Most of the existing AI bots which can play games use deep search from possible space and choose the best move. This is done by most of the chess, Go, Tic-Tac-Toe, etc bots.
However, there has been a recent breakthrough where (deep)neural nets with deep search techniques like monte-carlo search, etc; which might be more human-like and demonstrate a much more complex game behaviour than the above bots. One such example is the Google's Alpha-Go bot.