Thanks, this was great! I've been meaning to search for a good technical explanation like this for a while. This fit the bill perfectly.

I didn't realize that the mining process had a lottery-like nature to it. I always assumed that if you bother to mine then you are guaranteed to churn out coins. But I still don't quite get how this process scales to hundreds of thousands of people mining all over the world, as it seems like you could quickly end up with many many competing chains.