I ended up winning by a very large margin, and we talked a bit afterwards about why that happened. Andrew, it turns out, was trying to maximize his score each turn. He'd look at the board, figure out how to set up a big score, and go for it. On the other hand I was trying to maximize the difference between our scores. So I was taking care to not open up big plays for him, and to put low scoring boats where he wanted high scoring boats. And in the scoring phases I wasn't focusing on scoring big sectors for myself. Instead I was trying to take away his big scoring areas while keeping an eye on locking in my own big scoring areas for end game scoring.
It seems so obvious to me that if you want to win a 2 player game you need to look for ways to gain points on your opponent, not just score points for yourself. But I ended up playing an awful lot of 2 player games on Yucata with a lot of people and very few people seem to pay much attention to that at all. My record in 4 player games on the site was decent, but my record in 2 player games was really, really good. And I think the reason for that is I keep my eye out for 'blocking plays', where you make a move not to help yourself so much as to hurt your opponent. Sometimes these can be right in a 4 player game too, but they're almost always right in a 2 player game.
Blood Bowl also has opportunities for blocking plays, and I think one of the ways I really got better was when I was watching Sceadeau play a game and noticed him making a particular blocking play that I have since started calling 'operation look at the ball'.
Often the ball will end up on the ground near players of both teams. When this situation happens at the start of your turn most people seem to look for the way to maximize their chance at picking up the ball themselves. Do they want to knock down the opponent's guys around the ball? Push someone into the ball? Run in and take the big penalty to the pick-up roll? All 3 options tend to be pretty mediocre but one of them will be better than the others and people will try the one they like best. They end up completely ignoring another option which is to leave the ball sitting on the ground. Don't try to pick it up at all! Instead do what you can to put your opponent in a terrible spot on his next turn. Run more guys over beside the ball and just have them look at the ball. Maybe you'll have a better shot at the ball next turn with more guys in the area. More likely your opponent will end up taking a low percentage shot at the ball themselves and really give you a good play.
It's like in Snooker, where you don't have to try the bad shot yourself. Instead try to give your opponent no shot at all!