1+2 is an exception, it gives 1+0
"obviously games with zero initial time (like 0+1 or 0+2) cannot be berserked.
Because the clock would then be 0+0. Even hiimgosu can't win that. I think."
Of course it can. Instead of getting 0+2, you get 0+1 etc. :-)
Who will berserk in this conditions ?? :-(
The experienced player can read faster the position. No insreament is not a big deal for her. On the other side the weaker player is searching for a good move after the opponent's move, always need some increament [the more the better for the endgame (dignity)].
