"Against whom" vs "Whom against"
Solution 1:
Grammatically correct are: "Against whom are you playing?" (in the very formal English), "Whom are you playing against?.
These questions derive from statements: "He is the man against whom I am playing", "He is the man whom (or who) I am playing against". "Whom" is a complement of a preposition "against". A preposition can precede its complement or be moved to the end-position.