I got Minecraft to run decently for the first time in ages.
I decided to play on a friend's server.
I built my home underground. From there, I started a mine. My shaft is a square 3 blocks to a side.
I went down at least 20 blocks already. I have stairs.
I suspect I'll hit the bottom of the map in 2-3 days (assuming I don't play much).
I also suspect I'll hit the bottom of the map before I put a bed in my house, because I do stuff like that.