Aws plays a solitaire game on a fifty-two card deck: whenever two cards of the same color are adjacent, he can remove them. Aws wins the game if he removes all the cards. If Aws starts with the cards in a random order, what is the probability for him to win?
@arkanm: the problem statement says that whenever two cards of the same color are adjacent, they can be removed; you discuss a totally different version where two cards of different color can be removed.
I think the idea is that we have cards in two colors - black and red.So noticing that in every move we take a card that has been on an even position and a card that has been on an odd position (the card on the top is on the first position and so on) so a necessary condition is that we have 13 black cards on odd positions and 13 black cards on even positions. It is not hard to see that this allows us to take a couple of black cards and then a couple of red ones and so on.So that is why the answer seems to be $\frac{\binom{26}{13}^2}{\binom{52}{26}}$