Guess the lowest integer

[Larimani]

I chose 31, which is very close to your guess.

I don't think you should chose an 'common number' such as 10 or 20 or even 13 because they are just too common to be unique... but then again if everyone thinks like this 10 is a good choice...

[SonofJen]

Reverse pyschology. Choose 1.

[Larimani]

Reverse reverse psychology. Don't chose 1.

I'll pick 1 and hope no one else is stupid enough to pick that.

Ah, right.
So, if the first 299 people are using the proper strategy then the likelyhood of the 300th person winning with any particular number is going to be equal. So, we can calculate the probability that each number should be chosen.

For example, the probability that a particular player should pick 1 is going to be 1 - the 299th root of 1 / 300 -- roughly .01885

[soko]

pick 999 and hope your the only one with a unique number

[UATrewqaz]

Your goal is to pick the lowest number nobody else will pick so the EV of a number comes from a simple fomula

Odds of it being lowests * Odds nobody else will pick it

The range of all possible entries is infinite (positive integers) however let's limit it to 1-300, due to the fact that nobody serious about winning would ever select a number above 300 due to the fact that there are only 300 entrants.

The numbers 150-300 all have a great chance of being unique, however i would say the odds of there existing a lower number selected that is unique is quite high, so we can rule them out as "good chances" (aka they will win occasionally, but very very rarely).

We now have positive numbers 1-150. I think we should group them into "classes"

1-5 (ultra low numbers) <- Stand no chance due to the fact someone will pick them

5-10 (near ultra low numbers) <- Once again a hot property, most likely will all be selected by other users

10-25 (low numbers) **** I think this is our sweet spot.

25-50 (marginal numbers)

50-100 (high numbers)

100-150 (very high numbers)

You would need to repeat the "contest" many many many times with groups of 300 people ot see where the "best" numbers are. I'm guessing 17 is a good number....

[pzhon]

What happens if there is no unique integer?

[zipppy]

I would pick 32, as every integer before it is a day that someone could be born on, and it is unlikely that someone was born in the year '32.

>>ZIP

[Larimani]

[ QUOTE ]
What happens if there is no unique integer?

[/ QUOTE ]

No winners are declared. However in a field of 300, I really think this possibility would be quite improbable.