The "I'm feeling lucky" button on Google. What's the deal with it?

I can say that I know what the function of the "I'm feeling lucky" button on Google's homepage is, and that's more than most people. It seems like there are a lot of people who know that it exists, seeing as how it's one of the most prominent objects on the world's most popular search engine, but don't know quite what it does. They're programmed not to get sidetracked on their quest for instant gratification that is the Google search.
So what does this mysterious button do? It's a lot simpler than you might think. It just sends you directly to the whichever page ranks #1 in the results for whatever term you entered in for your search. From a user-standpoint, there's no use for this button other than providing a bit of instant playful fun - sort of like the Magic 8 Balls that will give you an answer to whatever you ask it. If you're going to Google's homepage to conduct a search hoping to find that thing that you're looking for as most people do when they go to Google.com, there is absolutely no reason why you would press this button.

So then why does Google still keep it there? I can really think of only one - for branding purposes. In line with their logo, they want searching to seem fun and enjoyable, and not some serious tool used only by emotionless workoholic drones for business purposes. "Hey, Googling is fun. You can even make it a game if you'd like," it appears to call.

And there's nothing wrong with that.