How Would You Choose the Winning Number in This Game?

[kaleidoscope]

a group of 1000 players are asked to write a number greater than 0. the player who writes the lowest non-repeated number wins a prize.

how would you determine which number to pick?

 

[tauon]

case A: if it can be any "type" of number (if the game is not limited to natural numbers- which is what I assume to be the case) just go for an infinitesimal hyperreal infinitely close to 0 (non-standard analysis thingie). not many will think of that one, and besides there is an infinity of such numbers so the chances of 2 people picking the same number are rather low. :P

B: if the game is limited to natural numbers between 0 and 1000... hmmm, that's tricky- I'm not sure.
is there any probabilities and human psychology expert around?

EDIT:
... ooops, I wasn't quite paying attention... 1000 players must choose a positive number... not a number between 0 and 1000... well, I guess case A is a good choice then. :D

 

[Redbelly98]

If we can choose any positive real number, this is basically the same as trying to think of the largest number you possibly can, then take it's reciprocal.

This is interesting only if it is restricted to positive integers. Psychology is definitely involved, since you have to imagine what numbers the other 1000 might choose. I'm thinking I'd choose something fairly high to avoid repeating another's pick. Perhaps 63 or somewhere thereabouts?

It would be interesting to repeat this game a number of times and see what sort of distribution the numbers follow.

 

[zli034]

I like to argue that suppose a player chose numbers follow an exponential distribution. Positive skewed exponential mean incline to choose small number but not too small.

The 1000 chosen numbers is certainly an ordered finite set. Use binomial principle I can know the probability of X number of people chose numbers lower than me.