June 14th, 2007

Math Problem

Veloso sent this to me today.

You're in hell, and you're playing a gambling game where P is your odds of winning each wager. (Each wager pays even money, and you can only wager one unit at a time.) You have unlimited credit, so can play forever. You decide you'll quit playing if you ever become even one unit ahead Otherwise you're forced to play forever. What are the odds of being able to stop?

I eventually got the answer, but I had to rely on some guess work. Veloso actually proved it rigorously. I wish I were better trained in mathematics. Also I am not sure why you have to be in hell for the problem to work.