Offense equals defense

In Hex, good offense and good defense are entirely equivalent. If you complete a connection between your sides, then your opponent is prevented from completing theirs.

Conversely, if your opponent is prevented from completing a connection, then you must have completed yours (draws cannot occur in Hex). Furthermore, the only way to complete a connection is to prevent your opponent from making a connection and the only way to prevent your opponent from connecting is to complete your connection.

In a very real sense, you don't have to worry about whether you should play offensively or defensively since they are the same. The critical point to remember is that unless you are making a sequence of forcing plays, it is generally easier to think in terms of good defense than good offense regardless of whether you are currently winning or losing.

This point about thinking defensively should frequently be used with the strategy about the weakest link. Suppose for example that your opponent's most difficult connection to complete looks like the connection to the right edge of the board. Then you should look for good defensive moves that make it even more difficult for your opponent to connect up to the right edge. This is very sound strategy.