Repost: Unbeatable Hand

[LetYouDown]

I asked this question before and it entails either a "key" that I'm overlooking or a fair amount of computation to solve. A computer could probably give a really close approximation in several million runs, but I don't feel like writing the program. Just curious if anyone has any thoughts or has seen this solved somewhere.

You are dealt two random cards. A flop, turn and river are presented. What are the odds that you will be guaranteed at least a chop (i.e. A-K qualifies on an A-A-K-7-2 board...as does a board of As-Ks-Qs-Js-10s, regardless of your hole cards)?