So you say you want to invent a casino game?
Casinos are in the business of making money. Players want to have fun while playing and feel that they have a chance to win. When coming up with a game idea, you can't lose sight of these two key components, but this is just the beginning of developing a game idea.
One of the most prolific inventors of all time, Roger Snow, loves to say that when inventing a game he is a slave to the math. When dealing with a deck of cards, most of the frequencies are out of your control. You have to deal with the hand you are dealt (pun intended) and learn to work with the math. Generally speaking, don't waste your time trying to pitch a game without having had the math done. The first question you are likely to be asked is "Who did the math?"
The next steps
I was very surprised when I got into this industry to find out that it shared a lot of similarities with the pharmaceutical industry. It is all about intellectual property (i.e. patents). If your game idea is not patentable or if someone already has a patent for it, you're wasting your time.
Once you are done with the inventing half, what can you do to get the game into the casino?