ok

👍

First

??th

I disagree with u.

I thought something similar at first too, but actually it is all carefully crafted to prevent this from being a valid answer. It is only when she is put "back to sleep" that she forgets, and what she forgets, is being woken up. So every time she is asked the question, she remembers the original explanation, the original time being put to sleep, and being woken up that time.

That would logically mean X, but I don't like X, so it doesn't mean X. Great science right there, chief 👍

Wait, why am I naked?

you are either a mechanical engineer or a philosopher 👍

@@stilldreamy5181This comment still makes sense, since the paradox itself stands because it introduces "knowledge about the system", which leads to the "simulation theory" aspect of the question. If you are exclusively a part of the system, meaning you can't imagine a system containing the system you are in, then the question will have only one valid answer; it's when you assume the possibility of a "hyper-system", a system that contains the system you are in, that the question becomes a paradox. Therefore, questioning the reality of a "system within a system", like the original comment does, is the key to "solve" the paradox. In other words, the hundreds of papers discussing this paradox, are really people debating their belief in the multiverse or simulation theory (which is actually unprovable, therefore a theological debate).

fax

Amen

In the particular universe that produces Canadian dominance of Brazil in soccer...pigs can fly. Pig guano everywhere.

As a Brazilian, I’m happy there’s at least one scenario where we are more likely to win against Canada

​@@diegototti we are also more likely to win against canada in a war. they would apologize for being involved in a fight and raise the white flag

Thank you

Exactly. Seems fairly obvious

But what if it was a 1% chance ( a 1 on a 100-sided die) to wake up 1 million times? Even if you were asked what the probability of the die being 1 WAS, it was still only 1%. Its unlikely that you were put to sleep a million times in the first place.

@@alexs1277 Not clear what variation you are describing here. But If 99% to wake once, and 1% to wake 10^6 times, chance die WAS 1/100 is 99.990%. No?

Changing the tense of the question has no impact. Again just consult the soccer game analogy. It’s obvious

aandd you became a thirder

exactly

Reminds me of the football coach who didn't want his quarterback to throw because two of three possible outcomes were bad. Interception and incomplete.😅

@Glenn Clark ahh the coach is wrong. It's still 50-50. The pass either reaches the teammate or it doesn't. 🤣

Average mulla thought process

No. It’s not. If that was true, you would win any game every second round on average making only random choices, i.e., tossing a coin. Clearly, that’s absurd.

That would logically mean X, but I don't like X, so it doesn't mean X. Great science right there, chief 👍

the researcher just wanted to kiss sleeping beauty multiple times

that is so much better of a question, kudos

No the question is clear, after being woken up what are the odds that the coin flip landed on heads/tails. The answer's 50/50.

Now 2,479...

How are you able to see number of dislikes?

@@Varma17 the title is the amount of likes (agree) to dislike (disagree)

@@Varma17 I think the title updates periodically, the number of people disagree

@@Varma17 there are browser plug-ins to show dislikes again. the one I use is "return youtube dislikes". cheers

Yeah, it just seems like semantics. I depends on whose perspective you are using

Semantics, asking the wrong question, wrong definition, etc.

That's what makes Monty Hall problem so great - it's not about words, it's about the actual concept itself.

Yeah, "what was the probability that it came up heads?" vs "what is the probability that it came up heads?" can already make a difference to the answer. Only if you define questions properly can you answer them. I suppose that's why they were philosophy papers and not mathematics. In mathematics you need things to be defined unambiguously.

There is clearly a majority consensus on the entire thing with most people leaning towards the real world side instead of the fairytale book side. Why do you think they use a literal fairytale character to point this out? Math is 100% disconnected from reality. A concept. She's literally missing 25% of her ability to know what actually happened. She is at 75% comprehension of her reality since she can't tell the difference between waking up once or waking up twice. But the knowledge shown to her is letting her know, that she has two chances to respond on a tails flip, or once chance to respond on a heads flip. So she can take the chance of being right or wrong about a 50/50 chance twice in a row, or once. Her best chance of answering correctly on monday heads, monday tails, or tuesday tails is to realize that there is no tuesday heads and eliminate 25% of her ability to answer. Thus leaving 3 equal chance scenarios. Her real world probability is skewed by lack of information. Her fairytale probability is 1/2, because 1/2 is 1/2 and everyone knows 1/2 is 1/2.

I changed due to this

I agree.

Exactly my thoughts! "Tuesday tails" simply doesn't exist, if we're talking about coin flipping.

I'm actually changing my answer to 1/3 because while a coinflip is obviously 1/2, the way the problem is constructed is : heads gets only one question, while tails gets 2 questions (questions not flips!) , so by saying tails you are going to be right twice as much just because you get 2 questions instead of 1 . IF the coin would have been flipped again between monday and tuesday, then the answer would obviously be 1/2. This way it's just 1/2 heads and 1/2 tails, but tails gets double points every time.

Change it again :) Imagine that if heads, she's not waken up at all. She's only waken when tails. She's asked the same question. What should she answer 1/2 or 0?

That's not correct. No matter which day it is, she's got a 50% chance of being right. We don't compound the tails days together. It's just as likely that she's waking up on the Monday from heads than it is she's waking up on either Monday or Tuesday from tails.

@@TheShepdawg9 The difference is that if tails came up, they are asked twice. That changes the likelihood of heads vs tails when asked

@@TheShepdawg9 she can litterally not be asked anything if it's both Tuesday and heads. This means that the probability of the coin having fell on heads on a Saturday is 0. So yes, the day it is when the question is asked does influence the probability of the result.

No, it’s “is this a heads sequence of days (1 day long) or is this a tails sequence of days (2 days long)”.

Agree.

I like the way you explained this. His statement “Something changed” was important because it matters that an event occurred between observations.

This is the correct answer. It depends on how the question is interpreted.

But if sleeping beauty doesn't remember any times she's been woken up, every time is her first. So to her it's always 50/50. Any other wake-up (Tuesday) in _her_ existence never actually happened

I think there should be a distinction between asking "What is the probability A coin came up heads?" and "What is the probability THE coin came up heads?" The question is about THE coin, and given she is awake, the answer is the probability of her being awake.

Split the difference!

@@ChrisContin They divvied up the hadrons amongst themselves and Erwin got a new cat.

Ahh I dont have enough neurons in my brain to understand this, someone please do the honors.

@@bluzter it is a reference to Shrodinger’s Cat

@@bluzter The cat referenced above, plus they're saying that they flipped the coin and it landed on neither heads nor tails, landing instead on its edge and therefore she will never awaken. It's the hidden third result.

Then take them both to the consideration and calculate the average. That would be the real solution to this dilemma.

@@orka6848 no, these are not two approaches to the same question, they are two different questions. Averaging them is kind of meaningless. Estimating the distribution is not the same as minimizing expected error.

@@johnmorrell3187 I think you hit the nail on the head - those who agree with him are answering a different question than those who do not.

funny, but no: the imbalance of the heads and tails here is only due to a deliberate mistake in sampling; because of a sampling error you record "tails" twice when a single "tails" event occurs, but only a single "heads" event is recorded for "heads" events. The dataset is seriously screwed up; when presented with a new "instance", the "thirder's classifier" will have its probability estimates wrong: it will be predicting "tails" with prob. 0.66 but it will only be "tails" with prob. 0.5.

@@orka6848 here we have the engeneer

Best way to start a Monday

That's why I pick heads everytime

Some people prefer waking up with tail.

By Veritasium? I'd only want it to be from Sleeping Beauty. If not, I'd pass

bruh

'What is the probability that you will wake up from this much heroin dosage'

If 'heads' wipe out all life on earth, and 'tails' doesn't. After the coin has been flipped and before you have seen it, someone asks you, "what is the probability of 'heads'?" What would you answer?

@@Poppillon50

@@adampicki that's the answer to the question "what was the probability of the coin toss". Not the answer to the question "what is the probability that a particular event happened". The key to this is the implied impact of the circumstances under which the question was asked.

@@Poppillon but the probability was still 50 it happened, only because it landed it doesnt make it 100%

0.3 is probability of one side of the coin vs 0.707 probability of the other side

Well no sh*t

​@@aucklandnewzealand2023huh? Where does that come from?

@@aucklandnewzealand2023more like 0.33 and 0.66

As a Brazilian I'm thankful for 4 out of 5... Canadian team is getting better and better (Brazilian team have been a lot better).

And there's a 100% chance of another balloon flying over Canada will be shot down by an F22. :D :D

As a Croatian, we beat you both, even though Brazil was better but unlucky against us. It was that 1/5 win for us 🙂 Good luck to Brazil!

@@lukatore123 - I think it was more like 2/5. Croatia's got a great team (maybe the best one per capita - amongst Uruguay and Portugal). Brazilian team, of course, had better individual quality, but Croatia had a very interesting collective game. Afterall, i think it was very well deserved

@@BillAnt 🤫🤫🤫

Yes, that is the single point on which this hypothesis depends. Also it's not about just "people connected to the Matrix from outside" kind of simulation. It's about the people simulated inside it, i.e. conscious NPCs like the agents, etc. Ability to simulate many conscious beings would be probably much more complicated than just simulating sensory inputs for conscious beings that already exist.

So an estimate of probability is only correct if it is what the infinite repetition of a test would converge upon. Toss a coin and you'll get a head or a tail. Toss it 10, 100, 1000, a million times, and the ratio of heads and tails will converge upon 50/50. That's how you know you got it right. Here we're asking a princess to judge the likelihood that the coin landed heads. If we repeat the experiment 1000 times, then we will ask the question ~1500 times. If every answer is "1/2", then they will ALL be wrong, because in reality around 2/3 of the questions will be asked after a tail.

@@peelingOn 1000 experiments, you still ask the question 1000 times, not 1500. Even if you ask 10,000 times the coin flip is still 50/50. If the coin flip was heads, it will be heads on the first ask or the 10,000 ask.

@@claytoncourtney1309 No, over the course of 1000 experiments, you will ask the question approximately 1500 times (once per iteration if it was heads, twice if it was tails). Think about it this way: Suppose the experiment is run 1000 times, and each waking of the princess is recorded as a separate video. So there are ~1500 videos. One video is shown to you at random. What are the odds that video is from a waking that occurred after heads was tossed? It is ~1/3rd, right? You, watching the video, have exactly the same information that she did at the time it was recorded. So why should her answer be different to yours?

@@peelingI rethought it through, in the shower of course lol, and I agree with you. I DO like your idea of using the video. I still have problems with the question but am already late for work. I did, once i saw your your response wanted to let you know i now agree with you.

This seems like confusion about valid states to me. By adding the wake instances, you're artificially splitting a single outcome. TailsxTuesday is a different day of the same result, not a different result. The odds that it's Tuesday when she wakes is 1/3, but the odds of heads is 1/2. here's one to demonstrate this: if you get heads, i'll break one of your legs. if you get tails, i'll break both. The likelihood of having 1 leg broken is 50% (monday). The likelihood of having two broken is 50%(tuesday). There is no 1/3. you only have 2 legs and there are two outcomes. Breaking the second leg on a different day doesn't change this. Not knowing doesn't change the odds. Applying odds to a wake instance is simply nonsensical. it's just a parallel state.

Yeah I agree, it's more about semantic than statistic. Derek just found a nice trick to get tons of likes and views with a question that is more intellectual masturbation than anything else.

@@En_theo exactly. And I love Derek and his content but this video just felt like a gotchya. And the worst part is I can't even express this to him by downvoting the video

Maybe it's a social experiment on how much influence his opinion has

Exactly

I agree it's a trick question, but it's not two different questions. It's just one invalid question. The tail scenarios cannot be viewed as two separate outcomes: informationally they are identical to sleeping beauty, and therefore the same outcome. The question just arbitrarily labeled the tail scenarios as two outcomes, not with any kind logic compatible with reality, but with memory erasing magic.

The probability that she guesses the side of the coin is ~1/6. ~1/2*1/3=1/6 But if you ask about the probability objectively, then of course ~0.707 It has no corelation to multiverse unless it exists (probability of Multiverse unknown)

​@@aucklandnewzealand2023 stop dude you're talking to an anime pfp

@@aucklandnewzealand2023 Honestly, that isn't just as justifying seeing that she could have done any other operation

​@@roddraft3466 the general consensus is that your pfp doesn't affect your comment

He did not explain it well, leading some readers pondering possibilities unreasonably based on a misinterpretation of the Sleeping Beauty scenario. If that was unintentional, then fine. However, this is not a big statistics problem.

In this case, it's the probability of the day vs the coin.

Twice as many days for tails -- twice as likely she was asked this question on a tail flip.

Yeah, one of the confusions is that "what's the probability that the coin came up heads" can mean different things. Halfers think it's a question about the behaviour of coins. Thirders think it's a question about your on-the-spot beliefs about past events.

@@AzrgExplorers I agree. Thirders actually think that the question is, "what are the chances that you were woken up once before?"

yup, like nearly all things, the readers interpretation is what truly matters... and yet the world doesnt care

@@wordsofcheresie936 No, thirders are answering the exact question asked. Sleeping Beauty wasn't asked "did the coin come up heads?" She was asked, "what are the *chances* that the coin came up heads?" In the soccer analogy @veritasium used, he talked about this difference without actually pointing it out. About ten billion humans have been born. So the odds of you being born as you is one in 10 billion. So when I ask if you are you, what is your response? If I ask what were the *chances* that you would be born exactly as you are, what is your answer? The questions are different and so the answers are as well.

The best way to explain it is the way he already did. Let's Make a Deal gives you 3 doors, with only one valid prize, heads. The other two have tails behind them. Then they take away a confirmed wrong door, giving your probability of choosing heads an increase. That's why you always switch the door you choose after the removal of a tails door. This method is simply presenting you with two possible doors but then adding a 3rd confirmed possible door. Your safest bet is to be realistic and realize that the original two doors always had a 1/3 chance of having heads no matter what door you chose. Changing doors still results in a 1/3 chance of choosing the heads door.

Maybe that was the real point the originator was trying to make but people just totally missed it and now here we are

My first reaction was that the problem is too contrived to be interesting.

actually, the probability of it being monady or tuesday is 33 percent, but the odds of it being tails is 50 percent

@@Sad_cat_studio no the odds of it being Monday is 66%

That would logically mean X, but I don't like X, so it doesn't mean X. Great science right there, chief 👍

Not it’s still 1/3 when she awaken because she awakens twice if it’s tails

It's a fairly complex situation, but I agree completely. If you jump to a conclusion you are ignoring the actual dilemma, which is how semmantics may affect our perceptions of the universe. There's no truly correct answer, only a correct answer given a chosen context. You wanna know the probability of heads vs tails? 1/2 You wanna know the probability of Sleeping Beauty correctly guessing if today is Tuesday? 1/3 etc Makes me think how much of actual science is affected by linguistic biases, I would guess most of it.

It’s always the language that is the issue in these kind of paradoxes. Write this problem using only math and suddenly there is no paradoxes

I disagree. It’s a 50 50 chance if when she’s awake it’s heads or not. It’s a 50 25 25 chance if she is waken when MH, MT, TT respectively, because it’s 50/50 whether it’s head or tails and then if tails 50/50 whether it’s Monday or Tuesday.

Wittgenstein is proven right yet again

I've reasoned about this and I think it is correct to say 1/2. In my opinion 1/3 is simply wrong because it is not equally likely to be in any of the three cases. I'll copy here what I already said in other comments that are lost in the haystack. My opinion: When she is asked about the probability, the coin has already been flipped and its state is determined even if unknown to her. So here the word "probability" should be interpreted as her confidence that the coin landed heads. She is aware of the procedure and she knows that the coin is flipped one time at the beginning. Imagine she is asked the question immediately after the toss (of which she doesn't see the result) before being put to sleep. She would obviously answer 1/2. From now on there is no reason she should change her initial guess because the coin is tossed once for all and there is no subsequent event that could influence the output. It doesn't matter if it's the first or the millionth time she's being awakened: because she doesn't know what day it is she never gains new information and there's no reason she should update her initial guess. 1/3 is simply wrong because it assumes that the probability of being in one of the three cases is uniform while it is not. The probability is actually 1/2 of being Monday and it landed heads, 1/4 that is Monday and it landed tails and 1/4 that it is Tuesday and landed tails. The 1/3 argument moves from the wrong assumption that to the question "what day do you think it is today?" she should be 2/3 sure it is Monday. Actually she is instead 3/4 sure it is Monday to balance for the fact that there is no Tuesday/Heads combo. The probability it is Tuesday is in fact P(it landed tails) times P(it is Tuesday | it landed tails). I put video at 0.25x and he made a terrible error in his experiment. Look for yourself what he does. He simply writes a sign two times when the coin lands tails. He should have tossed the coin a second time to decide where to put ONE sign. If you do it right you get the expected 50-25-25 proportions. I wanna add something to make it more intuitive: in the case she is awakened 1 million times if it lands tails the probability that in any awakening that day is the first Monday is about 50% and not about 0%. Think of it this way: if she is asked "what day do you think it is today?" she is better off answering "The first Monday" because is much more likely to guess it landed heads and hence surely it is the first Monday than to guess it landed tails and then identify one of the million possible days.

Shocking take

The probability of the coin flip doesn't change with the way we want to measure it. If Sleeping Beauty was woken up a million times for a tails flip, it wouldn't make the coin flip any less likely to turn up heads. Being woken up two times instead of one doesn't make one outcome twice as likely as the other, as the thirder perspective implies. If we're asking about the probability of the coin flip alone, like the question in the video (1:04) very clearly is, then the answer cannot be anything other than 1/2. Now, if the question was anything like "For N times Sleeping Beauty was woken up, what is the probability of her being woken up because of a heads flip?", then it'd clearly be 1/3.

Let’s do a little thought experiment: I tell you: „I‘m about to flip a coin. If, and only if, the coin flips heads, I‘ll call you.“ The next day, I call you and say: „I flipped the coin now. What do you believe is the probability that the coin came up heads?“ What would be your answer?

I know it sounds counterintuitive,but the only correct answer for sleeping beauty is 1/3. When she wakes up, there are three possibilities: A: heads/monday, B: tails/monday, C: tails/tuesday. Obviously, A and B have the same probability, because it’s a fair coin flip, so if they would repeat the experiment every week, she would wake up every monday and the coin would have flipped each side 50% of the weeks. The probabilities of B and C must also be the same, because every week she wakes up on tails/monday, she also wakes up on tails/tuesday. So the probabilities of all three possible outcomes are the same. And the sum of the three possibilities must be 100%, because A, B and C are the only possible outcomes, and each time she wakes up, only one of them can be true. Thus, the probability of A: heads/monday is 1/3. P(A)+P(B)+P(C)=1 and P(A)=P(B)=P(C)=1/3

Facts I don’t get how the root problem is that complex or controversial lol

@@kuribohoverlord2432 cause you are a genius mate, congratulations

What if the rules dictated that she would only be awakened and asked the question if the coin flip game up tails? Then, there would still be a 50-50 chance that the coin flip was heads. But given the information that she was being asked the question, she would know that the coin flip was not heads. The fact that she is being asked the question gives her additional information. What makes this "controversial" is that some people are unwilling to adjust their beliefs when given new information.

It's still just a matter of what's meant by the question. If a flip a coin, and you see that it's heads, and I ask you, what are that chances the coin landed heads, there are two answers depending on how you interpret my question. Either you answer 50% if you take my question as "what was the chance of what you've just seen occuring in general" or 100% if you interpret my question as "what is the chance that what you saw (the coin landed heads) is the actual state of the world (the coin landed heads)"

Thank you. You phrased it beautifully

In half of all trials over 1 billion simulations, she will wake up because it is heads on day one. 50% of the pie is spoken for . If you agree that the odds of it being heads or tails on day 1 are 100%, then there is only 50% of that probability remaining for all results starting with tails on day 1. There cannot be a 2/3rd’s probabilities stemming from that 50%.

That's hilarious. I dominated that class because of multiple degrees in philosophy. And went on to teach deductive, inductive, and probabilistic logic. And intro to inductive and probability logic class is pretty much proving the laws of statistics and much harder than any statistics class I ever took. Stats prof definitely hated me tho.

Philosophy begins where science ends Or is it the other way round

​@@nyeaglesfootballgarbagemen8346 Mathematicians and physicists were philosophers at one time.

@@aglawe1 Science is born of philosophy The scientific method begins with a question

@@nyeaglesfootballgarbagemen8346 So it is an iterative process, philosophers ask questions and scientists try to answer them.

"what is the question being asked?" is not a dilemma. The question is clearly about "the probability that the coin came up Heads". Answer to that question is 50%. And I agree with you that those who answer 1/3 are answering the wrong question.

that is so perfect an answer. how did you make it so easy,, in that, what is your background?

@@jonathanlavoie3115 what is the challenge being set, then. Is it to answer correctly on what the coin toss was, or something else? That's the dilemma here - not what is the correct answer, but what is being asked of her in the first place.

If the challenge was « guess the outcome and I give you 1$ » she would answer Tails, not because the probability is 2/3 but because the reward is twice. Just like I give you 1$ if you guess Heads right, and 2$ if you guess Tails right. You would answer Tails not because the probability is higher. It remains 50%. In the SB experiment, the question is the probability it came un Heads.

@@uRealReels Thank you. You're the first person who reply to me so kindly! A short anecdote about me: In my programming course there was an exam in probability and statistics. Three of the questions were about the same problem. In a basket containing 9 blue balls and 11 red balls, what are the probabilities of A) draw 2 blue balls. B) 2 red balls. C) 2 balls not the same color. Questions A and B are very easy. But for question C I knew that the teacher wanted us to use a complicated formula learned by heart. I didn't want to use this formula because 1- The formula is complicated and I'm lazy, 2- I don't like to use a ready-made formula that I don't fully understand and 3- I wasn't sure if the formula really applied to the situation. So, I solved question C by following this simple reasoning: Probability of 2 blue balls + probability of 2 red + probabilities of 2 different = 100%. Total must be 100% because there is no other possibility. As expected, the teacher's formula answer was not the same as my answer, and I had to argue to get the point, but he had no choice but to acknowledge that his formula didn't apply to the situation, and that my answer was correct. I argued my point in front of the review board, not because I needed the point (my average was already 98%) but because I like the truth. That's who I am...

so your memory wasn't erased? :)

The formulation of the question directly tells you to consider it from sleeping beauty's perspective.

In other words, if we repeat the experiment every week for the rest of eternity, is she trying to be right most on *days* or right on most *weeks* ?

I really like how you worded this. And you're 100% percent correct. I personally believe that because of the way that the question was asked that it should be answered from sleeping beauty's perspective just as @rantingrodent416 stated, but the way you acknowledged both points of view without hating on either one I very much respect.

Flip heads, put one green bean in the bowl. Flip tails, put two red beans in the bowl. You pick a bean, what are the odds it is green?

@@rantingrodent416 Well she has no way of telling if she was awaken or not, so her only guiding point would be her understanding of the fact that a coin has only two outcomes, so it would be 50%. If someone flips a coin and ask you what are the pobability of it being heads, with no previous context (as sleeping beauty didnt remember if she had been awaken) you would answer 50%, because there is no way for you to say how many times you have been asked that question.

Underrated comment lol

I like how you state that the chance is a half as one of the two things that are 'sure', despite the dozens of scientific papers with discourse, this video, the other comments, and the whole nature of this debate. Guess you had the answer all along then.

2/3

You are incorrect about #1. The probability that the coin was tails is either 0% or 100%, depending on its result.

@@feha92 thats actually true no joke, since he specified "was tails" and anything that happened in the past either happened or didn't happen

It will scares me if one day this happens in real life

what is this man saying? is he from another universe?

I got a bounty commercial lmao and I also posted a comment about it before I saw yours😂

@@mgkelley2609 😂❤️

Well that's a nice dream!

EXACTLY, probability? heads, obviously, what you think the result for this run was? tails, obviously

My thoughts exactly! Was looking for this argument. What is the probability of coin came heads - 1/2, because that is the fact. What is the probability that we woke you because coin came heads - 1/3 and is very different question.

What I was about to type.

but she wasn't asked what is the probability a toss of a coin comes out heads. She was asked what is the probability the coin did come out heads. There is a big difference in asking about the probability of an event that has not occured vs the probability that a specific event has happened in the past so long as you gain knowledge when transition from that past point to the present. One view the point when asked what is the probability of A. Which is 50% What is the probability of A|B (A given B in statistics). The probability of A given I have information B modifies the probability of A having occurred. This is not an independent probability but a dependent one.

i agree with this because fundamentally she can't remember if she been woke up before (according to the experiment) so the fact that she is awake now can't be used to bias the answer dose 50/50 should be the right answer. correlation does not equal causation.

Exactly So the case (Tuesday + tails) is absolutely useless to the probability of heads occuring. As it was never defined that heads will result in her waking up in tuesday

I think the problem is she doesn’t know what day it is

@@Nanbread-bw7nq If the problem is dealing with what day it is that she was woken up vs. what is the probability that the coin landed on heads, then those are 2 independent probabilities. The probability of the coin flip (reminder that it only occurs on Sunday) landing on heads is and always will be 50% Now if we consider this specific problem and its wording, then there are only 2 days that she will be woken up: Monday and Tuesday. This information is what is always known (she doesn't forget the problem itself, only the outcomes she is told when she is woken up and then goes back to sleep). Okay, so now we can ask the following question: What is the probability that today is Monday? well we know based on the information provided in the problem as it was worded, that she would only be woken up on Monday or Monday and Tuesday, which means we can eliminate Wednesday through Sunday. This means that the probability of the day she wakes being Monday is 50% and Tuesday is 50%...if she assumes it's Monday then the probability of the coin flip stands to be 50/50...if she assumes it's Tuesday then it's a 100% probability that the coin landed on Tails. If the problem accounts for more days being woken up, then that changes the probability of what day it is that she is woken up, but that's a different question than "what is the probability that coin landed on [insert heads or tails]".

@@N8ive49er But the question is not asking what the probability of what a coin toss "will be". It's asking about probability of what it "was", given that you were already woken up after the experiment has started.

Knowing Derek, The like/dislike options is a study in of it's self. We'll get another video where the like is the wroner answer and then a later video examining the results.

@@brandonfrancey5592 That makes a lot of sense. I'd bet that is the actual purpose of this video.

I liked this question as a vote to the proposition that people expressing enjoying the video will have a massive distortive effect on any attempt at polling. (Edit: Wait don't use comments as polls! Dislikes just bury the poll itself!)

I have liked your comment because I agree with it.

I am pretty sure he knows enough scientific methodology to know this liking/disliking thing is complete bs. It helps increase interaction so I guess it's a smart trick

AI when it hear like it glows

Stolen from Tom Scott. Doesn't bother me, but it is.

KZfaq algo like that? It might get changed soon if it can be abused.

@@theeraphatsunthornwit6266 Pretty much all social media is optimised for controversy or moral outrage, because that's what drives the most interaction. I don't honestly have any idea about the YT algorithm, but we can be pretty sure it'll rank videos with a widely split opinion above a video that has just a high number of likes, especially if there are lots of comments too.

@@bingbongthegong what video did Tom Scott do that abused the like count?

​@@bingbongthegongThat would be the like and dislike number update The ideo of ratios was not stolen though

Only a Sith is based.

@@kaizokujimbei143 no obi-wan! no!!!!

hello there

Let me make you question it again, the answer is 60% tails and 40% heads for 2 flips :)

I sense great turmoil and hesitancy in you

Targeted ads. It means stop wasting your life on youtube and go to sleep. Rofl.

Had an ad for a Canadian University for the football match lol

Same , I mean not the same ad but perfectly timed

Veritasum: now, will you eat the red apple or the blue apple

Prince Charming: [kisses Sleeping beauty] Researcher 1: Stop! you're wrecking the experiment! Researcher 2: Interesting, this proves we live in a disney simuatoin.

@@blankregistration7301 Or do we? 🤔 * suspenseful veritasium music *

This is exactly it. I feel like this problem wasn’t really posed thoroughly and that causes confusion

​@@hisuianarcanine9379 Nah, the question was clearly "What is the probability that the coin came up heads", that fits perfectly the first case of OP and it's unambiguously 1/2

Exactly what I think! It's unclear which question is being asked from this video, and we have to be very specific when asking the question. Like you said, if the question is "what is the probability that the coin landed on heads", the answer is always 0.5. Sure, sleeping beauty will be wrong multiple times if the coin landed on tails, but that's not relevant to the question being asked here. The fact that the coin is two-sided does NOT change, and the sleeping beauty's knowledge is identical every single time. It's an entirely different question if sleeping beauty is trying to 'win' as many times as she can, then the best answer is quite obviously tails. If she is woken up N times when tails is thrown, and once when heads is thrown, she will get the correct answer N times out of N+1 guesses, on average when repeating the problem.

@@angivaretv4475 "The probability that a fair coin comes up heads" is undoubtedly 1/2, but "the probability that you are waking up on a heads monday" is 1/3.

@@myeloon It would be a waste of everyone's time to go into the exposition of her being waken up monday monday/tuesday if all we are going to ask is that given a random fair coin that is absolutely irrelevant to her situation. Of course the question is "given that you were just woken up, what is the probability that heads came up". If that is not the intention, I hope the people who developed this problem and six degrees of separation from themnever wakes up again.

This is a brilliant comment. Contrasts very well the difference that is muddled in the "what was the probability" question. The answer to, "what is the probability the coin was heads?" is objectively 50%. The answer to the question, "what is the probability that the coin was heads AND that your answer is correct?" is 1/3.

@@bbanks42 What? So for the first question your answer doesnt need to be correct for it be... correct? The answer for "what is the probability of the coin to flip heads" is indeed 50%. But thats not the question, the question is "what is the probability the coin FLIPPED heads" with the given that if you are being asked that question you woke up. Similarly if someone flips a coin and it results in a Tail, it would be correct to say the probability of flipping tails in the past is still 50%, but wouldnt be correct to say the probability the coin that was flipped was tails was 50%, because you are clearly already seeing the result, and its 100%. Imagine if the SB only woke up if the coin was Tails and was asked "what is the probability the coin FLIPPED heads?" , it would be ridiculous for her to say the chance is 50% after being asked that question, because she knows she wouldnt be asked that question if it was Heads.

Makes no sense. The setup is wrong. You cant make her forget that she woke up yesterday .... and then ask a logical realistic question. If she cannot remember yesterday, then the asking person might have forgotten who they are altogether, or whom to ask. Like : you are my banker, with a brilliant mind, and you can recall all of my bank statements from memory. But i always forget my adress, my name, my job and which bank to go to. Now you want to ask me a meaningful logical game theory question on how to save money better ? Makes no sense.

....also the coin is a half half deal. The monday or monday-tuesday thing is a scam. Please try Mon and then Mon Tue with a coin. Heads comes up .... or both sides come up. Great.

@@crockmans1386 go watch cartoon

agree with this, but would say I'm a halfer in this instance because the exact question asked is 'what do you believe the probability of the coin being heads?' not 'what do you believe the probability of being woken up by the coin being heads?' subtle difference, but to one question I'm a halfer, the other a thirder.

Danm

@@superkeefo6951 This. That question sounds to me like question that would be asked in a hospital to check if my brain functions correctly like what's the date, who is current president etc. It made me 1/2er just because of semantics but I understood what he meant and in that context I'm 1/3er, so I don't know whether I should like or dislike

@@0NeeN0 but if you're saying there is context then you are essentially adding it and rephrasing the question given to you to be the second question. That's the point momo was making, the implied context makes you think you need to answer the second question. But really the question should be asked with that context or else it's 50/50

This! 100% this! The problem is that the language being used isn't precise enough.

Good analysis!

exactly my answer. perspective and probability are two different things. and counting one event twice, as he did in the experiment when he got 1/3rd each does hurt people who do statistics.

In this case ‘probability’ refers to her ‘credence’ of the coin being heads, i.e. her subjective confidence all things considered that the coin was heads. That she would have slept through Monday on a tails flip is completely irrelevant as her credence of each scenario is not equal. It would only be rational to assign a higher probability to tails if her waking up eliminated some possibilities of heads which it doesn’t, so the chance of her being in a heads-world is exactly the same as being in a tails-world. Your doctor case is not analogous, since waking up eliminates all possibilities in which you die, so you gain information from the fact you wake up.

Sleeping Beauty actually does gain information from her awakening: It's no longer Sunday! It's either Mon- or Tuesday. On Sunday the coin is flipped: 50% chance for heads or tails. SB's Sunday credence is intact. Now she is awakened: Oops! Is it Monday? Is it Tuesday? She knows it not. Her presence depends on her past. Of course, her memory of the Sunday chance seems intact: 50% for heads or tails. But her memory of that past lies in the very presence which depends on it: a loop--not to be trusted! Ask her this question now: "What do you believe, my dear SB, is your chance of being awakened again?" Hm..., ...Monday 50%, ...Tuesday 0%. How to answer? She's no longer in a "Sunday mood". SB's credence has been compromised by the fact that her beautiful presence may have been tossed into a "Tuesdayish" tails-tails-nightmare already. The very bed she sleeps on has been gambled with. There's a chance she lies on a doomed bed (at least until the Prince of Mathematics appears on a white horse; allow me to cry for a while--but only with one eye). The SB-problem wants to not just entail the tossing of the coin but the tossing of the tossing itself. SB has already been tossed and turned in her bed (lousy sleep?) before she awakes. Her answer doesn't come from a 100% heads- or tails-world. Btw., to address another point in the video, I think, it doesn't matter if she'd be awakened 1.000.000 times with an original tails flip: It's Monday versus 999.999 days presenting Tuesday. The tossing has only been tossed once--not a million times.

Are the odds skewed for tails tough? When it's heads she won't actually wake up on tuesday. It's a variation on Pascal's wager.

There is no question to which the correct answer is 1/3. The whole thirder perspective is flawed because it treats the possible "states" as equally likely and independent, but they are not independent.

@@nekekaminger The question would be, ‘What is the probability you were woken up by a flip of heads?’ I think the answer to the sleeping beauty question is 1/2 though because like the original comment said they are answering two different questions.

@@reubensavage2067 She's always woken up, otherwise you couldn't ask her. Prepending the question with the pseudo-condition of her being woken up doesn't actually change anything because it always happens. The question is fully equivalent for "What's the chance heads came up?" which is clearly 50%. I see what you are trying to do. You view each waking up event as an independent event and try to assign a probability to that event (just like Derek proposes in the video), but that approach is flawed since they are not independent. Monday Tails and Tuesday Tails cannot happen without the their also happening. Imagine you have a somewhat unusual coin that instead of heads has one dot on one side and instead of tails it has two dots on the other side. Each dot represents a waking up "event". After the toss pick one of the dots you see (which is either just one, in which case the choice is simple, or two, in which case you just randomly pick one, since SB can't remember being woken up before, the order does not matter) and ask yourself "What is the chance I see this particular dot because the coin came up with the single dotted side?". If two dots were up you answer the same question for the other dot. The experiment is exactly equivalent (if you don't agree, please explain). Do you still think the answer is 1/3?

@@nekekaminger The part that I disagree with is that I'd argue they are independent events. She could be woken up on Monday Heads and be asked the question, or woken up on Monday Tails and be asked the question, or be woken up on Tuesday Tails and be asked a question. As others have stated, it really comes down to which question is asked of her. If she's asked "What do you believe is the probability that the coin came up heads?", then she should answer 1/2. Because the coin either came up heads, or it came up tails. It doesn't matter which day she woke up; the coin was either heads, or tails. If the question is "What do you believe is the probability that you were awoken on heads?", then she should answer 1/3. Because as I mentioned in my first paragraph, if she's asked this question on Monday Heads, she would be right. If she's asked on Monday Tails, she would be wrong. If she's asked on Tuesday Tails, then she would again be wrong. So it's a 1/3 chance of her being right about the 2nd question.

@@ThrowAway-hy5sp you haven’t tackled his point that these events are not independent. Monday tails and Tuesday tails are essentially the same event. For the example where she wakes up “a million times” it’s 1/2 chance that she’ll wake up a million times or 1/2 chance she wakes up once. Either way if she wakes up on the thousandth Tuesday and is asked “what’s the chance that you will wake up another thousand or so days”, its 1/2 as is “what’s the chance you only wake up today on the monday”. There’s not “more chance” of waking up in the millionth day like it’s compared to being in a simulation. It would be like saying the chance of you living in reality is 1/2, and the chance of you living in any of the millions of situations is also 1/2. 1/3 would be the answer to “what’s the probability today Is Tuesday” regarding the original question.

This! This right here.

The problem here was your approach to study. That last-minute "cramming" is easily forgotten, especially in a stressful situation. Repetition and practice over a much longer period, or reflective self-study to the point where you reach genuine understanding, was the way to make sure you passed those tests. But I'm completely aware that very few kids at school would heed that advice, including my younger self!

Exactly. This is an independent event. Probability conditional on being awake though, I think that's different although I'm not sophisticated enough in probability to know how 😂

@@aubreydeangelo Not necessarily. The claim of them being independent is contentious among theories of probability. According to Bayesian probability theory, probabilities aren’t objective; instead, they reflect our degree of belief in X given Y information, so the totality of our information on the scenario actively affects the “probability” in the epistemological sense of an outcome. The existence of objective probabilities is tenuous at best; Quantum mechanics wave function collapse is a possible exception, be it contested. They are of course competing frequantist theories of probability however it being independent is not at all intuitive or obviously true.

Exactly, the question is ambiguous. There are 2 questions being conflated. - what is the probability that a fair coin came up as heads this week? - what is the probability that we woke you up because the coin came up heads?

​@@nicksmith9521 thank you! None of the research papers would be necessary if the question was specified.

​@@nikhilweerakoon1793 There's no need to tap into some subjective probability nonsense. There are two probabilities at play. Implicitly, the question is stringing together two dependent probabilities: (1) a 50% chance of turning up as heads, and (2) 100% more likely to wake up due to Tails Let's use another example: I flip a coin. 50% chance it's heads and I wake you up. 50% chance it's tails and you die in your sleep. The next day you wake up. "What is the probability it landed on heads?" The probability is 100%. Because you have been woken up. The coin flip was a 50/50 chance, but the waking up was a 100/0 chance. Yes, flipping the coin _in general_ is a 50/50 shot at heads. But now that you have more information (the fact that you woke up), you need to factor that in. If you say "50% chance" because the independent coin flip had a 50% chance, you're just intentionally ignoring additional information in some kind of weird linguistic purism.

But then you would disregard the information she already has, and information is important in mathematics. If she gets woken up, theres a 1/3 chance that its tuesday.

@@gorgit That's not the question. First, she has no information other than the rules of the game. The question is "what does she believe the probability is that the coin landed on heads?" When she gets up, she isn't given anything other than the question. 50%... problem solved.

@@JohnJJSchmidt she is given knowledge that one of the days she could be awoken is Tuesday, but she doesn't have the ability to tell what day it is when she is awake. Therefore she has the knowledge that it could either be Monday after a heads, Monday after tails or Tuesday after tails. Even though the question she is asked doesn't change the probability the pre existing knowledge she has does.

@@jaredhahn7970 The probability of what? Again. The question is what does SHE THINK the prob the coin landed heads, not the prob of it being a certain day. If she says anything other than 50% with a blank mind, she is letting the pre-existing knowledge of the rules interfere with really basic reasoning.

If we phrase it as “what is the probability that she woke up in a scenario that the coin was heads?”, it’s 1/3; but yeah, given that the question is, “which way did the coin come up?”, it’s still just 1/2.

Correct.

It is a 50/50 chance on sleeping 1 day or a million. However, each time she wakes up its a 1/1000000 chance of being tails

@@joshpollnitz1618 Each time she wakes up it's 50/50 chance she either exists in the heads sequence or the tails sequence. The sequence is one complete package. It doesn't matter how long the sequence is, it's still one package. The reason being that the conditional statement is the fair coin which only has two outcomes at 50% chance each.

You are confusing the probability of the coin coming up heads _before_ it was flipped with the probability that it _did_ comes up heads, after it was flipped and the observer has some amount of information pertaining to what the outcome was. These are two very different things. The answer to the first is always 50%, but the answer to the second is not necessarily 50%, depending on what information the observer has observed. This is the fundamental principle behind Bayesian probability.

​@@therainman7777 Sigh. Leftism is a religion upon which the idea that an individual's perceptions can dictate reality is the central object of divine worship, thus the solipsistic imposition of the self's mind onto the world makes the Leftist a god in his own eyes. Pay attention to me. There is no secondary set of probabilities. There exists no such thing as metaphysical probability. That's a perceptual lie that the illogical parts of the human brain concoct in order to alleviate the pain and stress caused by the sheer gravity of reality pressing on you from all sides forcing you to accept that you cannot escape objective truth. There is no such thing as "probability after the fact" nor is there any such thing as a "choose your own adventure" kind of probability. Probability is determined by material scientific forces that can be measured and predicted to a certain level of accuracy. In this case though we have from the outset a theoretical "perfect" object in the form of the fair coin. We know from the get go what the probabilities are because those probabilities are deterministic and they are determined by a physical object whose attributes are already established -- the coin is an ideal one. According to the parameters set by the use of such an ideal instrument we are bound to make the conclusion IMPOSED by the parameters set by the ideal instrument. You cannot escape the physical imposition of physical laws even when those laws are purely theoretical because those laws still follow the rules of logic. The coin is set to have a 50/50 chance to land either heads or tails therefore those are THE ONLY outcomes you can measure in the experiment. Nothing else besides those two outcomes exist. Period. End of story. --

The number is still being transmitted with the page, but not being displayed. If you want to see the numbers again, you can use a browser extension such as "Return KZfaq Dislike". This is why I'm able to tell you that at the moment, this video has 114k likes and 61k dislikes.

@@mattgies unfortunately that does not work for mobile. and that extension is not accurate, it is only a rough estimate :/

@@mattgies The KZfaq API doesn't include the Dislike Dataset no more. The Extension just looks at every Extension user which likes or dislikes the video and extrapolate the data to get a rough estimation of the like to dislike ratio

@@therealdnold Oh wow! I had no idea

@@anonymouscommentator Youtubе Vanced on mobile does include Return KZfaq Dislike as a toggleable setting, so it is still possible to use. However, that estimation is still a factor.

What if we change the problem, such that if the coin lands heads, she is never woken up. If the coin lands tails, she is woken and asked the question. In this situation, it's the same as if she can still see the coin on the table showing tails. The probability is 100% that the coin landed tails.

Bruh that's the same question

If she's asked EVERY time she woke up, then it'd be 1/3 because two times when asked, it had been tails. If she was asked only once, decided by the coin flipper, then it should be 1/2.

I don't think it matters to rephrase the question. If she had a record of how many times she guessed the face of the coin correctly through trial and error she would get to the probability being 1/3rd for heads. But this is only because she doesn't know if its Monday or Tuesday. So I agree with the first part of what you said. She you and I know the coin toss 50-50. But what's asked if is it's actually heads when she wakes up. This actually flips the assumptions around where it becomes obvious it should be 1/3. But I think people misunderstand what 1/2 would actually mean. It means that because she has no connected information between the time she wakes up the probability remains 1/2. So to believe 1/3 means you believe her inability to have information about waking up a second time is information.

@@Furiends wording matters. P(head) and P(head|awake) are two different question, the video seems to be asking the former

i also feel like they just missing the obvious lol

If the question for the sleeping beauty was to tell if the coin flipped heads or tails. She is woken up three times,two times if it's tails and just one time if it's heads. If she says tails all three times, she'd be correct 2/3 times. If she says heads, she'll be correct 1/3 times. In conclusion, the probability of her getting the answer correct if the outcome is heads is 1/3. Whereas,the probability of the coin flipping to either heads or tails is 1/2. She would be right 1/3 times,but then answer is 1/2 as per the question.

@@architlal8594 the question doesn't ask her to predict whether the coin was heads or tails. it asks her what the probability is that it was heads. so her response wouldn't be 'heads' or 'tails'. the trick with this problem is that people are fooled into thinking that monday (tails) and tuesday (tails) are independent events. but they aren't. they're actually the same event. the reason you get the 1/3 distribution is that she gets woken up twice on a tails. and therefore gets asked twice from the same coin flip.

I feel like that arguing with people about politics and society all the time. In the absence of an obvious answer on a lot of those issues - unless you are very well informed on them, which a lot of people aren't, often times people just try to roll you with fallacies like that. I believe usually even unknowingly so and thinking "they got you". But it's very tough to effectively counter that, especially in the moment, because, as this video shows, unraveling such fallacies can be very hard. Often much harder than coming up with them.

Actually a lot people that understoodd this question as "did I flip a heads or tails?" respond with "I dont know its 50/50." This isnt some word game this is a sort of paradox. The people that disliked this video isnt arguing that a coinflip is always 50/50.

Exactly, I feel like this is convoluted for the sake of being convoluted cos the question is confusing. Interesting nonetheless

This is what confused me about the question. The probability the coin flip was heads is 1/2; but the probability that she was woken up by a "heads" coin is 1/3.

Took me two watches to catch that. I even simulated the second “unasked” question, confirmed the 1/3 outcome, but that wasn’t what she was asked.

Yeah. Depending on the exact framing of the question, either answer is valid.

Yep. It's a whole genre, these silly faux-dilemmas. They try to pass-off a multi-step process as a one-and-done. In the case of SB and similar DT puzzles, it's, as you say, more than one prediction, serially. In this guy's argument, he even replaces the fair coin with an extremely unfair coin, if you will, and STILL courts the controversy. Infantilizing, if you ask me.

Yeah. It's more like reaching into a bag with one white marble and one black marble, but if you pull out the black marble you find out that it's actually a string of beads with 999999 other black marbles hanging out the bottom of the bag.

Yeahhh now I am getting it after reading this comment

Savagely well understood.

@@johnoldroyd94 you as well.

It’s like having 2 same size bags: one with 1 white marble and the other one with million black marbles. And putting your hand into a random bag to grab all the marbles. According to Derek, the chance of picking a black marble is million times higher. Well, you’ll have more black marbles in average, but the fact that you forget that all the black marbles are a result of a single outcome doesn’t make them being picked independently.

Agreed. It is the perspective.

"Came" is the keyword. It's past tense. When an event has already occurred, any information you can access regarding that event changes the probability that it occurred one way or another. What's the probability that the card I pulled out of the deck is the ace of spades? 1/52. But now you draw a card. It's not the ace of spades. Since you've removed that card from the list of possible cards I might have, the probability that the card I pulled at the beginning was the ace of spades is now 1/51. Since it's a past event, new information about it changes the probability. I draw another card. Now it's a 2/51 probability that I have the ace of spades. You draw another. One less possible card I could have, so now it's a 2/50 probability that I have the ace. And so on and so on until all the cards have been drawn and the probability becomes 1/1 whether I have the ace or not.

I do think at least for those fully understanding it that it's about how we value information. Thirders are incorporating the fact she lacks information. Halfers are assuming lacking information is irrelevant. For the sake of Halfers it's important we define the problem of her guess in one single instance based on the rules. There is inaruguably three states in the state space. She's awake on a Monday with tails, she's awake on Tuesday with tails and she's awake on Monday with heads. I actually think it's Halfers that have one extra step of justification. (unless you completely missed this is about the shared information that she lacks information.. it's not a matter of perspective). That extra step is say even though she knows there's three states in the state space there's ultimately only two that matter. The third being she doesn't know it's not Tuesday and heads so the question is like saying it's 50-50 on Monday or Tuesday.

It's pretty clear that he asked the first question, it's explicitly written on the screen. So thirders are just wrong.

I agree. And as a halfer I have to point that the question is "What is the probability that the coin was heads"

There is now a 50/25/25 chance of you falling asleep :V

I can put your mind at ease....Just think about the coin landing *ON EDGE*

Don't worry, I got the same one later.

If you really think about it, why should tails be weighted twice as much as heads (i.e. why should tails receive 2 tick marks and heads only receive 1 tick mark)? Then the coin will no longer be a "fair" coin since the results is weighted.

As he gets too at the end, they're really answering two different questions Halfers are answering the question what percentage of the time the coin was flipped did it land heads Thirders are answering the question what percentage of the times the question was askwed was heads the correct asnwer For the weighted coin flip at the end, 4/5 times the coin landed B, but 30/34 times the correct answer was C

Perfect

Ye but it's not the coin toss itself so the question is a trick (and wrong)

@@Trepur349 thank you. Very good summary and re-explanation