Gambler's ruin problem

Posted by XIPP on Oct 08, 2013; 2:10am
URL: http://discussion-forum.276.s1.nabble.com/Gambler-s-ruin-problem-tp7584096.html

Question from DeGroot:

Consider the following three different possible conditions in the gambler’s ruin problem: (a) The initial fortune of gambler A is two dollars, and the initial fortune of gambler B is one dollar. (b) The initial fortune of gambler A is 20 dollars, and the initial fortune of gambler B is 10 dollars. (c) The initial fortune of gambler A is 200 dollars, and the initial fortune of gambler B is 100 dollars. Suppose that p<1/2. For which of these three conditions is there the greatest probability that gambler A will win the initial fortune of gambler B before he loses his own initial fortune?


I know the answer is condition (a), but how is answer obtained ?
Please explain.