The Most Controversial Problem in Philosophy

If you want to vote by liking/disliking the video: “Agree with me” means 1/3 and “Disagree” means 1/2. Latest update (Nov 23, 2023): 217,332 agree with me, and 97,502 disagree with me.

"What coin? What are you talking about? Where am I? Who are you?"

As a Canadian, I would be quite happy for a 20% chance of winning against Brazil

When I reached your poll, I didn't understand the controversy. If the question is "What is the probability that the coin WILL be heads?" the answer is 1/2. If the question is "What is the probability that the coin WAS heads?" is 1/3. These are two completely different questions. The first has to do with flipping a coin. The second is about what day it is.

My reactions when I see a Veritasium video. Amazed by the title-> Understands the concept-> Trying to understand deeply-> Gets lost-> Forgets what was the video about-> Perplexed about the reality-->Video ends->Hits the like button.

Lessons learned: never let a researcher put you to sleep and never pay them in cash

Whenever there's no consensus in probability puzzles like this one, it usually does boil down to subtle disagreements about what is actually being asked, not the answers themselves.

Derik: vote with like and dislike button Youtube: makes dislikes invisible

For me it becomes less paradoxical when I think of the question as rephrased as "How likely is it that Heads is responsible for you waking up this particular time?"

If sleeping beauty was asked "What's the probability the coin came up heads?", I think she should say 1/2. If she was asked "What's the probability that you've been woken up as part of the outcome of a heads result?", I think she should say 1/3. I think the key thing with this question and the reason there isn't (and probably can't be) consensus comes down to how it's communicated and how we as individuals interpret what's being asked of us with the answer. If your goal is to reinforce your understanding about how the coin works, you are probably a halfer. If your goal is to be correct in answering the question from the perspective of sleeping beauty, you are probably a thirder.

I'm changing my answer to 1/2 - it doesn't matter how many times she is woken up the probability the coin came up heads in the initial toss remains the same. The experiment where you count your coin toss and then mark the outcome as either Monday heads, Monday tails, Tuesday tails - is seeing the chance of being woken up by a heads flip. This is different to the probability of the initial flip.

In my opinion the question you seem to ask is: What is the probability that today isn’t Monday? The probability of a coin flip is always a coin flip as we say(50-50).. but the question refers to the coins state only in regard to what day it might be.. meaning that if it was H she’ll be asked once, while if it was T she’ll be asked twice, so it’s not really a philosophical problem, just that the question appears to be misleading

I'm a simple man. The probability of everything is always 50-50. It either happens, or it doesn't.

“Do not hit the like button” 87 people instantly ignored him

It's 1/2, think of it like this. You randomly get assigned a red or blue magnet, which you cannot see. They only attract coins of the same color. You are given a bag with 1 million blue coins and 1 single red coin. You will then stick in and pull out a coin with your unknown color magnet. What is probability that reaching in with the unknown color magnet that it will pull out a red coin? If the random 50% chance assigned you a red one you will therefore will pull out the 1 red coin. If the 50% chance assigned you a blue magnet, therefore you will pull out a blue coin, which will be one of those 1 million blue coins. The 1 red coin will always be pulled every time yours is red, but any specific blue coin (outcome) will only be pulled one / one millionth of the time yours is blue, the 50% blue probability is split amongst the one million blue coins you have a random chance at pulling, so those specific outcomes has far less weighted probability than the red coin. The red magnet's 50% will never split its probability because there's only 1 coin. More blue coins added just further dilutes the probablity of any specific coin being pulled from the blue magnets probability, but the sum will always still just be 50%.

Its not that theres a 1 in 3 of heads, its a 1 in 3 that she was awoken for it being heads

The experimenters look on in horror as the coin rests upon its edge. They somberly pull the sheet over Sleeping Beauty's face. After an appropriate period of silence, Erwin asks, "You guys wanna put my cat in a box with an unstable nucleus, a hammer, and a vial of nerve gas?" "Not again, Erwin..."

"Waking up on Monday with head" gets me every time.

I'm extremely happy you posted this content! Pure creative thought in action is a beautiful art form! ...and more importantly there's so many perspectives on this idea! Anyway... just really happy to see someone explain this so well! Thank you!

I think the question asked is really: "is this a heads day or a tails day?" and the chance of it being a tails day is twice as high as it being a heads day.