I was trying to solve this problem on topcoder. The output for the problem is the probability that Jane wins the game, but my problem is that I think that the probabilty of each player to win the game is always 0.5 and that isn't correct according to the output of some given testcases in the problem. The reason of my thinking is that both players have the same number of turns and both of them have exactly the same choices to play. So I wonder if somebody could explain to me why the probabiltiy isn't always 0.5.