I wrote an entry about two years ago: http://www.rpscontest.com/entry/614005
The comment in the program is, of course, a joke. What I actually did was download every other bot on the site, pick out all the ones that made no calls to `random` and let a brute force search for a good constant run for a few days.
The trick is that random play wins about 50% of the time, and this hack, despite being totally deterministic, has play that is indistinguishable from random within the constraints of the contest unless specifically accounted for. For each other program that also has deterministic play, about half of all possible constants will win. Try enough constants and eventually you'll find one that wins against a moderate majority of the other entries.