Fat Models, Skinny Controllers | Where should I put this logic?

I have an old web-game that I'm overhauling completely. The game was not designed with a MVC architecture, so I'm laboring over how to separate the logic as I rebuild it in cakePHP.

In this application, users create and train fighting characters, and pit those characters against one another in combat. Combat consists of a script that:

# loops through many rounds
# determines what the