Re: [MLUG - DISCUSSION] fun math thing

["Jonathan King" <EMAIL:PROTECTED>]

On 6/1/06, Stephen Montgomery-Smith <EMAIL:PROTECTED> wrote:
> I similar event which is theoretically possible but has probability zero
> is to keep tossing a coin, and it never comes up with a head.

Yes, and this is the essence of the St. Petersburg Problem.

Imagine you could play a game where you flip a coin, and if it come up
heads on the first toss, you get a dollar.  With each additional head
you toss, the stake doubles, so that after a second head, you would
win $2, and after N consecutive heads in N tosses, 2^(N-1) dollars.
If you ever toss the coin and it comes up tails, the game ends and you
can claim your winnings.

It's easy to show that your expected winnings are infinite, so you
should be willing to pay an infinite amount of money to play the game,
certainly trillions of dollars would be more than fair.  And
yet...nobody in their right mind would do this.

Anyway, wikipedia does a fair job of explaining the problem here.

http://en.wikipedia.org/wiki/St._Petersburg_paradox

jking

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