Hi cat,
I’m not sure if it makes much of a difference. One advantage of using relative links (i.e. games.html) instead of absolute links (http://www.site.com/games.html) is that you can check your website links offline while you’re building it. Just open the HTML file in your browser, and click on the links to make sure they work. If all your files are in the proper folder, then your links should work.
My preference is to use absolute links for everything. My goal was to have a consistent structure for all of my links. Since links to online casinos and other affiliate websites are absolute links, I decided to make the rest of my links absolute as well. Doing this adds a bit more code to the page, and I really don’t know if it does anything for the search engines. But, since I wanted everything to be clean and consistent, I had to take the absolute route.
Again, I don’t know if it’s necessarily “better” to do it this way, but I don’t think it would hurt either. I would be surprised if a search engine punished you for using absolute links to pages within your own site (someone please correct me if I’m wrong).
One other tip — if you do use absolute links, make sure you stay consistent with the prefix — i.e. don’t use http://www.site.com in one place and http://site.com in another place. Keep it consistent.
Hope that helps.