The comparison to chess is spot on. I used to play competitive chess when I was younger and I currently compete in bjj. One interesting book on the relationship between martial arts and chess is the Art of Learning http://www.amazon.com/Art-Learning-Journey-Optimal-Performan...

The author was a top ranked chess prodigy (remember the movie Looking for Bobby Fisher?) and now is a Marcelo Garcia student (one of the top bjj masters)

If you are getting into competitive martial arts, I highly recommend that you read The Art of Learning (http://www.amazon.com/Art-Learning-Journey-Optimal-Performan...).