suppose there are 100 guys... and each of them pick any number between 0 and 100 once everybody has picked a number....you add all of the numbers and multiply that by 2/3 so...if everybody picked 100....the average would be 100 and after multiplying by 2/3, you get 66.67... now, whoever's picked number is closest to the average multiplied by 2/3, wins the game and gets $100..... what no I should I choose to maximize my chance of winning?

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suppose there are 100 guys... and each of them pick any number between 0 and 100 once everybody has picked a number....you add all of the numbers and multiply that by 2/3 so...if everybody picked 100....the average would be 100 and after multiplying by 2/3, you get 66.67... now, whoever's picked number is closest to the average multiplied by 2/3, wins the game and gets $100..... what no I should I choose to maximize my chance of winning?

Mathematics
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Just a stab in the dark, but if you multiplied each number by 2/3, and found the average of those. Wouldn't that be the best number to guess?
Idk....I've no idea at all :/
Use Bayes' Theorem!

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Bayes????????
what is the most likely number that 100 guys would pick?
1 ?
Not getting it..........
good! so if 100 guys pick one, then the result would be 2/3!
so if you picked 1, then you would be winning
come on....i don't think it is solved like this guy1=59 guy2=31 . . . . . . . . . . .guy100=3 Wht now?
alright, try having all guys pick different numbers: guy 1 pick 1, guy 2 pick 2... guy 100 pick 100
find\[\sum_{i=1}^{100}i\]
this is \[\frac{100*(100+1)}{2}=10100/2 = 5050\]
i did smth like |dw:1317896959755:dw|
yes!
hmm....
silly me whn i was finding the average i divided it by 2(God knows why i did tht) and i got 1683...O.o Thnx ^^
If you don't like that answer, set up a simulation. For every trial, make it create a list of 100 random integers. Sum those elements, divide by 100, and multiply that sum by 2./3. Repeat for about 10000-1000000 trials, adding the results of each trial together, and finding the average result.
|dw:1317897551125:dw|
yep, I got the same 33.3 answer after 10000 trials

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