The correct answer is rock. The reason you don't choose scissors is because you didn't know that your opponent was going to use paper. If you did the situation would be 100% paper 0% rock/scissors. Saying that you should have thrown scissors is the same as saying to always play the winning lottery numbers. The result that happens isn't available when you make the decision, thus you can't use that to determine what you should have done. This relates to fighting games when you're trying to predict what your opponent is going to do. Saying you simply should have done whatever counters what your opponent did is retarded. If that's the case you should just say you should throw out a random dp, super, ex, or whatever you have every time your opponent presses a button. Anyone who knows what a dp, super, or ex is knows that that doesn't work. When figuring out what you should have done you need to analyze what information you have on what your opponent might do, such as if they reversal on about 80% of wakeups you should be baiting reversals, even if your opponent doesn't do one baiting it is still what you should do. You predict what your opponent is going to do, run a quick risk/reward formula in your head, and act accordingly. In doing random dps you probably need to be correct about 90% of the time for it to be worthwhile, although this is just a general guesstimate, the actual value varies greatly depending on the situation, 90% from a start of round neutral state sounds about right.
I didn't expect anyone to say to use scissors to be safe because it simply isn't true. Rock and scissors both lose 15% of the time, however rock wins more making it better even if not losing is your priority. I'm guessing it's just trolling but I wanted to include it because I don't rule out that there are people dumb enough to believe it.
What was said about the ideal way to play rps being 1/3 of each is true only if you have no idea what your opponent will do. If your opponent is either doing something other than 1/3 of each or is in some sort of pattern you should change to exploit the weakness. Playing 1/3 of each means you win half the time, assuming rethrow on ties. Similarly, if you're playing a fighting game and your opponent never reversals then doing the ideal of sometimes baiting and sometimes attacking is wrong. You should be attacking every time against this opponent.
For those interested, the best response to someone who is leaning outside of the ideal medium is doing the counter 100% of the time. If someone does rock 40%, paper 30%, and scissors 30% you will win the most by playing paper 100%. Then there are people who will say if you use paper 100% of the time your opponent will stop playing rock. Any intelligent opponent would however I present two counter arguments. One, many people are dumb. Two, if they do switch they aren't playing 40/30/30 anymore and thus your 100% paper counter no longer applies. You need to realize when your opponent switches. This is beginning to go past the point I wanted to bring up, but the next step is factoring in how much you should give up(aka purposely lose/not play perfectly/sandbag) to ensure that your opponent keeps playing their 40/30/30.