Is there a website on game design?

I would start with Game Theory.
http://en.wikipedia.org/wiki/Game_theory

and math, lots and lots of math.

Also, there’s the experimental gameplay project: http://www.experimentalgameplay.com/

but—are you looking to make card games, dice games, computer games, board games?

I’m sorry, computer games. Like NASCAR racing, grand theft auto, football, etc.

Most game development sites are about how to program games rather than how to design them. There are many sites out there.

Which kind of games? For computer games, you could browse through gamasutra.com. For board games I’d suggest looking through the boardgamegeek.com forums. For roleplaying games, try rpg.net and their game design forums.

You should check out Pangea Software’s free book about Game Development (if you use Mac)

This probably isn’t what your looking for, but I enjoy creating games on it. http://www.sploder.com/free-game-creator.php

It’s an enourmous topic, so not really, no. However, I am a pretty experienced game developer, and I can tell you that starting from scratch on my first big project was really tough. Before you even start, immediately decide how much time you can put into it. If the answer is ‘not much,’ it might not be your thing. If you can give time, here’s what you’ll need to do:
Learn a programming language (reccomend C++ very strongly) from a book or course, or learn online. Then, buy some more specific books on game theory, game engines (that’s the BIG one), and rendering vector fields. Check out some open source games, see how they’re layed out. Look at lots of code. TONS of code. Read it and immerse your life and soul into it. Be ready to fight or die to finish that game, and keep your head above the water.

So, no.
No website.