Anyone that thinks that RPS is in ANY WAY random chance is a fool.
Even if you think you're just going to go with whatever throw you think of at the last minute, there's a subconscious reason behind every throw you make, if not a conscious one.
There are many psychological strategies involved in RPS, even more than just psyching your opponent out - though, that is effective as well. In several games against me, Sean Foisy has said "I'm going to throw ____, are you ready?" and then thrown what he said he was going to throw. Then, the next time we played RPS, he'd say that again (with a different throw, of course) and then thrown something different.
That example is one of the more overt strategies used. Many subtle psychological hints can be used to manipulate your opponent's throws, and predictions based on what you know about a person can be used to help decide what you're going to throw.
Of course, you have to know what you're doing. One major key is that you must be comfortable with throwing on both the third (Rock, Paper, Scissors) and the fourth (Rock, Paper, Scissors, Shoot). Some people throw on the third, some throw on the fourth, and if you agree to throw on the one that you usually don't, problems arise. If you usually throw on the fourth and agree to throw on the third, you'll most likely throw rock, because your brain thinks that's what you're supposed to be doing for one more time. If you usually throw on the third and agree to throw on the fourth, you might not throw that fourth time, causing a do-over. Either way, it messes up your psychological strategies.
Yeah... RPS is a pretty complicated game, really.