From the web page:
A truly random game of rock-paper-scissors would result in a statistical tie with each player winning, tying and losing one-third of the time. However, people are not truly random and thus can be studied and analyzed. While this computer won’t win all rounds, over time it can exploit a person’s tendencies and patterns to gain an advantage over its opponent.
As Mingy Jongo said, it is really nearly impossible for humans to produce random series. So George’s strategy is not bad. But without analyzing what the other is doing, or not being able to do it because the other plays really random, one cannot hope effectively to beat the other in longer games of many rounds. So trying to find a pattern in the opponents moves is the only way to do better, even if it fails against a random player. See the contest, I linked before. I expect you to see that the best program at the moment will beat you when you do not use an external randomiser (like George did). The best program (bayes14) has already proven to do better against the other programs.
As additional funny story: a colleague of mine told me in his school days he faked a lot of absences in his ‘absence book’. The math teacher did a statistical analysis on it, and could show that the absences were faked.
In the program in the OP, the ‘veteran’ expects you to play as an average player. So your best chance is being not average. In novice mode the program analyses you. The better you can simulate a random series, the better you can do, but really beating the program, way from the 50/50 is then very difficult.