Here is a good connection game, from the inventor of Grand Chess:
Havannah
It has very simple rules (so even backgammonplayers could play it ) and great depth. It feels a bit like 'GO' but with the advantage it has fewer moves, simpler rules and no 'counting dead groups'-problem.

If there is going to be a connection game, I think this one would be a very good choice.

You can try the game yourself by copying the board and 'floodfill' with black and white in your paint program (that's how I play the game with Mirjam).