You can do better than random after a while by starting to learn how to be "bizarre" in its terms, for example it seems to not expect lots of paper in a row. Anyway if you start to feel out its biases you can exploit that.
Rock-Paper-Scissors: You vs. the Computer
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OMG!!! This is like the most Awesome but Simple Artificial Intelligence ever. Give it a try its just Rock Paper Scissors, but you are facing a robot who decides with calculations and statistics almost equivalent to the human brain. You will surprise yourself.
The fact it has 200k very non random data makes it very deeply biased, since it is using such a simple algorithm. I was behind for the first couple hundred plays and then found a simple sequence that never lost. I bet you guys at hunch could make one that is nearly unbeatable, since your whole business is predicting people.
Quartz parchment shears! Go AI!
I recently tied someone at rock paper scissors at least 10 times in a row (not sure of the exact number since we only realized something amazing was happening half way in...) It made me want to cry with soul mating joy! :'(