One thing that I find particularly interesting about Yury Shulman’s Chess: Lessons From a Grandmaster is the series of “wolf and sheep” mini-games presented along with the basic information about how each piece moves. It provides an elegant (if not entirely scientific) illustration of why a bishop is worth 3 points, a rook 5 and a queen 9 in the traditional estimation of material.
In reading material on endgame play, I’ve seen a few references to the king’s being worth roughly 4 points in its capacity as an offensive piece – not that the king can be traded, but that its power is slightly greater than that of any minor piece, slightly less than the rook.
What I’m wondering is whether a similar “wolf and sheep” scenario, pitting a king on its starting square against four pawns on theirs, would be an even fight, and whether the pawns’ being connected or not would make a difference. Is this a question that’s reducible to fundamental endgame principles or the sort of thing that would have to be tested by trial and error? To put it another way: Knowing at what point a king can no longer stop the advance of n connected pawns, what square/rank must the king reach in order to have a chance of intercepting/capturing the “sheep,” can he do it against four, and is four the greatest number he can do it against?
The King cannot stop 4 pawns that are grouped together along a rank. If the pawns are split two and two, the King can stop one pair but not the other from marching forward. Pawns that are isolated are vulnerable, but if they are far enough apart - 3 or 4 files, or far enough advanced, then the King cannot stop them all.
A King may stop 3 pawns that are grouped together, but it depends on how advanced the pawns are and whether a favorable zugswang for the King is possible.
This is a fun exercise to use with students to show them the powers of the King and the strength of pawns working together in pairs and arrays. It is sort of like Space Invaders; you have to keep any alien pawn from “landing.”
That is interesting. The permutations of the position is astonomical. But, it might be curious to have that as an endgame tablebase. I know an 8 piece ending would take an enormous chunk of hard drive space, and not sure how long it would take to calculate. -I surmise it would take some sort of cluster with a large amount of ram and possible even a bank of hard drives to pull it off. As far as I know, all the 7 piece endings are non-pawn endings. -Or at least, I have yet to see a Namilov 7 piece position with any pawns on it.
In any event, from what I understand, engines are now at the point in which the more common 3-4-5-6 piece nalimov tables give then little to no elo improvement. Thus is the march of the raw speed of computers. (Not withstanding that Corr GM’s would say engines are still not very good at endings.)
Of course, Nalimov tables can’t underpromote, as far as I know. That alone might make for some interesting “blind spots” in thier analysis.
In fact, recently I was playing a game in which I underpromoted to a knight.
I always wondered if he was known as a Szen-master? I think he was, because I’ve heard that when he worked as a hot-dog vendor someone walked up to him and said “Make me one with everything.”
But that graphic appears to have five pawns in it.
Let me just nitpick the rules of this mini-game a bit. Does the player with the pawns win when he checkmates the opponent, or when he queens, or when he queens without the queen being immediately captured, or – ? These are not equivalent, for one because of stalemate, for another because lone Q cannot checkmate lone K. Question 2: Is underpromotion permitted?
In wolf and sheep, the wolf (the king) wins by capturing all the opposing pawns, while the sheep (the pawns) win by getting just one pawn to the promotion rank. The sheep player has no king.
Yikes! That looks like the sort of position you and I might have gotten into. But if we had, I’d surely remember it. Kb2 wins, Kc1 only draws.
It must be nice to have reached, in a tournament, such a pure problem-like position (even if from the losing end). I have long fantasized about actually achieving that K+R+R vs K+R position I keep inflicting on everybody as a puzzle.
After Kc1 they drew. Better for black was
Kc1 c3
d7+ Kxd7
f7 b2+ (the move Bill missed)
Kxc2 Ke7
P.S. I was directing and this was the final game in the section with mutual extreme time pressure. When I got to the board the K was on d2 and the black pawns were on b4, c4 and c5. It went … c3+, Kc2 (Kd3 wins more easily) c4, Kc1 (Kb1 wins more easily) b3, Kb1 c2+ (if the K was already on c1 after black’s b3 then it wouldn’t be able to move to the losing square) and then we reach Bill’s position.
1.Kc1?? (keep in mind that this was a time scramble) actually loses! And even though I won, it wasn’t until 15 minutes after the game was over that I realized what had happened.
