I believe that the random thread should choose threads no older than one month, because we cannot reply, and that it should prioritize threads from today that we have not seen and go older and older, to increase activity on new threads and revive activity on older threads for users who like to click random, then once we've viewed all threads we haven't viewed it should go into true randomization. Sure, this is defeating 'random' but it's also a way to increase activity I believe.
Or perhaps this could lead to a new button all together..