Without looking, peeking, or even cheating, you will be able to figure out who will win in a virtual game of rock-paper-scissors.
Method: This is a brilliant trick developed by Robert Neale and can be found in his book "Tricks of the Imagination". Start by grabbing three markers to represent the players (in this episode, Brian used three different colors of sweetener packets). Next, grab three items to represent the paper, rock, and scissors (in a pinch, you can use scraps of paper with names of each player or item written on them).
Lay out three players in a row, with a weapon in front of each of them. As explained in the video, set them up in a configuration wherein Red beats White, White beats Blue, and Blue beats Red. Now, in your mind, picture the colors/players arranged in a circle, such that the "circle of victory" moves clockwise (with red beating white beating blue).
Now, as strange as it seems, any one swap of two weapons OR swap of two players (no matter which ones) will cause that imaginary "circle of victory" to change directions and go counter-clockwise. In other words, after making just one change (of any type), blue will then beat white, and white will beat red. Make another change (of any type), and the circle goes back to clockwise.
With this in mind, you can know at all times which player will win, no matter what changes have been made, as long as you know HOW MANY changes have been made.
Watch the video for a more detailed explanation, but remember when performing this, to start small and get bigger. Start by first having your volunteer change the weapons. Next, have them move some of the players. Finally, allow them to make changes both to the weapons AND to the players, and finish with the big reveal of All three victors.