While my husband mostly dislikes Catan (too much luck for him and not enough strategy), he knows that I enjoy it so we play. Catan itself doesn’t work all that well as a two-player game. But recently we found The Rivals for Catan, which is a modified Catan made for two players (it even has expansions).
It’s a great variation with 1 flaw. Whoever gets one particular action card tends to win. Normally, when building a settlement, the resources you get are random. But with this over-powered card, you can go through the resources stack and pick the best resources with the best die-roll. It’s really gives an unfair advantage. I’m considering playing the game without this card in the deck.
Despite that, the two player game plays similar enough to Catan, but without it being so heavily luck based or irritating. A player rolls two dice, which determines what resources you gain that turn and what event happens. Events are: plentiful harvest (one resource of your choice), celebration (one resource for the one with the most skill), trade (one resource from your opponent if you have the trade advantage), brigand attack (lose all gold & wool if you have more than 7 resources), or an event (draw a card event).
Besides events, you can play action cards from your hand, build a variety of buildings or trade ships, hire heroes, buy settlements/roads/cities, draw new cards, and exchange cards with the stacks. Plenty to do.
While the dice rolling is luck based, there’s no getting cut off at the beginning like there is in Catan. Also, people start with equal opportunities. Much better balance to Rivals. There’s no trading resources with other players either. The built-in expansions in the box add quite a bit to the game, not to mention the two full expansions that bring more strategy and variance to the game.