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.
White to move.
- 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