Three Cards, One Chance to Stop

Three cards carry three distinct numbers you know nothing about -- no range, no distribution. They are shuffled and placed face down, and you turn them over one at a time. After each card you must either stop on it or discard it permanently; if you discard the first two, you are stuck with the third.

You win only if the card you stop on is the largest of the three. You can compare the values you have seen, but the numbers themselves tell you nothing about what is still face down.

What is the best strategy, and what is your probability of winning? Beat the two obvious answers of $\tfrac{1}{3}$.