### Coin Toss Bankruptcy

Source: Mailed to me by Sudeep Kamath (EECS PhD Student, UC Berkeley, EE IITB 2008 Alumnus) Problem: Three people start with integer amounts a,b and c. In each round, each one tosses a fair coin. If not all faces are the same, the person with the different face gets a rupee from each of the other two. If all faces are the same, no money is exchanged. This process is repeated till one of them gets bankrupt. What is the expected number of rounds till the game ends? Related Problems: http://pratikpoddarcse.blogspot.com/2009/10/lets-say-keep-tossing-fair-coin-until.html http://pratikpoddarcse.blogspot.com/2010/11/source-credit-suisse-placement-test-at.html http://pratikpoddarcse.blogspot.com/2011/02/equal-heads-and-tail.html Update (15/03/2011): Hint: Given away by Sudeep. (* Define a martingale of the form Y_n=A_n*B_n*C_n + some other term (where A_n,B_n,C_n are the fortunes of the three players at time n). *) Solution: Posted by chera (Gaurav Sinha, IITK 1996