Question re: maths and a pitch

Hi all, I'm working on developing a game and want to get an idea of how much math should be down on paper when working on a pitch, beyond just the basic combination calculations, odds for bets and RTP/house edge, etc. What other mathematical things should I have on paper before I think about pitching the idea for my game? Should i bother running the game on my own and writing down my results? I've already recorded about 250 hands on my own in order to get an idea of the win/push/loss ratio based on the rules of the game.

On a side note, are there firms that deal with game analysis? Will a prospective provider even look at a basic analysis (ie one that's not done by a stats major) or is that something that's absolutely required?

Cheers, looking forward to talking with everyone.

A good start would be to read everything in the Game Inventors Corner.