Maximize Red Marble Probability with Two Drawers

You have 100 marbles -- 50 red and 50 blue. You must distribute all 100 marbles between two drawers, subject to two constraints: no marbles left outside, and each drawer must contain at least one marble. Once the marbles are placed, you pick one of the two drawers uniformly at random, then draw one marble uniformly at random from that drawer. How should you distribute the marbles to maximize the probability of drawing a red marble? What is that maximum probability?