I've been playing RPS competitively with friends for a while... most commonly in the local pub where I play darts; I like to suggest a single-throw round of rock paper scissors to determine who shoots first in the dart match.
The first site mentioned here has an interesting examination of the "gambits," but in a single-throw competition those only are helpful if you come against the same opponents over time and they remember what moves you've made in the past (I try to do that, but I don't think many of my opponents do).
In the single-throw game, the most important tool is the bluff: simply look your opponent in the eyes before the throw and say, for example, "I'm going scissors." The effect is similar to that of a well-played gambit; your opponent is caught second guessing himself and has one more thing to worry about: would you really telegraph your move like that? Of course, like using gambits or like bluffing in poker, variety is the key.
It's the perfect setup for a dart match, since I strongly believe that game, too, is primarily "all in your head." Once you've manipulated your opponent through the RPS preliminary, you're completely in control in the bigger game that comes after.
I had one regular opponent who eventually began approaching our matches by pleading, "Please don't say anything!" He moved out of state recently, apparently unable to live with the pressure.
Offhand I'd say I've won over 75% of my RPS encounters. And some of the losses were quite intentional; just like bluffing in a group of regular poker players sometimes you want to lose, sometimes you intentionally misplay a hand, just to keep them off-balance.