It also helps that we invite the top 10 users who achieve the highest score everyday so that people have a goal to reach to get the invite. And of course, the Facebook share button helps with spreading the word.
---edit---
Here's a pic of our old landing page http://i.imgur.com/ZhURi.png
It was pretty straight forward, full size image in the background with a simple Request Invitation button in the middle. Hope that helps.
In our last HN post, a reader named zem had commented that they didn't like the 3-invite system. http://news.ycombinator.com/item?id=3194012 (click parent to see the original post). As i mentioned earlier, we saw it as pretty standard practice and hadn't given it an extra thought when we implemented it, but the comment sparked the question, how could we make beta invites more engaging when just about every other company out there is doing the same thing.
Edit: and now myself. I had accidentally typed the wrong id.
I'm a programmer. I always have dozens of apps running. The point was, it's silly that you can't smoothly translate a few images at a mere 30 Hz with plenty of CPU power to spare.
If you do: $('div.ducks').mousedown(); in the developer console it's pretty hilarious.