Remember when Carter said he didn't want to hurt Percy? He said he felt pretty bad for starting the fight so he started to explain but Percy just wanted to turn him into a Kane-flavored barbecue sandwich.
It's funny. Everyone is trashing Percy but when you actually read the books Percy would probably beat Carter. the first example is on Percy's wiki page. It says "he was able to disarm Luke, the most skilled swordsman at Camp Half-Blood for the last three hundred years, in a swordsmanship class with a complex maneuver he just learnt" Percy just did that move. now, I bet some people are going to say "that was just luck" but there's more. Percy has Superhuman Durabilityand Superhuman Strength etc. etc. Another thing is how Percy has been training for years and his abilities have amazingly improved. He can summon a fricking hurricane. Carter had to tie Percy up so he wouldn't be slaughtered. that is my case.