I think. I’m pretty drunk today, so don’t take this at face value.
Yeah, the more I think about this, the more it seems like I have it wrong lol.
There is definitely a 1/e involved in the limiting case. As for the rest… I’ll let others elaborate.
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That doesn’t sound right. When interviewing them you don’t know their rank relative to the pool, you only know their rank relative to the others you already interviewed.
Also if we follow your method, it doesn’t seem like this would happen:
It doesn’t seem like you’re going to get the very best one 37% of the time with your approach.
Yeah I already corrected myself, sort of. I was wrong.
Please return when you’ve sobered up sufficiently. I’m actually quite curious about the answer.
Which is fucking annoying, since I fancy myself for this problem. I am going to go and think about this and return tomorrow.
Maybe I’m thinking about it wrong, but it seems like a different problem that happens to have the same answer.
It’s an optimisation problem, I think it’s the same problem but I am reticent to make any definitive statements now that I got the last one wrong.
Anyway, when I need something like this solved definitively, I ask Donkey (eeeAwww, he is the one who directed me to this thread)
If he can’t solve it, I sure as fuck can’t.
And the rest, as they say, is trigonometry.
2/root 2 is just a weird way of writing root 2 btw. Multiply the numerator and denominator by root(2)/root(2) and cancel, and you get root(2)/1
Or just in general… x/root(x) is… wait for it… root x. Square root x if you don’t believe me.
Recognizing x as x^1 and root(x) as x^(1/2) and recognizing that multiplying/dividing powers of the same base can be simplified by adding/subtracting respectively the exponents it’s even easier to visualize the simplification.
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Not really, the secretary problem is one-sided (optimal stopping), here there is a game element which means you do not just optimize your expectation but also have to take into account your opponent’s distribution.
(This is probably mentioned in the first 5 posts of this thread btw)
(Also the 63 here doesnt have anything to do with e…but maybe it appears if the number of rolls goes to infinity, who knows…)
Alright man, way put the knife in. Already admitted I was wrong.
Also, I am definitely putting a knife in HeeeeWaw. Fuck, he might like that.
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Huh, I don’t know this weirdo
I think the game as originally stated has been solved, so I wanted to propose a variation.
What if player two gets to see if the first player rerolls (but not their result) before deciding whether to roll again?