Parametrize this!
.
.
Let's have a closer look at the endgame we studied lately. We found quite a few topics that need further investigation:
- With no pieces, the remaining pawnending was a win.
- With pieces, be it minor or heavy, the ending was drawn. On advice of Ed I have tested KNppp+KBpp on a wing in stead of the center, but that doesn't alter the outcome.
- Ed casted doubt on the accuracy of the computer which calculates the ending notouriously faulthy. He is right about that in the sense that I cannot say that the outcome is 100% proven. But different engines have calculated the position 30 ply deep with over 100 million tablebase hits. I am convinced. But I must admit I'm somewhat biassed since the outcome of the computer is according to my reasoning.
- Both Ed and Likesforests feel that white has great winning chances in practical play with N vs B. Are they one-eyed kings in the land where only patzers screw up this drawn ending?
- Both felt that R vs R was a clear draw. Why do patzers play this ending well?
- The fact that Ed made a difference between center pawns and wing pawns shows that he has access to some secret knowledge which I haven't.
- The relative difficulty for humans to keep the draw in a N vs B ending in comparison with the easy to draw R vs R is not shown in the figures the computer comes up with.
- Piece activity.
- Distance to the promotion squares.
- Amount of pawns.
Besides that there are parameters which interfere with general rules.
- Unexpected mates .
- Forced trade of pieces.
- Piece sacrifices.
- The rim of the board.
- Exact placement of the pawns.
Added piece activity on both sides tends to change the outcome from a win into a draw.
- ppp vs pp = easy win
- added K = not so easy win
- added K + minor pieces = quite difficult draw
- added K + heavy pieces = easy draw
Distance to the promotion squares.
Let's have a look at the following diagram.
diagram 1.
.
.
White to move.
Parameters:
- distance to promotion square: 1 tempo
- piece activity: 2 tempi
The white rook needs 2 tempi to perform een action.
Een action is one of the following:
- take possession of the promotion square.
- take possession of one of the squares between the pawn and the promotion square (not possible here).
- conquer the pawn.
Amount of pawns.
What is the role of more pawns? The pawns are standing abreast at their initial squares to avoid complications as much as possible. Kings on e1 and e8 to elimante piece activity. Just to get a general idea:
- p vs - = mate in 22
- pp vs p = mate in 23
- ppp vs pp = +10.73 and moving up at ply 27
- pppp vs ppp = +2.25 and moving up at ply 28
I don't really understand your post, will need to re-read.
ReplyDeleteBut that picture. LOL it's harsh!
Your conclusion that it's probably a good idea to exchange pawns when trying to win is contradicted by a famous maxim: "Trade pieces when ahead, trade pawns when behind."
ReplyDeleteIf you are a pawn down and trying to draw, in general your chances increase with every pawn trade, since 1 vs 0 pawns is often drawn with any piece configuration (of course the defender will try to avoid exchanging into a known LOSING theoretical position).
Conversely, the more pawns on the board the more winning chances. For example the general case of R + 4p vs R + 3p with all pawns on the same side (i.e. kingside) is a draw, while R + 5p vs R + 4p may be a draw but is trickier.
The computer sees the mate more easily when there are fewer pawns of course, but *How QUICKLY a winning position leads to mate* is a very different thing from *How LIKELY a position with that material distribution is to be winning*.
Basically more complexity usually means more winning chances, but simultaneously longer time required to win. The side trying to win should only exchange pawns when he can force a known winning position, or has some other very good reason (penetrate with the king, create a passed pawn, etc.).
"So the hierarchy of trades for the winning side becomes Q, R, BN, p. For the losing side it is either the other way around (p, BN, R, Q) or to avoid trades alltogether. Are there any maxims or rules of thumb that confirm or deny this?"
ReplyDeleteFine gives a set of maxims for the endgame at the end of _Basic Chess Endings_. One of them is (from memory): "When ahead in material, trade pieces but not Pawns. When behind, trade Pawns but not pieces." He also gives some advice for what particular endings are easiest to win or draw.
Re the "hierarchy of trades" maybe it's more useful to consider which pieces each side wants to REMAIN with. Aside from exchanging as many pawns as possible, the defender's first choice should be B vs B (opposite colors), then R vs R. After that I'm not sure, but B vs B (same) and Q vs Q can sometimes be difficult to win a pawn up.
ReplyDeletePawn endings are normally considered the most "winnable", followed by knight endings, so the attacking side should be happy to go for those positions unless they are known draws.
Ed,
ReplyDeletethanks, I have ordered Fine's book.
Stig,
ReplyDeletethe hierarchy suggests only to trade pawns after you trade all pieces. Which isn't necessarily in contradiction with "when ahead, trade pieces, not pawns", since there are no pieces.
*How QUICKLY a winning position leads to mate* is a very different thing from *How LIKELY a position with that material distribution is to be winning*.
You are quite right.
Right, Temposchlucker. I should have read more closely before I posted, sorry.
ReplyDeleteIn pawn endings I'm not sure how useful the guideline "it is a good idea to trade pawns in order to try to win" might be. Pawn endings (and the decision to enter them) are really all about calculation, sometimes extremely long and difficult, but still helped by known patterns and techniques of course. In a sense the moment the players exchange into a pawn ending the result of the game is already determined.
Also most of the well-known draws in pawn endings are with very reduced material (i.e. 0 vs 1 or 1 vs 2), so such a guideline would have frustratingly many exceptions, perhaps.