Okay, there are plenty of places online with instructions on randomizing posts in WordPress; even WordPress tells how. But here's my version along with the code I used.
Basically, I randomized the loop, and this required replacing the standard loop like this:
Replace…
::CODECOLORER_BLOCK_1::
with…
::CODECOLORER_BLOCK_2::
That worked for me. (note: setup_postdata() prepares the $post array as if it had been part of a standard loop, and the code did not work without it)