Connection is not a 'grand theme'. But Havannah is special because in playing it, humans do something they cannot evaluate in measurable terms! In resisting programmability, this simple game is as hard as a diamond.
Apart from the sunny side, human superiority over the machine, this raises an interesting question. What exactly do humans do when they play this game? One thing is sure: they think. And that's still a human prerogative.
The Zillions game machine, a program that can play hundreds of games, is very apt at chess variants and elimination games, but predictably it plays Havannah like a moron. This is no fault of this magnificent program and a specific havannah program wouldn't do much better.
Ironically it is the absence of a lot of things that makes Havannah so easy to understand for humans and so hard for computers:
Goals are very easy to understand, but very hard to implement in a program. Threats to win in two or three moves could be noticed, but many are irrelevant in a strategic sense and Havannah is decided on a strategical level.
Lately programs using the Monte Carlo method have made significant progress on smaller boards, and creeping upwards.
Havannah is a pencil and paper game: it can be played with two distinct markers and a pen for move numbers. Completed games are implicitly their own notation. The inventor has in the summer 2002 put €1000.- prize money on a program that can beat him one out of ten games on a base-10 board within the next decade. Several serious attempts are underway (not so much money driven).