Two players, Player A goes first, Player B goes second, are playing Concentration game. Every cards face down, we have 2 green cards, 2 blue cards and 1 red card. On player's turn, she selects one card and turn it over, then select another card and turn it over. If they match, then she keeps those cards (called a set) and gets another turn. If they don't match, she turns the cards back over and another player goes.
My question is: If you are playing this game, is it better to go first or second by finding the following probabilities:
- Player A (first player) gets two sets and wins
- Player B (second player) gets two sets and wins
- Each player gets one set, then they are tie
For this first question, I have 5!/2!2!1! = 30 ways for player A to pick up the order of the cards, and there are two ways to get the sets consecutively: BBGGR, GGBBR, so P(A>=2) = 2/30
But I'm not sure how to solve for 2 and 3.