The Pokémon TCG Pocket game has a mechanic where you are shown 5 cards face down, in which there is usually only one desirable card, and let you pick one at random to keep

That's all well-and-good, but recently they added an event where you get to "peak" at one of the cards before you make your choice.

Now - if the one you peak is correct, you can just pick it, so that math ends there. However, if the card you pick is incorrect, does the logic of the Monty Hall problem apply?

I, and I think most others, mentally decide a card to pick before it's even time (I always pick the bottom right). If I reveal a different card and it's incorrect, is it statistically probable for me to forsake my mental guess and pick one of the other 3 cards? This feels wrong, the game didn't know that was my choice, it feels like it should now be no less likely than the other 3 cards.

However, wouldn't the logic of the Monty Hall problem apply to this, and say it is incorrect? That, logically speaking, my initial probability doesn't change from 1/5 despite the fact another one was eliminate (this is, to be clear, under the theoretical that the 'peaked' card is wrong, as the peaked card being correct ends the scenario). If there was a 1/5 chance my initial guess was correct, there is a 4/5 chance it was wrong. If a card is revealed, there is still a 4/5 chance I was initially wrong, but if there are only 3 possible cards to switch to, they split that 4/5 3-ways, making them each 26.66% likely to be correct (as opposed to my 20%), no?

This is my way of understanding the Monty Hall problem but practically speaking I don't feel like that can be incorrect? The game doesn't even know my initial 'mental' pick, so how could there be a statistical difference if I choose it or swap it.

And if any of the 3 swaps are really 26.66% likely in that scenario, wouldn't that mean mentally envisioning one and then swapping it is actually (very slightly) more likely than peaking at one at random and then picking one of the remaining 4 (25%)? Again, in both these scenarios just not factoring in the possibility that the peak is correct, which should apply to both scenarios equally anyway and not change the end result.

I don't know what the flaw in my logic is but I can't imagine that 26.66% correct. If the 1/5 chance the "peaked" card was incorrect is distributed to all 4 cards then it's 25%, but wouldn't that mean the Monty Hall problem results in a 50% chance instead of a 66% chance?

Can anyone help me break down the probability in this scenario? Is there a flaw in my understanding of the probabiltiy or do you really increase your chances by mentally choosing one and then refusing to take it?

Ye I know it's a movie but what will actually happen(hope you cna use links here):
https://www.youtube.com/shorts/EtS7FQZ4Lcg

way smaller bullet hit centrally bigger bullet (I assume they have same speed)

My son sent me this. My immediate thought based on nothing is that it’s unsurvivable regardless of the depth.

Edit: 2 duodecillion in rubles. And also, it's debt only to TV channels, which I'm interested in.

I was reading a fiction book (One Piece), and a certain situation that happens WAY LATE into the story intrigued me, and thinking about what could have happened led me to make this weird question.

If there was a hole big enough for the mass and area of an entire island (average) to fall through to the center of the Earth, considering drag in either water or air or magma, how long would it take? Because whenever I search it up, the quickest answer always discounts any resistance from any fluid at all, and example results that do take it into account wouldn't translate well into this particular question.

As the title says.

Imagine you had some structure, like a tower or space elevator that extended into space, well beyond the atmosphere (ignoring the difficulties of creating such as structure).

If you were standing on the Earth's surface, and assuming relatively level terrain (we'll say approximately "at sea level"), how far away would you be able to be and still see at least a glimpse of this structure?

Bonus question (not really math, more optics/physics): What would the "top" of the tower look like at the point where you can no longer see it going up? Would it just kind of fade to a "vanishing point", have some clear cut-off, or basically fade as if someone put a transparent gradient at the top?

Thanks.

I'm talking about big servers like things used for chat got, YouTube, Facebook, crypto mining, etc.

People are speculating on the expected payments for a huge anti-trust suit against many schools, who colluded to cook the books on financial aid calculations.

So the question is. If there is 200M dollars available, and 200k POSSIBLE claimants, and the claim amount varies by the number of years attended for undergrad... what is the expected claim amount if every possible person submits a claim... for the classes of people who attended for 1, 2, 3, and 4 years of the relevant window.

I think it is a pretty interesting question.

I'm reading The Sun Also Rises, and its mentioned that the whiskey and soda the characters but from a bar costs 12 francs. Would that have been a lot of money? Not quite a straightforward currency conversion as both France and Australia use different currencies than they did when the book was written.

In the recently concluded Kumbh Festival in India in 2025 it was said that almost 650 million people visited one place (City of Prayagraj) in 45 days.

Now the people came to the river banks, did the rituals and went back. some people stayed 1 night at the place. Some people stayed for 2 nights whereas a lot of people just came in the day and did not stay and went back the same day. There were some people who came stayed in the car and did not book hotels or stayed in open grounds

Is it possible that 650 million people visited in for 45 days? Is it possible logistically for transport, stay to manage this crowd

some sources of the info

https://en.wikipedia.org/wiki/2025_Prayag_Maha_Kumbh_Mela

This video gives an idea of the temp tent area where people stay

https://www.youtube.com/watch?v=kcxShS71QyQ

There are almost 100K tents build

https://www.moneycontrol.com/news/india/68-lakh-wooden-poles-100-km-fabric-and-3000-workers-making-of-tent-city-in-maha-kumbh-12907258.html