Listen, lad. I built this kingdom up from nothing. When I started here, all there was was swamp. Other kings said I was daft to build a castle on a swamp, but I built it all the same, just to show 'em. It sank into the swamp. So, I built a second one. That sank into the swamp. So, I built a third one. That burned down, fell over, then sank into the swamp, but the fourth one… stayed up! And that's what you're gonna get, lad: the strongest castle in these islands.

Note the square towers. I can't tell for sure from the pictures, but the walls look like they are think enough for a cannonball or trebuchet to knock over. In the 13th century the above were just starting to arrive in battle and so square was easier to build and good enough, but soon either thicker (read expensive!) or round walls would be needed.