[TomCollins]

Here's why it doesn't matter. You have no criteria for "best hand". Secondly, it is not transitive. You cannot stick hand ranks on a number line and expect since A > B, B > C, A > C. This greatly increases the complexity of the problem. It's very hard to produce a mathematically precise answer of a poorly defined problem. So there is no way to find a "median" of them. Suppose you did three samples, and the best hands were 4s 4c, Ad Kc, Jh Th. Which of these three is the median? Each lose to one and beat another heads up.

If you actually put up a mathematical percise definition of the problem, I'm willing to bet someone will simulate it.