3 on 2

I ended up in a situation somewhat like this in one of my latest games and it got me thinking about 3 on 2 pawn endgames. Is this position always a draw or always a win, does it depend on who moves first? How different would the position have to be before we could say its always a draw or always a win?

I would be gratefull for anyone who spend some time educateing me.  

There are no road signs for you to read. Pawn endgames are pure calculation. Since with this pawn structure there is no way for black to force a passed pawn, it all comes down to whether the black king can outflank the white king. In this position he can't, so it's a draw. It's still worth playing on, because if white messes up (which is likely), there may be winning chances.

This one is a very close call. It's a draw with black to move but black wins when also pawn a2 starts on a3 or pawn b2 starts on b3. I didn't analyze it (would take hours) but asked the tablebase god