In the experiment, Zhijian noticed that winning players tended to stick with their winning strategy, while losers tended to switch to the next strategy in the sequence of rock-paper-scissors, following, what he calls, “persistent cyclic flows.”
Here's how it works in practice: Player A and Player B both start by using random strategies. If Player A uses rock and Player B uses paper, Player A loses. In the next round, Player A can assume that Player B will use paper again and should therefore use scissors to win. In the round after that, because Player B lost, Player A can assume that Player B will use the next strategy in the sequence — scissors — and Player A should then use rock, thus winning again.
If you take the game on a theoretical level, the most mathematically sound way to play Rock-Paper-Scissors is by choosing your strategy at random. Because there are three outcomes — a win, a loss, or a tie — and each strategy has one other strategy that it can beat and one other strategy that can beat it, and we don’t care what strategy we win with, it makes the most sense to pick paper exactly 1/3 of the time, rock 1/3 of the time, and scissors 1/3 of the time. This is called the game's Nash equilibrium.