Stacking the Urns

A game-show host hands you 50 gold tokens, 50 silver tokens, and two indistinguishable urns. You may split the 100 tokens between the urns however you like (every token must go in one of them). The host will then pick an urn uniformly at random and draw a single token from it, also uniformly at random. You win if the drawn token is gold. What allocation maximizes your winning probability, and what does that probability equal?