New And Improved Wallet Game

[Jazza]

there was a post a little while ago about a game called wallet, which got me thinking about the game and the best way to play it

so here are the rules: you and an opponent choose how much money to put in your wallet, when you both have done this you put your wallets on the table, and the person who's wallet has the most money gets his money doubled by the loser (this was different in my other goofed up thread)

you both have infinite bankrolls, but have to choose a finite non-zero amount of money

so what strategy can you use to guarantee a minimum EV of 0?

also, i will create a contest for those who wish to enter:

everyone PM's me their prefered strategy (in the form of a probability distribution function), and after say 3 days i will see who's strategy is best overall, by having a round robin tournament between all participents

2 points for a win, 1 for a tie, and 0 for a loss

most total points wins

one thing to note is that the best strategy for the contest may not be the strategy that guarantees a minimum EV of 0

and btw i have tried to work out the answer (to avoid further embarrisment

[Jazza]

upon further thought i'm not sure there is a strategy that guarantees a minimum EV of 0, however there are strategies that beat the strategy of picking one number no matter what the number is (as long as the number is finite)

but this doesn't have to halt the contest

[kyro]

call me stupid but i don't see how this is any different from the first game. i choose a bazillion. oh you choose a bazillion and one? damn.

[Jazza]

allrighty i'll bust out with a strategy to beat all these pick a number strategies

my probability distribution function p(x) is:

0 if x<1
1/x^2 if x>=1

according to my calculations, no matter how large a number you choose, this strategy will win with a positive infinite EV

[mostsmooth]

[ QUOTE ]
allrighty i'll bust out with a strategy to beat all these pick a number strategies

my probability distribution function p(x) is:

0 if x<1
1/x^2 if x>=1

according to my calculations, no matter how large a number you choose, this strategy will win with a positive infinite EV

[/ QUOTE ]
i agree with kyro
this game appears equally as stupid as the first game

[kyro]

ok, i still pick a bazillion. you still lose.

[mostsmooth]

[ QUOTE ]
allrighty i'll bust out with a strategy to beat all these pick a number strategies

my probability distribution function p(x) is:

0 if x<1
1/x^2 if x>=1

according to my calculations, no matter how large a number you choose, this strategy will win with a positive infinite EV

[/ QUOTE ]
and wheres the strategy? is it hidden ? (im not that good at math)

[kyro]

[ QUOTE ]
[ QUOTE ]
allrighty i'll bust out with a strategy to beat all these pick a number strategies

my probability distribution function p(x) is:

0 if x<1
1/x^2 if x>=1

according to my calculations, no matter how large a number you choose, this strategy will win with a positive infinite EV

[/ QUOTE ]
and wheres the strategy? is it hidden ? (im not that good at math)

[/ QUOTE ]

I think he's trying to apply a probability distribution to an infinite range which is really quite silly.

[Jazza]

[ QUOTE ]
I think he's trying to apply a probability distribution to an infinite range which is really quite silly.

[/ QUOTE ]

if you're talking about the fact that the probability density function is non-zero on the interval [1,infinity) why is this silly?

and according to my calculations if you picked a bazzilion you would lose to this strategy on average

[kyro]

Fine, humor me. Pick a random number using your method.