#1:

Inspect all of your opponent's moves closely. If you suspect that they use a pattern (such as SPRSPR or SSPPRR) pick the option that will beat it.

#2:

Look at your moves. If it looks like YOU use a pattern, then assume your opponent sees this and move accordingly. For example, if you, by coincidence, have played SSPPR, your opponent will expect you to play rock and will play paper. Play scissors and you might catch them off-guard. Every point counts.

I don't have much experience with RPS games with more than one opponent, but I think the second strategy could really help in those situations, when it's hard to predict everybody's moves.

There is strategy to RPS--not just luck. But good luck anyway!