I think many people would take exception with a statement that "Roll dice, move counter, get to the end first" type games require no thinking. Perhaps you've never played a match of Backgammon using the doubling cube. By playing multiple games and understanding the odds of any given position a good player can easily use the element of chance to his or her advantage. Personally, I think Backgammon is the best two player game, even better than Go or Chess precisely because of the element of chance which gives a beginner an opportunity to win any given game although they might lose the majority of games against a stronger player.

Gin Rummy is an excellent two player game with lots of strategy, but also has an element of chance. I think it's a mistake to assume that just because there's an element of chance that there's no strategy.

One two player only, pure strategy game that "feels" like a racing game (such as Senet, Backgammon, or Parcheesi) is Mancala. It's been a popular game for hundreds of years for a reason. Everyone I know seems to like it even if they don't get into the strategy of it, but it can be played on amore strategic plane, so that it's challenging for a "thinker". Very nice sets can be bought cheaply and your wife will enjoy the tactile elements.

Pirateer is an excellent two to four player game that plays very well as a two player game with the simple rule alteration of a single player controlling two fleets. You can control the element of luck with slight changes to the rules included in the set. The rules are very simple and the components are excellent, including a "gold" coin. The roll-up version includes a doubling cube to give it more of a Backgammon feel. Since it plays well with more players, you'll be able to play it with your kids or when you have visitors.

Carcassonne is an excellent game that can be played by only two people. It's a well-supported, well-regarded, expandable game with simple rules and an excellent balance of strategy and luck.

Sequence is a very popular game that can be played by as few as two people.Probably more on the luck side than you like, but there is definitely an element of strategy and it scales well to large groups.

Stratego is a pure strategy game that might play fast enough for your wife not to get board and still has a war game feel to it.

Scrabble is a hugely popular game in some sectors with lots of strategy and requiring lots of knowledge. Lots of women tend to like word games because they tend to be good at language skills. It plays very well as a two playergame, is available in lots of configurations, is well supported, and has an excellent tactile component.

Pente is a very interesting two player (or teams) game played on a Go board (and derived from Go Moku) where you have to make five in a row or five captures to win. This is not as trivial as it may sound. I have a glass set with colored beads that's beautiful, but you can find it in various configurations including a roll-up mat that's kind of nice. Again, it scales well to four players, it's well supported, has passed the test of time, and has an excellent tactile component. You could even buy a set of black and white stones and learn Go while you're at it, but I think your wife will prefer the simplicity of the rules for winning Pente and the strategy will still be deep enough to keep you interested for a while.

Finally, there are many good two player Domino games that vary in the ratio of luck to strategy. Most of the highly strategic Domino games such as 42 or Latin Tournament are four player games with a 6-6 set, but there are several good two player games with enough strategy to keep you interested. I would strongly recommend investing in a set of Dominoes if you don't have one already. Some Domino games are simple enough for kids to play and some, such as 42, are nearly as complicated as Bridge. Dominoes have been around a long time for a good reason. Check out the available sets and complete rules to many games at www.domi noes.com which is located here in Texas. Dominoes are versatile. The are available in a very wide price range from cheap to personalized professional sets. They can be passed on to your kids. They have passed the test of time. They have a great tactile component. And bigger sets scale well to large groups with games such as Chicken Foot or Mexican Train.