A question for you math geeks....

[Daddys_Visa]

In the NVG thread there is a long discussion about whether poker is actually gambling. There are several subdiscussions in the thread, one of which I would like answered by you theoretical math types. I made the following statement which has been challenged, and while I intuitively believe it to be correct I cannot make a very articulate proof of it. I stated:

Every poker will eventually bust out if the following conditions are met:

1.) Every player plays for an infinite amount of time.
2.) There is an infinite amount of money available to be won in the poker community.

I believe this to be true regardless of the players edge in the game (assuming they are not 100% to win each hand), their bankroll, or the stakes they play.

Is this true?