Originally posted by @moonbus
Hey Blue, I've had a few piece-vs-peeve situations myself.
PS I'm in favour of auto-draw when insufficient material to mate remains on the board.
Well, that's my point.
If either side has a rook, queein or pawn, then that side can mate. Not necessarily force mate against whatever the opponent still has, but nevertheless you can stumble into mate. None of those cases are, therefore, an auto-draw.
We're left with only minor pieces.
It is well-known that two bishops and bishop+knight can (painfully) force mate against a lone king, but any two minor pieces can get
mate against a blunderer. Not an auto-draw.
We're left with at most one minor piece each.
One minor piece vs. lone king and LK vs. LK can obviously not mate, so they're auto-draws.
Dubious cases left: minor piece vs. minor piece. With N vs. N or N vs. B it is possible to construct a corner mate. Again you have to be an idiot to get mated that way, but it's always possible. No auto-mate.
But now bishop against bishop. You have to get mated in a corner of the opponent's bishop. The king can block two escape squares. The third must be occupied by your own bishop. This is only possible if you have unequal bishops. A same-coloured bishop can only block the mate, not aid it.
Therefore: two lone kings, lone king versus king plus one minor piece, and king plus bishop versus king plus same-coloured
bishop should be automatic draws. Nothing else is.
(Except for things like blockades, but those are nearly impossible to detect automatically.)