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        riddles >> medium >> Probability game
        
(Message started by: Grimbal on Sep 1^st, 2009, 9:16am)

Title: Probability game
Post by Grimbal on Sep 1^st, 2009, 9:16am

M people play a game to earn a prize.
Each person k selects secretly a number n[k].
After that, independently for each person, a random draw is made. It returns n[k] with probability 1/n[k] and 0 with probability 1-1/n[k].
The person with the highest result wins. If multiple people reach the maximum, they share the prize.

What is the best strategy? (i.e. how to maximize the earning expectancy).

(I don't know the answer myself. But it is related to a real-life problem)

Title: Re: Probability game
Post by SMQ on Sep 1^st, 2009, 9:37am

If everyone draws 0, does everyone win (prize split M ways) or does no one win (prize unawarded)? The answer appears to make a lagre difference to the strategy with M small.

--SMQ

Title: Re: Probability game
Post by Grimbal on Sep 1^st, 2009, 9:39am

Good remark. It would be split among all.