Don't ever say science never did anything for you: Chinese researchers have published a paper tracking player behavior over tens of thousands of games of Rock-Paper-Scissors, information that provides an optimal strategy for winning the game. Unsurprisingly, players don't choose their throws randomly. Instead, they choose their throws in very predictable ways.
Via the BBC, the upshot is this: When a player wins a game, he or she is slightly more likely to play the same action on the next throw. When a player loses, they are slightly more likely to move to the next action in the sequence, in the order of the game's name.
So for example, you throw rock. Your opponent throws paper and wins. For the next throw, your opponent has a slightly more than one-in-three chance of repeating paper. So throw scissors for your best chance at getting back that point.
Let's say you throw rock, while your opponent throws scissors and loses. They are more likely to move to the next action—in this case rock. So when you win, you ought to cycle as well, and throw down that paper.
This is obviously easier said than done in the heat of battle, and only bears out over a long series. If you need a quick-and-dirty tip to take best-out-of-three for shotgun, just know that male players tend to throw rock the most often, followed by paper and scissors. (Because of the name of the game, or because those actions require increasingly physical action from the wind-up, I don't know.) Force the action with a quick count that doesn't give your opponent time to strategize, and throw paper.
(Obviously, no strategy is foolproof. But these seem sounder than relying on the metaphysical aspects of each action ["scissors represent aggression that is controlled, contained, re-channeled into something constructive"] spelled out on the World RPS Society website.)