Re: cranky challenge - beating a game
- From: "Risto Lankinen" <rlankine@xxxxxxxxxxx>
- Date: Fri, 01 Jul 2005 08:45:57 GMT
""Gary Z."" <gangxu_csu@xxxxxxxxx> wrote in message
news:22134911.1120003163981.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxxxxx
> two players :
>
> player 1 writes down two positive numbers A & B, A is NOT equal to B.
>
> number A is shown to player 2, knowing nothing about how A & B were
generated. now player 2 has to guess which one is larger, A or B?
>
> Question: can player 2 guess it correctly in the probability > 50%? how
can he?
Yes, he can. He guesses 'A' with probability '(A-1)/A' and 'B'
with probability '1/A'.
If 'A' and 'B can also be negative, you can use any monotonously
growing function defined for -oo..oo and returning values between
0..1 . One such function is the [deltoid?] 'p=1/(1+1/e^A)'.
- Risto -
.
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