Problem : Link
It's a game.Let’s say at the beginning of round i, Alice has a Taka (Currency of Bangladesh) and Bob has b Taka. and c is the minimum of a and b. Alice and Bob are equally likely to win the round. If Alice wins, she gets c Taka from Bob, otherwise Bob gets c Taka from her and go to the next round and so on. Game ends when one of them has 0(Zero) Taka and obviously the person with 0 taka loses.
The initial amount Alice has is a and the initial amount that Bob has is b, you have to find the probability that Alice is going to win and expected number of rounds the game is played.
My solution Idea: There are a situation when playing rounds , we found same position of (a,b) as started .This situation will come when min(a,b) will win the round.Every round the probability to win the round 0.5.
But my solution didn't work ,but why ?
Can anyone explain how to solution ?