[xeyownt]

Yeah, I don't know what my intuition was.

But the problem is symmetric, and even if pick a red, you end up with two reds and one blue, so not so much imbalanced.

And even if the mix becomes really imbalanced, say 7 red and one blue, picking the rarest color will have more effect than picking the most common one. So you could consider that the system tries to balance itself naturally, hence avoiding huge swings in some direction or the other.