What's the entropy of smartphone "pattern passwords"? Through how many nodes do I have to go until I'm safe (say, a reasonable 42 bits of strength)?
You cannot reach 42 bits of entropy with a regular android unlock pattern. The 3x3 grid is limited to 389,112 distinct patterns, giving you an entropy of 18.57 bits. This is less than you might assume since a dot cannot be selected twice and you cannot skip intermediate dots on a straight line.
Additionally, research has shown that many actual patterns are predictable and in fact much less complex than they could be. For instance, a majority of users begin their pattern in one of the four corners.
BTW, some mods (e.g. Cyanogen mod) support bigger grid sizes but I personally find a truly random pattern harder to remember than an equivalent PIN code.