I have "beaten" it. Play initially like you would - typically a human would change his choice often. The network would learn from you and gain a lead of say 10 points. After this, if you pick something that gives you a win start sticking to it while it gives you a win. You will quickly regain the lost points and gain a small lead. This seems to work every time I try it. After 60 moves I always lead a bit. Btw, the game gets slow then.

Not sure a bigram or trigram model would not do better than the neural network.