It depends on what your opponent knows. Let’s first assume that neither player knows anything about the statistics or analysis of RPS. (Yeah, RPS is not only an accepted acronym, there are even RPS tournaments. Wowzies.) A and B are innocent players, but we want to give A an advantage. The new study says that, unbeknownst to the players, rock is the most popular move. That means ignorant B will throw more rock than average, so A can win by throwing more paper against it. So we should whisper into A’s ear that he should throw more paper. But what if B has read about this study? His “beknownst” state has flipped to true. Then we expect B to favor paper, so in this case we instruct A to favor scissors.