Investigating the parameters
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.
diagram 1
Forced win for white
diagram 2
draw
diagram 3
draw
diagram 4
draw
diagram 5
draw
diagram 6
draw
diagram 7
draw
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.
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.
diagram 1
Forced win for white
diagram 2
draw
diagram 3
draw
diagram 4
draw
diagram 5
draw
diagram 6
draw
diagram 7
draw
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.
More helpful stuff here. I was always taught, 'When ahead, trade material, especially queens and rooks.' This was always explained by pointing out the proportion by which you are ahead (calculated as the ratio of your material count to his material count) gets higher as you trade major pieces.
ReplyDeleteBut your study in the post points out gives a more concrete reason such trades can help.
Interesting. Usually when considering 3P vs 2P endings, I think of all the pawns on one side, or pawns on both sides (both common in practice); all the pawns in the center is unusual.
ReplyDeleteI'd be surprised not to win the N vs. B ending with the extra Pawn, even with the Pawns in the center, and the Rook ending is a harder draw then with the pawns on one side. I think.
Also, I don't think that computers play these positions well even today, until tablebases are in sight. Are you having the computer analyze by itself? You might gain more insight if you played against it instead, for each side.
Believe me, if I thought you were rigid about it, I wouldn't bother commenting. I've given up on a few bloggers in the past because they couldn't be reached.