An Idea for a Game-What Now?

I help my grandsons do their homework on Mondays and Wednesdays and make my own resources as I go along to suit what we are studying. I've come up with an idea for a game to help them with something and I'm wondering if it's good enough to go to market.

I know we've discussed how to publish books, get an invention off the ground etc but what about a game idea? Anybody done anything like this and what's the process?

Do I approach a games company? Are there games companies that specialise in particular games? Do I patent(?) the idea first then approach them? Do I make up a bodgie game first to show them the idea in practice.

Mine is an educational game (literacy/grammar) and would be suitable for schools and home tutors-once kids know the rules they can play amongst themselves. The general concept of the game can also be adapted into a maths game so I've actually got an idea for 2 games.
I'm assuming computer game here ... board games are more like books.

You made of money?

You could hire some freelancers to do it for you and pay upfront, then approach publishers or self-publish.

Approaching a company with an idea and expecting a slice of the profits? Zero chance.

Approaching a publisher expecting them to find a company who'll give you a slice of the profits? Less than zero chance.

Most schmucks with a game idea write it themselves ... we've been writing a game on and off for the last 3 years (admittedly it is a huge scope game and will probably take us the best part of a FULL 3 years) but keep getting sidetracked for very extended periods of time by renovating, other projects, babies ... basically other things that either are more likely to make money in the short term or keep you awake at night screaming so we don't get any work done even if we wanted to.

Of course this also depends heavily on what sort of game ...
same, same, try it, build it, sell over 500 copies/sets. and then your talking, untill then its just another , pie in the sky idea, ;)
This is an extremely competitive niche; you have about as much chance of a game manufacturer taking you on as you do of having your debut novel published. But hey, if JK Rowling had been put off by the statistics, she'd be a lot poorer. :)

I'd also be inclined to self-publish at least initially, provided you have the drive and ability to promote, promote, promote. Then if you decide you don't want the hassle, if you've been able to establish a decent sales history, you may have some chance of selling the concept to a games publisher for a decent amount.
Yeah, self publish and try and get some sales on a website or via schools.

Publishers are hell to deal with and they take most of your money. Computer game would be easier ;)