It's not a set number though, from the start of the level system, antag affinity was always set to 10% of the total level up requirement. XP needed to level up will naturally need larger amounts as your level goes up too, but it does eventually cap out. 1 or 2 games should indeed be plenty, depending on win/loss, but back when i cared about changing to antag affinity in the fewest possible games, I always bought a 1.5 booster before antagging. It would guarantee I got the affinity I needed, win or lose, and that booster is priced enough that you can make that gold back in about as many games as it gives the boost for.