[Ygorl]

Graeme, I read it was 95%.
Tauren, even just using rand() is pretty damn good. It's not perfect; if you look closely, you can tease out a little bit of structure from it... But it's nothing that you'd notice by playing a game.
What IS noteworthy is the human brain's ability to find structure and pattern... even when it's not there, or when it's there only by chance. Once we've convinced ourselves it's there, another one of our great skills is disregarding evidence to the contrary.
To make it concrete: there's an enormous amount of variability and complexity in Dominions (and, to some extent, most video games). Just by chance, sometimes things that look like patterns emerge (just like, if you flip a coin long enough, you'll see a run of ten heads; if you flip a thousand coins, you'll probably see such a run pretty frequently). Those tend to stand out, and we look for them. When we see them again, the tendency is to say "See? This isn't random!", while missing (because they're not salient) all the times we could have seen them but didn't.