Splitting black and white balls between two urns

Your life depends on a draw. There are $50$ white balls, $50$ black balls and two empty urns, and you must place every ball into one urn or the other, in any split you like. Then, blindfolded, you choose one of the urns at random and pull out a single ball: white means you go free, black means execution. If you arrange the balls as well as possible, what is your probability of surviving?

$\tfrac{74}{99}$. Put one white ball alone in the first urn and the other $99$ balls ($49$ white, $50$ black) in the second. Then you survive with probability $\tfrac12\cdot1+\tfrac12\cdot\tfrac{49}{99}=\tfrac{74}{99}\approx 0.747$, which is as close as possible to the $\tfrac34$ ceiling of a sure urn plus a fair one.