicious. Sure, it MIGHT be a red herring and you DID pick the prize first time, but you'd have had to be very lucky. You KNOW the prize is almost definitely behind the other door, a 99.9% chance. Only a fool wouldn't switch.
Gareth Dean then, after you’re left with two doors, suppose you’re introducing a third person who is completely unaware of what previously happened. And you ask him to choose. Will then the probability, from his perspective, be 50/50?
@@naiffvii4196 Well yes, but it becomes a different problem entirely. No longer is it a question of whether to switch your choice, but rather a game of trying to guess which door was left by the host. It's a 50/50 chance to guess the door that had a 99.9% chance to be the winning door.
you deserve more likes
@@static-ky Clear! Thanx
That explanation really helps, thank you!
Dude, it took me three years to realize that he was left handed.
Or maybe he has a mirror effect on video..
IDK guys this is making me a bit trippy
@@fosterdawson8810 but is it!....
TIL
What if he's both handed and he flips it when he's using his right hand😲
The monty hall problem blew my mind. I couldn't believe it until I tested it and played a demo of the game on paper multiple times.
Then it finally 'clicked' when I realized what was happening - the act of showing one of the doors (which was not a car) meant, the odds have now been altered.
6:04 that is French words
It's so funny to see him reading so differently than us only because of some letters pronunciations
Kevin : Right?
Me who read the comments :
*I have foreseen my mistake, I shall overcome it!*
Hold up, is that a jojo refe-
Captain Nomekop -rence
finally not an overused one
Vsauce keven here and im going to *S T R E T C H. M Y. W I N K E Y. U N T I L. I T. S N A P S*
2:23 “do this for me Kevin, *PWEASE* ”
Lol
Pwease
How do you make it bold?
BrodyTEM
* (what you want to say) *
@@cjfdnqkn4374 *hi*
In simpler terms, if you drew a gold coin, it's more likely that you drew from the box containing two gold coins.
The reason that it doesn't make sense to most people is that they completely ignore the probability of the thing they've chosen and then move on to the porbability of the second choice as if they're unrelated
"I'm about to stretch my winky until it snaps" is a line straight out of a sexually charged nightmare.
I love the sentence:
"The math isn't wrong, we are"
That is... because I program my calculator to get answers MUCH faster
After debugging it 3-5 times
I know that if the answer makes no sense:
I'm wrong... not the program
NOMASAN i do this too
i think this video has made me more confused about the right way of thinking about the solution than i was before.
thankfully some of the comments made more sense to my brain.
i will now choose to switch if i'm in that situation, and know why it is the better answer.
“Math isn’t the problem… we are”
I felt that
yeah...
Current mood:
"Orange: I'm dead."
h
The mad man actually did it, congratulations Internet Historian
9:16 he missed the opprotunity to say, " Now that the Vsauce, sauce is cleaned up we can..."
One of the reasons it is so hard to get this is that we frame the problem as a counting problem rather than an information problem.
0:02 Should we consider we need "Vsauce2 but out of context?"
Yes. No consideration, just do it.
No
@@petrusandersen198 ew
Lol
Absolutely, he says so many out of context things, it EVERY VIDEO
i’ve read so many examples in the comments and i’ve just come to admit that i will never understand how it isn’t 50/50
It's based on the probability of drawing the gold coin in the first place (box example), where you were more likely to have a second gold because you are more likely to draw a gold from a box with 2 gold (100%) compared to 1 gold 1 silver (50%). In the prisoner it would be more likely to have picked blue if it was purple (100%), rather than having picked blue if it was orange (50%). At least that's my idea as to why the math unfolds that way.
Hope this helps you understand it better
honestly same
this probably wont make any sense, but instead of thinking of the gold coin problem as 50/50, think of it as the chance of drawing a gold coin. there are three gold coins, but only two boxes. when you draw a gold coin, it will probably be from the box with more gold coins in it.
The problem with the coins (G = gold, S = silver):
You have 3 boxes with 2 coins each.
GG - GS - SS
You pick a coin from a random box, and it's gold. We know there are 3 gold coins.
2/3 of them are in box 1. (GG)
1/3 of them are in box 2. (GS)
0/3 of them are in box 3. (SS)
That means:
There is a 2/3 chance you picked GG, so the other coin is gold.
There is a 1/3 chance you picked GS, so the other coin is silver.
That means the chance of the other coin being gold is 2/3.
and for the monty hall, think about it like this: because there are more goats then cars, you are more likely to choose a goat then a car. the chance that you chose a goat is 66%, as opposed to the 33% chance you chose a car. if you don't switch your door, the chance of winning a car neither increases or decreases. However, if you originally pick a goat and you switch, you get the car; and because you probably chose the goat, you will probably get the car. as simply as possible- you probably get the goat, so if you switch, you probably get the car.
I just tried to explain the monty hall problem to my dad who has a degree in math. I even showed the three by three grid that shows the win state depending on which door you choose and which has the good thing. Telling him that simulations have shown that people win 2/3 of the time when switching didn't change his mind. Even explaining the problem with 100 doors and opening 98 of them didn't help.
He insisted that after a door is opened, it is no longer part of the equation/probability, you have two doors. One has the good thing, the other has the wrong thing. Since one door is known from the original three, you take the known door out of the probability, you need to create a new equation/probability (is two doors, one is good so you have 1/2 or fifty fifty chance. At least this is how I remember his explanation.
I couldn't get him to see his fallicy and he insistent I was the one making the fallacy. I eventually had to give up.
So I understood the prisoner problem immediately, but only because of my familiarity with the Monty Hall problem. When you switched to the pudding problem, I admit I had to think a bit more, but kind of knowing that it was a similar problem, I was able to work it out.
"CaLcuL dEs ProbAbIliTéS"
I'm french and it made me laugh so hard thanks Kevin
What does it say?
@@ayouzid calculate the probabilities i think
But he said it in a weird way lol
He added j at the end of the words and said the last letter(in french you don't read the last letter but there is some exceptions i think)
I am french and it can be translate as "probabilities calculations"
@@ayouzid really?
Same zijdhisjhkdj
Kevin: you are a smart, curious person
Me eating a whole plate of chicken nuggets, guzzling Powerade in my underwear on my couch: THANKS!
Ah... Noice
If you didn't order 43 chicken nuggets combined of the regular boxes that should be fine :)
#quarentineLife
The simplest way to look at the Monty Hall problem is that since the 3 doors are goat, goat, car, when you pick a random one of them you have a 2/3 chance of having picked goat. The two times you actually did pick goat Monty has no choice but to reveal the other goat, because he can't reveal the car. That leaves only the door with the car. So the 2/3 times you picked goat you definitely will get the car by switching to the remaining unopened door. The 1/3 time that you picked car you will definitely lose by switching because the unopened door has to be a goat. So those are the exact chances you have by switching, 2/3 chance of switching from goat to car and 1/3 chance of switching from car to goat, therefore you should always switch.
When im home alone: *maths stuff*
When my mum walks in: My winky is talking to me!
OMG YESSSS I WAS CORRECT, I had this question in an English class and had a literal meltdown after no one trusted my maths. i have ascended. Thank you Kevin. Thank you.
Soooo, how did everyone respond now that you have prove you all right?
@@walkertang I went onto the class group chat linked the video and typed (i quote) "hahahahhaa you're all numbnuts bow before my glory." they took it pretty well and we all laughed it off.
@@tommuinnit omg me too my mom doesn’t believe me lol even after I showed her this video she still doesn’t believe me-
@@tommuinnit are u indian?!
@@whyareyouexisting7285 nah?
*the easiest problem everyone gets wrong*
Then it ain't so easy
U
But it is easy, that's the paradox
nope, its actually easy.
what comes into play is :
People cockiness
People that think they are smart
People who don't think much.
People that don't understand even if you explain because they think they're right. (look at flat earthers,/ women in general XD)
So it is easy, but people make it hard with their behavior/reasoning.
Mabye I need to say I was joking
@@jesuschrist5516 maybe it ain't so easy to get XD
14:06 I didn't watch this video because of that but _kept watching the video_ because of that. I saw the title "game you get wrong", got interested and then you triggered my neuron-filled brain throughout the video
This was more educational than school lol
The explanation with the arrows helped me understand this alot easier
Me, an intellectual: there's a 100 percent chance the two orange guys are in the jar he pulled from first because he had to set up the problem by initially pulling orange
looks liko quarantine laziness is making us intellectual being
Nope… He could draw randomly, and ask about yellow if he drew that...
@@jensterstrup4700 He said he knew that one colour was yellow and not the other one.
@@mrsplays9817 the colour serves no purpose outside differentiating the winkeys. He doesn't have to know what the other colour is he just needs to know there is another colour
@@skullbroski Then why specify ahead of time that he knows one colour and not the other? He could just say that there are two different colours.
"Was it cause I called you fat"
"I am dead"
Another way of looking at the Monty Hall problem is that, when you first make a pick, there's a 1/3 chance you're right. When the host takes away an incorrect door, that 1/3 chance of being right on your first pick doesn't just disappear, which means the doors you didn't pick still have a 2/3 combined chance of being right. Because there's only one door you didn't pick remaining, that door now bears the full 2/3 chance.
With the coloured coins, there's a 2/3 chance of picking a box with two of the same colour. It doesn't matter what colour you pick, the fact of the matter is, there is a 2/3 chance of picking a box with the same colour.
Bertrand's box was the hardest one for me to comprehend, but I finally understood it by conducting this hypothetical experiment in my head:
You have the three boxes and obviously each one has a 1/3 chance of being chosen. When you choose a box, take only one coin out of the box. If the first coin is gold, look at the other coin and note down its colour. If the first coin is silver, put the coin back in the box, don't look at the other coin, and shuffle them around again. Do this 100 times. You will end up looking at the both coins in the gold-gold box twice as often as the gold-silver box, because each time you select the gold-gold box there is a 100% chance you will get to look at the other coin to check its colour, but if you selected the gold-silver box there is a 50% chance you will pick out the silver coin and not get to see the other one.
The probability of each one of the coins has an equal likelihood of being the coin you pick to look at (1/6 as there are 6 coins). We are only considering gold coins here, so each coin has a 1/3 chance. Two of the coins are in the gold coin box, so there is a 2/3 chance that the other coin is also a gold coin.
To anyone struggling to grasp the concept let me explain it another way
i try to explain it to other people the same way my high school Math teacher tried to teach me this. which was with 20 buckets.
he stipulated that there are 20 buckets... 19 of which have a hole in the bottom, and one is filled with water. you have to guess which one has water in without looking "you could obviously change it to buckets upside down covering a ball or something , but the point remains there is no way to know which is correct without selecting one"
now, you have a 1/20 chance and there is a 19/20 chance the bucket with water is one you didn't select right? that's correct. so you pick a bucket, whichever bucket you feel is right or wrong.
then my teacher said OK, i will take away 18 of the other buckets that do not contain water. so he did. now that leaves you with 2 buckets. 1 that was left, and one that you chose. you would think that it's 50/50 when in fact it isn't!
it took me years after leaving high school that the memory came back and it suddenly hit me on what he meant
you have to look at it this way... if you were to select a bucket again from random from the 2 remaining buckets, then yes, you would have a 50/50 chance. but that situation doesn't apply because you selected it when the bucket only had a 1 in 20 chance of being right!
logically speaking you were far more likely to have gotten it wrong than gotten it right on your FIRST pick (1/20), the other buckets removed from the equation are just useless variables at this point it doesn't matter which buckets were taken away.
meaning since probability has to always equal 1 then the other bucket in fact has a 19/20 chance to be it.
if that's not enough then think of 1 million buckets... the chances of you picking the right one logically get so low that you would never take that bet. however say you pick one and afterwards 999'998 buckets that had holes in get taken away, leaving the one with water and one without. the chances of you getting it right the 1st time were so low that you know it most likely will be the other one right?
i hope that makes sense to anyone who doesn't fully understand it :) i hope that has helped you understand that in terms of the winky's, you only had a 1/3 chance regardless.and swapping logically and mathematically is always the correct answer.
That isn't going to make it easier. There are a whole lot of words there which confuse people.
I'll explain it this way: if there are three options and 2 are wrong, being shown one of the wrong ones changes exactly nothing. You had a 2/3 chance of choosing wrong and all you were told is one of the two things you didn't chose was wrong....which you knew. So given that you had a 2/3 chance of being wrong before what do you think the odds are now that nothing has changed?
omg thank you, I finally understood
@@ShiningDarknes it did not tell me about this comment. thank you for you input in sums up what i was saying in a simpler way. which words in particular do you think will confuse people? i have been a reading a lot and trying to improve my english skills so knowing where i am going wrong would be of great help :)
@@Gold3nEagle200 no, no. It isn’t that your word choice is bad or confusing. It is that the explanation is too long. When explaining a problem like this one to someone that has not understood other explanations long strings of text are naturally confusing i.e. hard to follow. I read your explanation and if you were to verbally explain it like that it would not be at all confusing. It is the reading that makes it so.
This is the internet after all, people tend to have shorter attention spans when using it as opposed to irl.
I find taking these things to the very extreme helps. You can choose any atom in the universe. If you choose the winning one you win.
Okay now you've chosen one I'm going to take away all of the other atoms except one (I will never take away the winning atom).
Now we have 2 atoms, one of them is the winning atom. Are you sure you want to keep the first atom you chose?
Kevin: Right????
me: yes finally i got something rig-
Kevin: WROOOOONG
Kevin is actually wrong
@@MM-ku4qu it's not
Regarding the Monty Hall problem: A big reason people struggle with this is that they are too optimistic. They become hopeful that they guessed correctly. You need to face the fact that with a 1 in 3 chance, you probably guessed incorrectly. If you embrace pessimism and decide that you guessed wrong, and Monty opens one incorrect door, then you can be certain that the prize is behind the other door. Sure, 1 in 3 times you'll be shocked to learn that you had it right originally. But usually pessimism is rewarded. I bet Russians and Irishmen have no problem understanding why you should switch.
People struggle with it because a situation very similar to the MH problem occurs frequently in life. Namely where a door is opened by chance and without an all knowing entity that is forced to open one of the remaining losing doors.
It feels like when you are looking too hard for something and then when you finally aren’t looking for it, it just pops out
The question is built to give this illusion of a 50/50 chance. Think of it in an extreme case where one pile contains 999 gold coins and 1 silver, another one with all silver, and another one with all gold. If you picked a silver coin, it becomes much more obvious that you are more likely to have selected the coin from the one with all silver since the other option would have been a 1/1000 chance.
Finaly I understand it
If you got gold it will be more posible that you picked up the 2 gold because it is 100% in that you pick gold in that one and 50% that you pick gold in the silver and gold
If you are at the Box with 1 Gold and 1 silver there is a 50/50 chance to get the gold coin but if you are at the box with gold gold there is a 100% chance to get gold. So if you got gold its more likely that you got it out of the gold gold Box. So if you have the gold coin its a 2/3 chance that your own box is the gold gold box. But if you get to the other two boxes and think about which box contains at least one gold coin you have two options (gold and ?) (Silver silver) ==> 50/50. The actual 50/50 chance is only existing, when you opened one of the boxes and look at both coins at the same time 🤯
Ohhhhhhhh, thank you! I finally understood it
yeah i was kinda thinking something like this but you definitely helped
"I'm going to stretch my winky"
Me - umm what
Oh
DEMONITIZED!
“And WILL require me, to stick my winkeys in pudding.”
*UMM WHAT*
What?
"I'm going to stick my winky in this pudding" I bet british people are going to have a laugh out of this one.
I think simplest way to say monty hall is
If the chance you’re right the first time is 1/3, the chance your first guess was wrong is 2/3.
Switching your answer brings you into that 2/3, and you get to choose which one you want from there
"I'm going to stretch my winky until it snaps."
Woah don't go THAT far...
Yes, stop at the point where it starts to tear apart.
yeah, there are so many winkies that deserve to be stretched until they snap, but i have a feeling that kevin has a good winkey that deserves to live 😅
lol hi
@@GDNachoo czcams.com/video/ryrdHIQmJBA/video.html
I had a hard time wrapping my head around the first scenario, but the coin one actually makes perfect sense to me. How does that make any sense if they are basically the same issue?
Preference. Your mind prefers the explanation of the coins
Same
The fact that there is 6 objects to "study" instead of 3 (although it's the same problem) makes it easier to grasp
I could explain it if u want
What I don't get is, why is the other gold coin calculated into the probability? I get that the second coin is either gold, gold or silver. But it's not a box with 4 coins. It's a box with 2 coins, with the second one being either silver or gold. Can someone help me understand?
I was hesitant at first, but yes! This is a reimagining of the 3 door problem.
3 doors. 1 prize. Choose a door. It won't be opened yet, but one of the other two is, revealing no prize. Will you keep the door you chose or switch to the last remaining door?mathematically, CHANGING your answer increases your odds.
Love this problem, love probability
wow. Incredible, you posted the same problem hundred other youtubes have. Such creative youtube video. It is quite fitting with the originality of your name.
The really interesting question here is “Do any other game show hosts have famous math problems named after them?” The rest is just stretching your Winky.
"Like Mrs. Incredible on a first date" What an absolute memer. pools closed due to corona
i watched a man stick his hand in goop while explaining advanced probability. now im left with the question “was it worth my time” answer, yes.
I think a lot of the confusion comes from the perspective of your selection being two separate choices, meaning that your first choice netted you a gold coin, and your second choice becomes 50/50 for you to get two gold coins or one gold and one silver.
The dissonance comes from abandoning the third part of the system, because it is presumably no longer relevant.
When you make your initial selection, you're taking 1/3 odds on success. When the host then removes a wrong answer from play, your selection still has a 1/3 chance of success.
HOWEVER, when given the option to switch, your initial choice is still 1/3, but the probability of the other two options still exists. You know there's a 2/3 chance that you chose the wrong option, AND you have additional information that one of the other options is incorrect. So if you have 1/3 chances of being correct from your first choice, the exposed choice has 0/3 chances of being correct, then naturally the selection you have the option to switch to has 2/3 chances of being correct.
To clarify, you aren't suddenly more likely to be correct because something was revealed to you. Your initial choice was ONE out of THREE options. 1/3. Receiving information after the fact doesn't affect the probability of the choice you made when you had less information.
IF you were given the information BEFORE your initial choice, then yes absolutely it would be 50/50. And if you treat each decision as something completely separate from the larger system, then it would still be 50/50, however that's not how the probability of the system functions. All choices are made in a specific order, under specific circumstances, and all information needs to be considered in the order that they happened.
I hope this clears this up for some people.
The fact that the choices are interconnected and conditional is definitely a slip up for some people. I've seen plenty of people claim that connecting the decisons is the "gamblers fallacy" while ignoring that fact that only applies to independent probability problems.
That said It's not strictly correct that receiving information after the fact cant affect the probability of the second decision, the critical thing to consider is what information is being revealed. In the Prisoners Problem you receive no new information about your own situation since you already knew that at least one of the other prisoners was not pardoned and there was no chance of the pardoned prisoner being revealed. The same applies to Monty Hall since the host only ever reveals a goat from the remaining doors, you gain no new information about your initial pick. By comparison in a game like Deal or No Deal the boxes revealed are random and so in that case each new reveal tells you information about the box you picked initially and the last two boxes are a genuine 50/50 scenario.
are we going to ignore that this guy actually got someone to voice the orange winkey
and barely even credited him
The Internet Historian of all people
@@allegrovivace6806 Someone? Barely credited? Did we watch the same video?
@@doommaker4000 usually aren't you supposed to put in any collaborations at the end of the video and officially state that you collaborated?
@@allegrovivace6806 Depends on what both creators agree to, this is not sponsorship. Besides, having a credit in the middle of the video will give it much more exposure than at the end.