Suppose the following solitaire with a standard deck. I turn four cards visible on the board and on each turn, I remove those suits that appears more than once in the board. Then I fill the board such that it has four cards and repeat removing. I win the game if I can remove all 52 cards from the board and lose otherwise, i.e. when all cards are from different suit. What is the probability to win this game?
I guess we need some kind of generating polynomial but I'm not sure how to solve that kind of problems.