Hi! I am wondering what is the expected return on earning an infinite sum of money which has an almost zero chance of occurrence - probability of, say, one in a trillion (but NOT zero). Will the expected return be still infinite? Thanks

Dig out your Introduction To Calculus book and reacquaint yourself with L^Hopital's Rule and other "limit as x approaches infinity" products and quotients.

E = p x W - (1-p)L where: p = probability of win ~ 0 W = infinity L = 0 plug in and you get: E = p x W If p is small but still finite , then E = infinity. As p goes to zero in the limit, E becomes an undefined quantity. This means it can be either 0 or infinity, as already assumed, or any other value in between depending on many other factors. The question is: when does E start becoming an undefined quantity? This is related to St Petersburg paradox. The paradox arises because of the use of infinity in a decision process. No natural decision process can involve infinity since the universe itself is not infinite. Drop infinity and you are ok. In this game your ticket will cost a lot of money.

thanks..but i do not understand why you think p the should go down to zero....it is a fairy small number but it is a fixed one..and infinity is also a "fixed" value - there is no need to approach it though a limit...

The simple question you should ask yourself is this -- is a fraction of infinity less than infinity? --------------------------------------- <i> That is whole, this is whole From the whole, the whole is subtracted When the whole is taken from the whole The whole still will remain â --Upanishad. </i>