Flowing Data posted about the NYT Rock, Paper, Scissors article, and while I work for the company that works hard to crush the humans in competitive games, there is no way a machine is going to be me at RPS**, even with a significant amount of training, because I'm learning about it while it's learning about me.  Results after 11 shakes against the expert machine below:

After snookering it rounds 4 and 5, I was impressed that it learned enough to go for paper instead of rock, and then to go for paper again, and then for scissors, and then to actually have the gall to get me in round 9.  I'm fairly confident I could stay slightly ahead of the machine (until mental exhaustion hit, which of course wouldn't be a problem for the machine), but I don't think it would be by much.