So, it sounds like you're serious about this. The problem is that game software is typically so complex that no single person would be able to accurately estimate the costs of the project.
Ideally what you want to do is contact a game development studio and pitch your idea. Unfortunately, every game development studio I've worked at does not contract work out to individuals; we only contract out to companies larger than ourselves, and usually only for porting an existing game to a different platform (i.e. make Wii ports from 360 games, etc).
If such a company exists somewhere that I don't know about, the usual flow works like this:
- Contact a company and find out if they do contracting/outsourcing work.
- Get a lawyer.
- Both you and the company sign NDAs.
- You pitch the general idea to the company to see if they're interested at all.
- If they're not interested, find a new company and start over.
- If they're interested, they will ask you for much more detailed information about what you want in the game, and they will attempt to estimate costs.
- Form a legal contract with the company with the help of your lawyer. This includes things like: when/how much you will pay them (i.e. pay them set amounts on certain milestones), who owns the IP, who owns the technology, what happens if the contract needs to be changed, and what happens if the contract is terminated by you or them.
- Either the game is completed or not.