I'm quite happy with the input of Ed and Likesforests, who force me to look deeper into matters. I'm investigating the general laws of the endgame and the parameters that play a role. That bears a suspect similarity with creating a few rules of thumb in order to get rid of some serious endgame study. But belief me, that's not what I'm after. So please don't be afraid that I shut down my mind while following ridgid rules.
You have to know the rules first before you can break them
I (the computer, that is) analyzed the following endgames with the aid of the Nalimov endgame tablebases. Only the first diagram has a forced win. All the other diagrams are drawn. White to move in all diagrams.
Forced win for white
If you think away all the pieces and the kings, it is a simple promotion.
If you add the kings it is a not so easy forced win.
If you add the kings and two minor pieces black has difficulty to hold the draw.
But it is a draw.
If you add the kings and two rooks it is an easy draw.
If you add the kings and two queens it is an easy draw.
This suggest that the more powerfull the pieces are the more difficult it is to promote the extra pawn. I purposefully placed the pawns on their initial squares far away from promotion and the pieces on as inactive as possible squares. Maybe when you place the white pawns more forward and/or the white pieces and king on more active squares a forced win with pieces is possible.
All this seems to suggest a hierarchy in trades: the most powerfull pieces first. The problem in the positions above is that you cannot force the pieces to trade since they ar too volatile.
The Curse of the Top Seed
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