Im not very familiar with this enviroment. But maybe CAPTCHA would help stop automated robots. You could also generate statistics for your users (games won/lost/average speed to move, etc). The first movements should be fast, but later on the movements should be slower as complexity increases. so you can highlight cheaters, monitor them and maybe ban their accounts as Wikipedia does with some editors. You could even make a point based system as stackoverflow does, to whitelist known good/clean players.
