Trébuchet
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| White to move |
8/5ppp/3k4/3p4/3P4/8/2K2PPP/8 w - - 3 1
There is only one winning move for white. White must reach one of the key squares a5, b5 or c5. You approach the key squares. Black tries to stop you by opposition. Then the pawns on the kingside get in motion, until black is in zugzwang. Then you can elbow your way in.
I've commented before [7 JAN 2016] about Euwe & Hooper's method for determining distant Opposition in situations where there are blocked pawns (usually in the center area) and the Kings are NOT in direct Opposition. It can be tedious to try to calculate everything using “I go here, he goes there, . . .”. Once you have determined you have the Opposition, you have to find a way to outflank the enemy King.
ReplyDeleteThe usual “trick” is to head for the key square that is farthest from the enemy King. Make sure at each move that you don’t allow the enemy King to gain the Opposition.
FWIW, here's that comment again:
COMMENT
Another "solution" to just "seeing" the Opposition is found in Dr. Max Euwe and David Hooper's book A Guide To Chess Endings, pg. 5, Diagram 6A.
This is entirely a visual solution. I'm going to describe it in words, because I cannot embed a diagram in Blogger. (At least, I don't know how to do it in a comment.)
Remember those 16 groups of 4 squares I described in another comment, about how I learned to visualize the board in order to play blindfold chess? Well, this is a similar solution.
Place the following letters on the following squares:
"A" on a2
"B" on b2
"C" on a1
"D" on b1
Using this group of 4 squares as an example, duplicate the same lettering on all of the rest of the 4-square groups on the board.
Euwe's Rule:
If you can move to a square that has the same letter as the opposing King, you have the distant Opposition; otherwise, you don't!
Initially, it will take some "looking" in order to "see" the group around one King and the corresponding group around the other King. There are some "speed ups" available: if the Kings are on the same color (VISUAL!), whoever has to move loses the Opposition.
END COMMENT
That's a good trick! I didn't know that.
DeleteThere are two directions to follow that emerge. One is to get better in judging winning pawn structures by fiddling around with pawns and kings. The other direction is: how to find invasion moves.
ReplyDeleteBoth directions must be following in the long run. But I'm inclined to focus on invasion for now.
There are a coupe of things to be aware of when dealing with this type of position (given in the blog post).
DeleteFirst, getting and maintaining the Opposition is NOT the goal; it is merely a means to the goal. In the position given, it would be trivially “obvious” (using the Euwe-Hooper idea) to take the distant Opposition by playing 1. Kb2. Note that the resulting shortest distance between the two Kings is two Knight’s moves. That “Knight’s distance” pattern comes up over and over again.
Second, it is vitally important to gain the Opposition on the queenside before the exhaustion of moves on the kingside begins. In short, the Opposition must be maintained throughout the entire process. Interestingly, after the kingside pawn moves are exhausted, Black will then have to move a Knight’s distance (to one side or the other). White then must move a Knight’s distance in response. This is the essential invasion movement, “shouldering off” the opposing King.
If you think about it, you will see that the Trébuchet position also involves a Knight’s distance between the two Kings.
It seems somewhat “strange” that this “Knight’s distance” pattern recurs so often in so many different positions.
A spelling correction and addendum to the preceding comment.
DeleteThe first sentence in the preceding comment: “There are a coupe of things. . .” should read “There are a couple of things. . .”
The second paragraph should read:
First, getting and maintaining the Opposition is NOT the goal; it is merely a means to the goal. In the position given, it would be trivially “obvious” (using the Euwe-Hooper idea) to take the distant Opposition by playing 1. Kb2. [THIS WOULD BE WRONG! As you noted, going directly to outflanking {the farthest key square away from the enemy King} with 1. Kb3 is the only way for White to win.] Note that the resulting shortest distance between the two Kings [if White takes the Opposition immediately] is two Knight’s moves. That “Knight’s distance” pattern comes up over and over again.
I thought that analysis out the preceding night while trying to get to sleep, and failed to reproduce my thinking completely when I originally wrote the comment.
The “trick” of heading to the farthest key square away from the enemy King can be simply illustrated with the following position (from Silman’s Complete Endgame Course, among other references):
FEN: 7k/8/8/8/3P4/8/8/5K2 w - - 0 1
White can take the distant Opposition (following the Euwe-Hooper idea or any other way of determining distant Opposition; there are several alternative methods) by playing 1. Kf2 and trying to get in front of the d4-pawn by going around the right side of the pawn. The result will be a draw.
Why?
Because Black can reach two of the key squares (e5 and d5, from e6) in time to prevent White from taking the Opposition in front of the pawn BUT cannot prevent White from reaching the farthest key square (c5). This is another example of why it is important to know when to go for the Opposition or to begin an immediate outflanking maneuver (heading toward the farthest key square away from the enemy King). Familiarity with the Réti idea that moving along the diagonal is just as fast (in terms of squares) as moving horizontally or vertically allows us to head for the farthest key square in the same amount of time, with an extra file between the two Kings. 1. Ke2 Kg7 2. Kd3 Kf6 3. Kc4 Ke6 [Black is holding the Opposition] 4. Kc5! [Moving to the square that is a Knight’s distance away from the enemy King] 4… Ke7 [What else? Another Knight’s distance!] 5. Kd5! [FINALLY! Regaining the Opposition with a winning position.
The rest, as they say, is just a matter of (hopefully, NOT) lack of technique.
Notice that the same process plays out in the blog post diagram. It is why 1. Kb2 (taking the distant Opposition) would be WRONG and only draw.
Thanks for the addendum. I thought Kb2 was a typo
DeleteA looked a bit deeper into it. What is the role of the six pawns on the kingside? When you fiddle them away it is a draw. The role of the six pawns is that they provide a spare tempo. Hence you can get the opposition by force when you need it.
Delete