The Sleeping Beauty Problem by Veritasium

Here's the youtube video and references (in case it gets taken down)

 https://www.youtube.com/watch?v=XeSu9fBJ2sI

References:

Elga, A. (2000). Self-locating belief and the Sleeping Beauty problem. Analysis, 60(2), 143-147. - https://ve42.co/Elga2000

Lewis, D. (2001). Sleeping beauty: reply to Elga. Analysis, 61(3), 171-176. - https://ve42.co/Lewis2001

Winkler, P. (2017). The sleeping beauty controversy. The American Mathematical Monthly, 124(7), 579-587. - https://ve42.co/Winkler2017

Titelbaum, M. G. (2013). Ten reasons to care about the Sleeping Beauty problem. Philosophy Compass, 8(11), 1003-1017. - https://ve42.co/Titelbaum2013

Mutalik, P. (2016). Solution: ‘Sleeping Beauty’s Dilemma’, Quanta Magazine - https://ve42.co/MutalikQ2016

Rec.Puzzles - Some “Sleeping Beauty” Postings - https://ve42.co/SBRecPuzzles

The Sleeping Beauty Paradox, Statistics SE - https://ve42.co/SBPSSE

The Sleeping Beauty Problem, Reddit - https://ve42.co/SBPReddit 

Sleeping Beauty paradox explained, GameFAQs - https://ve42.co/SBPGameFAQ

The Sleeping Beauty Problem, Physics Forums - https://ve42.co/SBPPhysicsForums 

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I just heard the problem statement in the video, but not yet the discussions. It seems to be a classic case of confusing what probability is.

There's no probability of a single event happening per se, but rather, a probability given a hypothetical model where some parameters are fixed and some are not.  For example, in a coin flip, in theory the probability is 50%, but that conventionally presumes that we don't know any parameters over how it was flipped (amount of force, etc.), how high it was flipped, materials of the coin and the ground etc. If you have more information, the probability is not 50%.  In addition, the knowns or unknowns could have a probability distribution as well, for example the force used in flipping may have a distribution (which is actually true in practice, I suppose).

So, the probability of the coin being tails in sleeping beauty story depends on the context. Assuming the coin flip is fair, then obviously the probability is 50%.   On the other hand, if you ask the girl "do you think it's heads or tails", obviously she will get it right 2/3 of the time if she answers tail.  If she had a chance to wager money every time she wakes up, there'd be a winning strategy to bet on tails. In that sense the answer is 1/3 for her. 

HOWEVER, it's meaningless to ask "what do you think is probability that the [single] coin flip ended up heads?"  From the objective perspective, already happened, so it's 100% either heads or tails, depending on what actually happened. From the subjective perspective, she doesn't know, and there's actually no meaningful probability distribution for figuring out which possible world you are in (I think).

I took a couple minutes trying to figure out what happened in this scenario, originally I thought this might lead to some profoundly insightful outcome, but after some contemplation I think the confusion is just about the way the question is asked, and the futile attempt at logicians (etc.) trying to figure out probabilities of things we actually don't know.

Hint: there's really no way to figure out probability of things we don't know. You can deceive yourself in trying, but no, it doesn't work.