A Subscriber Challenged Me To Explain This Position -Lasker-Reichhelm Position-Corresponding Squares
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- Опубліковано 31 лип 2022
- Explore the position yourself:
8/k7/3p4/p2P1p2/P2P1P2/8/8/K7 w - - 0 1
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Insane explanation. I really appreciate you showing the Wikipedia diagram, that really solidified the concept of corresponding squares
I was hoping 4 a "rule of thumb", i.e.; both Kings R on the same colour, etc. Just by luck I guessed the correct square, then probably would lose(as I'm newbie). I'm not going to memorize corespondents @ this point. Great vid, but I 4-got His name.
Oh, it's Nels...My bad
I think you did a good job of explaining the how and why but it was the diagram that provided the aha moment
Definitely vote for round 2
Nelson always tries to teach something new which is really important to know and so is a good person.
Who
I just have to admire the person or a group that came up with chess games rules cause chess is hard and a great master piece
Wait until you see the game of Go
Yes, I understand the explanation. As always you did a great job on explaining things so it is much easier to follow what's going on
this is exactly why opposion in king endgames is an important concept, just on a much more complicated level
Understood. Overall I now can see pattern in positions and how they evolve from your guidance. Before I saw your videos I knew arithmetic of game, now I can comprehend how function works. Started look for chess stuff for mind exercise, but it is fun now. Thanks for your work.
nelson u explained that complicated position perfectly, thank you for the effort u put into this video
super interesting concept of the corresponding squares and I felt that you explained pretty well what they are and how they work, the only thing I felt was missing is how to identify which squares are corresponding
Well a7 is a 2 and a1 is a 5.
@@jaideepshekhar4621 He meant in a live game, not one with a chart provided.
@@shanewells6853 That could be an upcoming video.
the same
That was super helpful. I hadn’t heard of corresponding squares before so absolutely would not have figured this out on my own. I get it now though, showing the diagram with the numbers is really cool!
The best explanation of the corresponding squares I have ever seen. Congratulation!
honestly, I would love to see the next quiz to be all about different positional concepts. This one particularly fascinated me and I believe that it'll be really fun and interesting.
Thank you Nelson for giving us an orderly approach to avoiding or forcing Zugzwang in advance.
Damn, the way you explained was not only informative and insightful but also really fun! Totally understood everything you said. Really appreciate your videos. Keep it up!
Yeah, it’s sort of like something you showed before Nelson, where the king does a waiting move in a triangular shape which forces the opponent to commit in a direction. After white Kb1 and black kb7, then white Kc2 black has to go kc7 to keep pace and white. Now white has to play a waiting move at some point because if he just keeps heading towards the h file in a couple of moves he’s overcommitted and ends up on a corresponding square first. So the waiting move for white is getting to kc3 last. Black can’t push straight down the board because of the pawn on d5 but has to move his king, but where…. If black goes kb6 he’s left the gate open for white to dash to the h file, but if he goes kd7 then he’s left the gate open for white to dash back to the a file, only other move is back up the board to the 8th rank putting the king too far back to save his pawn on a5. So first move for white critical and where to play the waiting move is just as critical…. Man I’m learning a lot from you!
A way that helps me understand this concept better is that you can go diagonnally two ways: up + down or actually moving diagonnaly, but moving up + down wastes a move.
Really easy to understand in your way of explaining.
Before watching your videos, I only new how chess pieces move.
GREAT WORK!
I understand perfectly. Thank you! This was very beneficial.
Explained nicely, my only problem is how you determine those corresponding squares without that sheet?
Calculation I suppose.
Edit: White's starting square is a 5 and black's starting square is a 2.
I didn't solve it using corresponding squares, but it's very similar nonetheless. You know that if the white king is on c4, then black's king must be on b6 to stop white. And if white's king is on d3, then black's king must be on c7.
So what if white's king is on c3? Since d3 connects to both d3 and c4, black must be prepared to go to both b6 and c7, in case white goes to either square. The only square that works for black is b7.
I'll do another square: d2. It connects to c3 and d3, so it must be prepared to go to b7 and c7. However, if black is on the b-file, white can run to the gh-files to infiltrate from there. So the only square for black is c8.
This basically repeats until you get your "corresponding squares" (in quotes because this process only considers how one side can stop the other but not the other way around)
I rarely ever play chess, I have just been enjoying chess puzzles like yours, and this was no different than your other ones, where I had very little trouble following! Your description and step by step examples of corresponding squares followed by that chart made sense and was easy to follow, so yeah I'd say you nailed the challenge!!
Great explanation! I'd have loved to see the resolution after the explanation of the concept, which you've done so well-just for the satisfaction factor :)
First move: 1. Kb1. This position is one of the two famous “Lasker-Reichhelm” positions appeared in 1901. You can find them in the Encyclopedia of Chess Endings, 2nd Ed., Vol. 1, page 386.
Fascinating, I was sure the first move would be B2 since you can go to any square that A2 and B1 allows and also excludes,. Needing to go to the B2 square on the second move never crossed my mind...
This is quite the complicated concept to understand but you did break it down well. The king can not move directly next to a king. Because of check.
After watching your video here It gave me another way to understand it.
Think of the king (in king vs king scenarios like here) as a 9 square piece, instead of a 1 square piece. The surrounding 8 squares are automatically defended. When both king's surrounding 8 squares overlap as shown very well at 11:45 in the video here. Neither king can move into the other's king's surrounding 8 squares. So when I say "your 8 squares", that is the 8 squares surrounding the king.
So you want to be the side that creates a surrounding overlap (ie you move your surrounding 8 squares into their surrounding 8 squares) . That forces them to have to move away from the overlap, so you can take the pawn (in this scenario) or do a better move than they can.
What your corresponding squares seem to be are a way to set up the above surrounding 8 square overlap scenario. The setup is essentially:
You arrive second at a pair of corresponding squares. When it is your move again, you choose the opposite way to go and will have just enough moves so at the end you are creating the 8 squares overlap. Forcing the other king to move out of it on his next turn.
Thinking of King vs King battles as two 3x3 (or 9 square pieces) instead of the usual 1 square a piece is, where the surrounding 8 squares can be overlapped into and then the other side has to (usually) use their next turn to get rid of the overlap to allow you to achieve your objective on the next turn.
Yes, this was a great explanation of corresponding squares. I can't claim that I'll be able to use it in a match, but I can say that after this video, I at least understand the principle of it.
Yes, understand. Tremendous!!! Never heard 'bout something like that. Appreciate it!
This is so incredibly fascinating!!
Wonderful. I had never considered extending the concept of opposition to more remote squares. I appreciated learning something today.
Beautifully explained. You are a wonderful teacher.
Well done explaining the concept, you made it very easy to understand.
I am at 3:42, pausing the video. After looking at the position, I believe the correct first move to be Kb2. So far, great explanation and easy to understand.
Wow nelson thank you I really liked the video and keep going this is the best chess channel ever
I haven't read the wikipedia page that you showed, but I feel it should be added that the square the black king is on in the starting position is a 2. On top of that, I will also claim that the only important corresponding squares are White's b-,c- and d-files and Blacks' a-,b- and c-files. All the squares on White's a-file are both 3 and 5 simultaneously. (i.e. Black to move in the starting position draws with both Kb7 and Kb8.)
Very interesting puzzle. Thanks for making the video.
Very clear and detailed explanation. Well done
Just found you a few days ago love you content. I havent played for ever and still understood. Well done.
Welcome aboard!
Thx. Great explanation!!!
I also never heard the term "corresponding squares", but your explanation made it crystal clear, it's like a generalization of the concept of opposition. So when you showed the Wikipedia diagram for the very first time, I knew immediately that Kb1 is the right move. Without the diagram it would have been really difficult, however. In fact, my instinct told me Ka2 would be winning, and my thought was something along the line of wasting a tempo in the horizontal direction, but yeah, doesn't work :)
16:50 There's actually 10 sets of corresponding squares, 1-9 and 0. Good video, I understand the concept but actually calculating these in a game would be next level.
Guessing off the bat, if only one move here wins I’m going to say diagonal because its the only square where the king can move in an option not available in another move, if moving up or to the side diagonal has access to all the follow up moves from those spaces
I'll never personally remember it well enough to apply it in play ... but I definitely understood your explanation and appreciated the concept.
The wiki picture of the corresponding squares really made me understand this thing. Thanks :P
I also have a question on how you can settle for a draw. It'll be interesting to see as I (and maybe some people) would want to know how to win in a losing position.
I saw the same 2 pairs you commented on (though in the reverse order because that's Path 1). I had not heard the term either... I've always understood these situations in terms of "opposition" and "tempi".
I think this study shows the pattern (and probably the math behind it) and the graphic representation may help connect with people but without a convenient method to derive the analysis, I don't know how useful it is.
Instinctively, I sometimes know when it's useful to "waste a move". This study could tell me how to do it.
Very interesting position. I did manage to find the correct answer before the explanation of what corresponding squares are, but I do believe that learning this concept can assist me in winning more endgames. Thank you very much for explaining this :)
wonderfull explanation love it
Amazing explanation, amazing position, Wikipedia diagram really help out. Keep up the great work!
I definitely understand the position pretty well now, thanks Nelson!
Nice explanation!
This has to be the most complicated chess puzzle I've seen. Very cool, and the explanation was a success as I guessed b1 after you explained before you said it was the right move, so you pass the challange I guess lol. Good stuff
Alright, it's been 2 hours and I think I finally cracked this.
So the first thing that I've noticed is that the black's king must be only on b6 and not on a6 when white's is on c4 in order to control b5 or black's king won't be in time to stop the infiltration from the king side. So if white's king starts from c4 and goes to d3, e3, f3, g3 and h4 black must respond with c7, d7, e7, f6 and g6 respectively. The same logic works on the king side. Black's king must be only on g6 when white's is on h4 because from h6 it won't be able to stop white's king from infiltration on b5 (1. Kg3 Kg6 2. Kf3 Kf6 3. Ke3 Ke7 4. Kd3 Kd7 5. Kc4 1-0). At that point I figured out that I have a set of corresponding squares here and I tried to create a map.
Starting with c4-b6 and d3-c7 I got c3-b7 so black's king can meet c4 and d3 with a proper move. Now let's look at b2. It connected to c3 and to a1 so a corresponding square should also be connected to b7 and a7. That leaves us with a6, b6, a8 and b8. b6 loses because white moves the king to c2 and you must be on a square which in one square away from both b7 and c7 which is not possible from b6. b8 also loses because even if black's king goes to c8 white's king will go to d2 and again black cannot find a square to control both b7 and c7. a6 has the same issue after Kd2 from white. a8 doesn't have the same issue because after Kd2 black can follow it up with Kc8 and I wasn't been able to find a way to force black to move the king on the wrong square. So I got b2-a8, c2-b8, d2-c8 pairs and it means that 1. Kb2 draws the game. Knowing about c2-b8, c3-b7 and c4-b6 helped me deduce that b3 is linked to a7 (later on I figured out that c7 is also a corresponding square to b3 which created a branch of secondary corresponding squares such as d2-a8).
Next I tried to find a pair for a2. The corresponding square must be connected to a7 and a8. So that might be b7 or b8. I tried to distinguish which one is the one I need by checking Ka3 and Kb1 but I think they are equal. After Ka3 black simply can move the king to b7 or b8 and still having ability to reach the corresponding square for both b3 and b2. And after Ka2-Kb1 b1 becomes a corresponding square to a7 and c7. So Ka2 gives just a draw too.
However, if we move the king to b1 immediately then black is in a zugzwang. If black goes to a8 or b8 white goes to the correct corresponding square. If black goes to a6 then white follows it up with Kb2 and black cannot reach the corresponding square in one move. If black goes to b6 then white goes to c2 and the only way to regain the control of the turn would be Ka6 but then white's king just infiltrates on the king side. If black doesn't go Ka6 here then white just moves to the corresponding square. If black goes to b7 then it's a bit trickier because white cannot reach c3 in one move and white also doesn't want to move his king on the square corresponding to a8, b8 or c8 thus white goes Kc1. And if black tries to use the same logic here then after Kd7 white goes to c2 and suddenly black cannot reach the corresponding square. If black goes to d8 instead of d7 then white still goes to c2 and no matter what black does at this point white will either take the corresponding square opposition (idk if that's a real term) or infiltrate immediately on b5. And, of course, if black goes neither to the d7 nor d8 but to any other square white takes corresponding square opposition on that move.
Edit: damn, I was typing it for almost the entire hour. It's 2:50 am here. What am I doing ffs?
Not gonna lie, I didn't read all of that, but I admire your persistence 👍
@@ChessVibesOfficial fair enough. This puzzle is magnificent though. There is something special about endgame puzzles and endgames themselves. Do you know any book or any other source to study 2 bishops vs knight endgame?
I thought it was a good explanation that made sense. This study is also known as "Fine #70" because of its inclusion in Reuben Fine's Basic Endgames. I think you've mentioned having that book in other videos, so you might look up what Fine has to say about it to compare your explanation with his.
Great explaining
8:35 Best memory rules In that is Ke7-Ke8-Ke7-Ke8 and black always got draw
Understandable. I didnt guess correctly the first time, but once ive seen the coresponding squares numbers, I knew how to play
My favorite chess UA-camr without a doubt. Congrats on 150k Nelson!
Great explanation. The wiki diagram was a good include. After that I understood perfectly to a degree where you actually might have overexplained the corresponding squares a little bit. Thanks for a great video and I hope my comment is useful to you.
Joakim
Understood. Well taught. It comes to doing triangles instead of back n forth to get the sequence right for you.
This sort of analysis is common in Dvoretsky's first couple sections on KP endings. You basically have to work backwards from the opposition. My method is to sort of daydream a position where the kings are stopping each other, and in that case, white wins when it is black's turn. So then you work backwards trying to see if you can force that position. Since there are two weaknesses, you need to threaten them both in a way where black can't stop the other in time. A good keyword to search for is "corresponding squares."
The details can be quite tedious, and hard to work out in rapid or faster chess, but in a classical setting, these endings are actually some of the easiest to analyze, they just take a little while.
Edit: Nelson mentioned the corresponding squares.
You gave a good explanation. The idea of corresponding squares is clear.
Not sure I'd be able to calculate them, especially in real time.
Most of the time when there are corresponding squares, it's actually disguised as opposition. There's also distant opposition and diagonal opposition, which are also use the same concept as corresponding squares. It's very rare that corresponding squares are _not_ just opposition.
Interesting puzzle. Hadn't heard of this either. Only when the kings are close together, and you step into opposition. At the start of the video, when you said, only one of the three moves is correct, my immediate reaction was, it has to be B2 then because that was the only move where our king would not move forward. A bit further into the video, showing the routes, I still thought B2 was correct because you would be moving into a split path where you have choices. Later in the video when you showed the diagram, I immediately understood the concept and how it worked and knew B2 was correct. The rest of the video was just pure entertainment for me. :)
Do more of the Michael positions, because this was amazing. I don't know that I totally get it, but it was still enlightening and educational. I also stuck at chess. You didn't fail me at all.
Gotta say that u r the reason I fell in love with chess, keep it up brother
I've sent the position. Excellent explanation :) Thank you for doing this video!
On 13th minute I figured by myself, that Kb1 *is* the move! Thanks, Nelson, I understood pretty much everything! :D
Paused at 3:42. My solution: at the moment white moves Kc4 black must (be able to) play Kb6. Ka6 doesn't make sense assuming there was a race starting at the kings side of the board. Hence, due to this race - black must always be (goto) one column to the left of white and b3, c3, d3 - adjacent to c4 - correspond to a7, b7, c7 - adjacent to b6. b3,c3,d3 border c2 so that b3,c3,d3 are reflected in the second line to b1,c1,d1. The black king is already on a7 which corresponds to b3 and thus b1. If white plays 1.Kb1 then black can not respond with Ka7 and therefore loses.
Mind blowing explanation. Good one.
I got this puzzle immediately even though I’m not a good player because of one of the older vidoes you made where you need to “waste” a move in order to make the king a step behind you, glad I remembered!
Hi Nelson.
Although English is not my mother tonge, you did a great job. I have understood the idea. The hard part seems to discover those corresponding squares.
Excellent video. For further study, I recommend Naroditsky's king and pawn endgame YT videos, one covers corresponding squares in detail.
great explaination
This will actually help my endgames, thanks
Good explanation. Understood how it works, but how to find that squares is another question :DD
I'm not a great player but I love chess puzzles and watch a lot of your chess puzzle videos and my guess at 3:56 is b2, because it advances the king toward both paths without losing tempo on either and you can then respond to whatever black chooses to do. Black's best move is then b6 because it advances their king toward both paths as well. Then, c3 advances the white king toward both paths without losing tempo again. Black's only sensible moves are king to a6, doubling down on holding that side, or king to c7, advancing toward the other side. That's as much forethought as I'm willing to put into this before watching the solution lol.
Edit after seeing the solution: turns out I kinda figured out corresponding squares but I got it wrong on which squares correspond.
I love this channel so much
Love awesome video
Massive thumbs up
Great stuff!!
Seems they start with those two positions when kings are closest and one needs to back down, mark them as 0 and 1, and goes on adding one pair of fields at a time
I think the Black's starting square is a '2' (missing from the diagram) so the key is white always plays to the same corresponding square ID (whilst heading to the entry squares), to force black to choose a new ID, and so it repeats
Yes. It makes sense. However, it might be hard to figure out the corresponding squares in a different game set up during game time.
I understand. When uyou showed the diagram I instantly noticed that if we go to 2 the opponent cant move to it, and we won. Very amasing position : )
Great study! A bit of a shame though it doesn’t get appropriately introduced as the study by Lasker (ex World Champion, by the way) and Reichhelm who only get kind of footnote credits for “another diagram” from the article on corresponding squares.
Oh god, don't tell me I'm gonna spend an hour or so trying to solve an insane pawn endgame instead of sleeping.
Well explained
Wow. Deep. Really deep!
One of the best chess videos I've ever seen, also shows why computers can be so much better than us
I understand it completely sir thank you so much sir it was amazing ❤❤❤
Great video as always, had a question: What do you think about the 44th Chennai Olympiad? Will you be covering some of the games? And yep, I understood, nice explanation!
I understood everything. Insane explanation.
This is awesome. A Numberphile collab would be mindblowing!
Yes, this is a very mathematical puzzle, which is probably how I solved it as a former math competitor.
at 4:07 Im guessing b2 because it contributes to following either of the paths
Logic is fine if you know how to find corresponding squres. However thank you for giving new knowledge here and also for all other great videos.
Hey Nelson...this is my favourite UA-cam channel.
Love from India ❣️
Thanks, Moksh!
Understood the Lesson m'lord, very amazing teaching
Yes, that was a good explanation. I'm not sure how to actually work out all the numbers, but I'm sure explaining that would have taken much more time! One suggestion I would make, if early on you had highlighted all the squares attacked by the black pawns, this would make it clearer that there are only the two paths to consider.
I think the idea of "who has the advantage depends on whose move it is next" is a concept called "opposition". You mentioned this briefly but seemed to shy away from the term. Perhaps you could mention that, it may make things easier if people realise that these are just the same idea under a different name.
Likewise, in one of your other videos, you mentioned "triangulation", in which the white king takes two moves to get to a square it could get to in one, in order to reverse its synchronisation with the black king which is bouncing between just two locations. This seems much the same idea again.
Great explanation,i do not think you could have explained it better.
3:41 the moves is a1 to b2 to c1 to d2 to e1 to f2 to g3 to f4
I actually have a better solution : spam premoves until you win with time.
More seriously this is really well explained. I am trash at chess i'm elo 550 lmao but I rly understood well. You did your job great !
YES - TNX
I can’t believe I actually found the solution to this by myself
Very well explained. Ouy vey that is a complicated puzzle!
Good job, and keep in mind that this position has been created in 1901, with NI, not AI
( n is for natural....)
What is funny is that unless a7 is another 2 corresponding square, the move white king to b2 can be saved by moving to c1 the next turn because the black king is still two squares away from the corresponding square labeled 2.
Edit: this is possible because the because move forces the black king to a8 if 'perfect' plays are being made.
I figured out that white had to delay one move by counting moves but wasn't sure which move was first not knowing corresponding squares concept, but did guess A1.