So if there are two players playing a tile game where there are two sets of matching tiles $a_1, a_2, a_3$ and $b_1, b_2, b_3$, what would the optimal strategy be to maximize winning probability? Go first or second?
A turn consists of flipping over three of the cards to see if they match. If going first, then prob of winning is $1/6$? By going second, I can win $5/6$ of the time since I know that what he flipped over must be 2 from one set and 1 from another. Thus, flip any of the remaining three?