Capitalizing on Errors

Ok, to use one of the most basic scenarios. The optimal strategy in Rock Paper Scissors is to throw 1/3 of each in a completely random manner. Now let's say you are playing a long match against someone, and you suspect they actually throw 40% rock, 40% paper, and 20% scissors. To exploit this, you would throw more paper (and/or fewer rocks). What would you suggest as the best course of action to maximize the ability to capitalize on the misplay, and minimize your own vulnerability to being adjusted against?