Long story short; By being both observant and unpredictable, you can play like an RPS pro.
1. Watch your opponent play others. Often, they will lean towards one of the choices (for example, rock). If you have a chance to watch them play before they play you, look for an overall pattern.
2. Know rookie tendencies. The World RPS Society claims rookie men tend to lead with rock. If you're playing a spontaneous game against a male rookie, there's an increased chance that his opening throw will be rock, so you'll want to go with paper. Why do men start with rock? Perhaps the clenched fist evokes power and makes guys feel tough. If you're playing a female rookie, however, keep in mind that competitive player Jason Simmons claims that women tend to start with scissors, so go with rock.
3. "Train" the rookie. If an inexperienced player asks you to repeat the rules, you can subconsciously influence them to pick a certain gesture by dropping subtle hints. Physically demonstrate the gesture you want them to play more than any other gesture, and make sure it's the last gesture they see as you explain how the game works.
4. Play paper against an experienced player. A non-rookie may know that throwing an initial rock is too predictable, because of the tendency for male rookies to do this. They'll probably use scissors or paper. Therefore, you should start off with scissors, as it'll beat their paper or at least tie with their scissors. If your opponent is an experienced woman, she may be familiar with the "scissors" stereotype and will likely throw either rock or paper - thus, your best bet is paper.
5. Look for a double run. If someone makes the same throw twice, they will not want to make that same throw the third time, because they don't want to seem predictable. You can use this information to your advantage. For instance, if someone throws paper twice, they'll probably throw either rock or scissors on their third gesture; use rock so that you can either win or draw.
6. Beat your last move. This only works if you have just won; inexperienced or frustrated players tend to subconsciously throw the move that just beat them, so you should throw a gesture that will beat your own last move. For example, if you just won with rock against their scissors, they might throw rock next, so you should be prepared with paper.
7. Use probability to your advantage. In competition play, it's been statistically observed that scissors is the least common gesture. If you're at a loss for what to throw, using paper will give you a slight advantage, as it's slightly less probable that your opponent will use scissors.
8. Watch and react. Keep your eyes on your opponent's hand just as the gesture is being thrown. Watch what shape they are forming their hand into. If you see them extending into the paper gesture, for instance, you may have a split second within the count to react accordingly with scissors. But, be careful when trying to see what your opponent is doing because it could lead to slow throwing, which is illegal in competitive play.
9. There is no substitute for practice. Roshambo "RPS" can be played online in either a tournament or heads-up match setting at various websites. Although you won't be able to study the physical gestures of your opponent, you will be able to observe game play patterns and habits faster online. You can even earn money while playing RPS online with Moola.
10. Beware of non-rookies. An experienced pro may use all of these strategies against you. They might fake you out by, say, using scissors predominantly as their first gesture and then all of a sudden using paper when you least expect it.
For more advance RPS stategies, this article would be a good start. Oh and by the way; The 2007 championship was won by Andrea Farina - the first woman World RPS champion. Congratulations to Andrea!
Sources 1, 2.