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I had to play over 250 rounds to start winning. Of course, I was cheating.
Here's a winning strategy,

setInterval(function(){Move(a[p1][c1][p2][c2][0] < a[p1][c1][p2][c2][1]?0:1)}, 100);

goo.gl/2BYAQI

I was winning after about 60 moves but then got bored and made too long of a string of consecutive ones and the computer caught up. This would be a much better game if I could play it with the keyboard, as I was having difficulty clicking accurately with my mouse (going very fast).
> This would be a much better game if I could play it with the keyboard

You can. Just press 0 or 1.

Sadly, that doesn't appear to work on my browser. FireFox 11.0.
Indeed, this implementation let you cheat: while the program tries to learn your behavior, you can learn the program's and outguess it. The random sequence should be provided blindly, and the program should process it a posteriori, for the subtitle to be relevant.