Well first a little background.  Did you know RPS was also known as RPS.  OK that was easy.  But it is also known as Roshambo, Roshambow, Rochambeau (but funny enough not Sham WOW!).  See the complete history at the Straight Dope.

Now some people would think their odds of winning RPS would be 33% since there are 3 choices.  But you would be wrong since ties don’t count as a win or a loss but rather a do over (unless you play online or in Vegas where ties lose).  So therefore, conventional wisdom would say you have a 50% chance of winning and if the choices were truly random, that would be right.  However, much like with the toin coss there is the human element which can increase the odds.

According to my crack research, Rock is thrown 35% of the time, Paper 33% and Scissors 31%. 

 Now according to Graham Walker who actually wrote a book on the subject.  Here is your intial strategy:

1 – Rock is for Rookies
In RPS circles a common mantra is “Rock is for Rookies” because males have a tendency to lead with Rock on their opening throw. It has a lot to do with idea that Rock is perceived as “strong” and forceful”, so guys tend to fall back on it. Use this knowledge to take an easy first win by playing Paper. This tactic is best done in pedestrian matches against someone who doesn’t play that much and generally won’t work in tournament play.
2 – Scissors on First
The second step in the ‘Rock is for Rookies’ line of thinking is to play scissors as your opening move against a more experienced player. Since you know they won’t come out with rock (since it is too obvious), scissors is your obvious safe move to win against paper or stalemate to itself.

Now I disagree with Grahams strategy but then again I don’t belong to the World RPS Society.  I say whether you are playing an experienced player or a beginner, THROW Paper.  If a player is experienced and knows your experienced, he may assume you will already know of Grahams trick and you will throw Scissors.  Looking to beat you he is going to pick Rock but you have pulled the switch and won with paper. 

There endeth the lesson.