In some circumstances a "random" button might be a nice thing to have, rather than a predictable mid-point, as it would encourage real users to sample different

In some circumstances a "random" button might be a nice thing to have, rather than a predictable mid-point, as it would encourage real users to sample different things from deep in the long tail. The crawler could also use this to find jumping off points. You could also then leave out the "last" option, and therefore you wouldn't need a "first" option to look symmetrical for human users.