Usogui - Vol. 28 Ch. 302 - Intuition And Theory
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Ah, the Monty Hall Problem. I really hate that thing, it just hurts to think about it whenever it comes up. Nonetheless, nice chapter. Gakuto's essentially at 4 ships down so far, "only" 5 more to go!
I wonder if Lacy ended up putting all the ships near the points that Gakuto actually missed up until now. They did bring up how experienced Lacy is at this game during the chapter, so specifically putting it near the diagonal like that Gakuto theorized to use seems like something he might have done.
I wonder if Lacy ended up putting all the ships near the points that Gakuto actually missed up until now. They did bring up how experienced Lacy is at this game during the chapter, so specifically putting it near the diagonal like that Gakuto theorized to use seems like something he might have done.
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I also hate that problem because, seriously, whats the fucking difference? Is not as if you are choosing from another set of doors.
You chose 1/3.
Then there is a new 1/2 chance of choosing, changing the door you chose doesnt change that is a 1/2 only because it was a 1/3 before, and the proof of that is that you could have chosen the final door at the beggining and the answer would then be the door you currently chose.
But make no mistake I know this is just that I dont get it.
You chose 1/3.
Then there is a new 1/2 chance of choosing, changing the door you chose doesnt change that is a 1/2 only because it was a 1/3 before, and the proof of that is that you could have chosen the final door at the beggining and the answer would then be the door you currently chose.
But make no mistake I know this is just that I dont get it.
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You know, I kinda like how Oofuna's seemingly playing this game honest. No cheating or extreme mental gymnastics (at least, as far as we've seen). Just a guy taking straightforward gambles and getting them right.
I don't think it'll last, seeing how much more he has to go to win yet, but still, I like it.
I don't think it'll last, seeing how much more he has to go to win yet, but still, I like it.
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@belkrax
Really, the point of bringing the problem up in this chapter is, like you and I know firsthand, the fact that swapping is the "right" choice, but it doesn't make sense for us as to why. It's literally the difference between what we think is right, and what is mathematically right.
I like how the author managed to show that in a gambling match, it really feels like it got Lacy's mindset across too.
Really, the point of bringing the problem up in this chapter is, like you and I know firsthand, the fact that swapping is the "right" choice, but it doesn't make sense for us as to why. It's literally the difference between what we think is right, and what is mathematically right.
I like how the author managed to show that in a gambling match, it really feels like it got Lacy's mindset across too.
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@belkrax It effectively turns the problem of "choose the right door" into "choose a wrong door." The 100 door example illustrates it pretty well, in that you are effectively choosing a door you think is wrong, which is a 99/100 chance, and 98 other "wrong" doors will automatically be taken out for you, which means the remaining 1 door will be the "right" door, UNLESS the first door you chose (1 in 100) was the right one, but that's a 1% chance.
So you chose 1 door out of 3 that you think is empty, and one of the other doors will be taken out for you, which means chances are high the remaining door is the "right door," UNLESS the first door you chose (1 in 3) was the right one, but that's a 33% chance.
So you chose 1 door out of 3 that you think is empty, and one of the other doors will be taken out for you, which means chances are high the remaining door is the "right door," UNLESS the first door you chose (1 in 3) was the right one, but that's a 33% chance.
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@299792458 @Sinful_egg
Up to 304, possibly a bit further since our translators & typesetter are working super fast! I'll post if that happens.
Up to 304, possibly a bit further since our translators & typesetter are working super fast! I'll post if that happens.
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@belkrax It's exactly because you aren't choosing from another set of doors. It's also exactly because only doors that definitely will not win are opened for you.
You should think of the doors as two sets of doors. There are x doors. You may only choose one, which means the set of 1 door that you chose has a chance of 1/x of being correct, which means the set of the other x-1 doors has a 1 - 1/x chance of having the correct door.
In the case of 3 doors, this means that the set you didn't choose has a 2/3 chance of including the correct door. With 100 doors, the set you didn't initially choose has a 99/100 chance of including the correct door.
When all the incorrect doors of the not-chosen set are opened (except one, if you happened to initially choose the correct door), what remains is a single door that is included in that set with the higher 1 - 1/x chance.
To make it even easier: When presented with 100 doors, would you prefer to open 1 door, or 99 doors? With 3 doors, would you prefer 1 door, or 2 doors? With the first choice, you're essentially given the option to choose the one door that you don't want to pick.
On a side note, Michael from Vsauce was right about it being fun to think of a way to explain the dilemma lol
You should think of the doors as two sets of doors. There are x doors. You may only choose one, which means the set of 1 door that you chose has a chance of 1/x of being correct, which means the set of the other x-1 doors has a 1 - 1/x chance of having the correct door.
In the case of 3 doors, this means that the set you didn't choose has a 2/3 chance of including the correct door. With 100 doors, the set you didn't initially choose has a 99/100 chance of including the correct door.
When all the incorrect doors of the not-chosen set are opened (except one, if you happened to initially choose the correct door), what remains is a single door that is included in that set with the higher 1 - 1/x chance.
To make it even easier: When presented with 100 doors, would you prefer to open 1 door, or 99 doors? With 3 doors, would you prefer 1 door, or 2 doors? With the first choice, you're essentially given the option to choose the one door that you don't want to pick.
On a side note, Michael from Vsauce was right about it being fun to think of a way to explain the dilemma lol
