It's checkmate in 20 moves. White's queens circle around the board giving checks, and Black interposes horizontally/vertically moving pieces. Black only has one choice because the other piece is pinned from the previous check. That goes well, until the pawn needs to move sideways:
[FEN "3Q4/7Q/3rp3/2rkr3/2rrr3/7K/8/8 w - - 0 1"]
1. Qb7+ Rc6 2. Qa5+...
In this game Kasparov is showing a perfect demonstration of the triangulation technique in order to Zugzwang the white king.
To be in a Zugzwang means, any move loses or more generally, worsens your position, and one cannot simply pass the turn and maintain the position.
In the diagrammed position, the key idea to spot is that white would be in Zugzwang ...
Is it rude to ask my opponent to resign an online game when they have
a lost endgame?
Yes, it is rude, although you are in good company. In one Olympiad Victor Korchnoi is alleged to have asked his opponent - "Do you speak English?" When they said "Yes" he replied "Then please resign". I may be misquoting. He may not have said "please" :-)
I believe that the game you speak of is the extremely famous Lasker-Thomas match in which Lasker forces Black to accept his queen "sacrifice" on move 11. It is followed by a king hunt in which Black's king is forced to the last rank by White, who then finishes the game with the king giving a discovered check from the unmoved a8 rook. The game is ...
If you promote to a queen with 1. b8Q, black has:
1...Re2+ 2. Kd1 Rb2
attacking the queen and hinting at mate with Rb1++. If white takes the rook 3. Qxb2 it is stalemate.
Because of the mate threat white does not have any other good square for the queen either (no good check and no square that would defend b1).
If you promote to a rook, black does ...
It's quite a fun problem to think about, before getting to the
calculation of long variations, try to first spot the key idea needed to crack the problem.
Here are the first observations that come to my mind which eventually
led me to spot the solution, let's break them down step by step:
a) With our bishop eyeing g7 and our doubled pawn formation on g6-g7,...
White is one tempo short of catching the pawn - if White could make two moves immediately it would be a draw as white would just take the black pawn. But they can't, so white has to find a threat which black has to respond to which gains them that move. The only threat they can make is to queen their pawn, and apparently black can stop that with their bishop ...
Brian Towers answered the question, but to help you understand why people don't resign, I recommend you watch this lecture by GM Finegold Blunders, with GM Ben Finegold. The gist of it is:
Never resign, and look for resources no matter how bad your position
is. And when you are winning, don't let your guard down.
This position is a draw, the game is over. It is not possible for either side to checkmate the other from this position, not even if the side with the bare king would try to help.
The same is true for king and knight vs king. A single knight or bishop without any pawns or other pieces is not enough to win the game.
With king and two knights vs king it is in ...
I believe your question essentially boils down to the topic of whether it is possible to completely "solve" chess. Wikipedia has an excellent article on the topic which should give you a good overview.
To summarise, the number of possible game variations in chess is estimated to be 10^120. This is a staggeringly huge number, for comparison, consider that ...
The position given by Akavall is indeed a draw by perpetual, but it's a bit difficult to see because White has many different options at some moves. They can even choose to sacrifice the h2 queen, which effectively ends the perpetual (but it's still a draw).
A position where this is much easier to see is the following one:
[FEN "5k2/8/8/8/8/5q2/7Q/6QK w ...
It's always rude to ask your opponent to resign. They should resign of their own accord once they're convinced that you're overwhelmingly likely to win the game. In my case, that always meant you'd have to convince me that you knew how to play the endgame in question and that both of us knew how you would win it.
If your opponent hasn't resigned yet, it ...
I know you're a FIDE Master :), so I suppose you're more interested in this question from a teaching perspective.
The simplest way to understand a checkmate with King and Rook vs King is the idea of the rectangle of the opposing king. Consider this position-
Here, the Black King is restricted by the White Rook in this giant rectangular area of the ...
In short, the key idea is to prevent white from playing h2-h3!
Bc4 forces the exchange of light square bishops, and thus, sets up Rh3 which blocks the h2 pawn and keeps both the h2 and g4 pawns weak.
Concretely, the only piece currently covering h3 is the light squared bishop on f1, so by trading the bishop with Bc4, which white cannot prevent as Bg2 leaves ...
This is a fortress and a draw.
The black king can't advance as the rook, shuffling between h3 and f3, prevents it. The only way to break the fortress is to trade the queen for the rook and pawn, but the resulting endgame is still a draw.
This is not a blunder, expected behaviour from the engine. Everything worked as intended. Try to copy the FEN string out, and you'll know.
Although the position looked winning, White didn't have enough moves to force checkmate before the 50 moves rule. Stockfish, knowing the position was a dead draw immediately asked for simplification.
The position you ...
Shirov resigned: the thinking was that despite both sides left with pawns and a knight, the advantage went to Black.
Black has an extra pawn and Black's pawn chain is mutually supporting. White is down a pawn and they are split. White's king is buried too deeply in the corner to either prevent a black pawn advance to promotion or to save White's pawns.
The simple and obvious answer is that it all depends on the position of black's pawns and king. In general the further up the board the pawns the better for black provided the king is in contact with the pawns, preferably in front of them.
Worth pointing out that the position you give is winning for white because the pawns aren't far enough forward. From ...
The check must come from the knight (D'uh!)
The black king must be on c5 for the mate
The white king must be used to cover any empty squares to the right of the black king - thus the white king must move, thus there must be at least one non-checking move
On a non-checking move Black can try to release the prison by Ra4
The only way white can cover this ...
I always like to explain this in a visual way.
Basic Idea: Keep the bishops together. They form a large net (restricted area) from which the opponent king cannot escape.
Step 1: Push Opponent's King To Edge Rank or File
Keeping the bishops together and using the king for support, make the restricted area smaller to push the opponent's king back to an ...
If White can get the Black king to the first rank, then it will not be fast enough to catch the g-pawn from promoting. White starts by playing 1. Qg5, and after 1...Kh7 2. Qf6 Kg8 3. Qh6, the White queen can simply imitate the Black king's movements until she can start forcing the king down towards the first rank.
[FEN "7k/8/8/8/6p1/4QpPb/5PpP/6K1 w - -...
According to the Lomonosov tablebases, it's mate in 40 for black. While the queen can't force mate by herself, she can force a zugzwang. In this case, when the bishop is forced to move to e8. Then, it's a matter of giving checks until the queen forks the king and bishop.
One of the longest variations given is as follows:
[FEN "7k/5BpP/3K2P1/8/8/8/8/4q3 w -...
Actually, the bishop and knight mate is not as slippery as it appears. I have checked this on a tablebase program I wrote. On a 10x10 board, the side with the bishop and knight (say white) can force mate in at most 47 moves. White can even force mate on a 16x16 board, in at most 93 moves. I believe mate can be forced on an arbitrarily large even size ...
It's probably a trick problem with a promotion to a black knight.
Such promotions to the wrong colour are not allowed, and never were. In the official rules it is now specifically pointed out that the new piece has to have the same colour as the promoted pawn.
FIDE's laws of chess, Article 3.7 e:
When a pawn reaches the rank furthest from its starting ...
Why is there no rule allowing a player to claim a draw in lonely king
For the simple reason that there is no need. If you are the player with the extra material you can offer a draw and be almost guaranteed that your opponent will accept the offer. If you have an opponent who is ignorant of the rules you can walk away and let your clock time ...
There are several key positions from which it is easy to memorize the win. The basic idea is to drive the opposing king to the edge of the board, and then to the corner, where you can force the rook to separate from the king.
[White "King and Queen"]
[Black "King and Rook"]
The weaker side needs to keep Knight close to his King in order to achieve draw.
There are some special cases where the stronger side wins even in those situations, like when Knight is cornered or pinned in such a way that puts weaker side in zugzwang.
If the Knight is far away from the King then the result of the game depends whether or not the defending ...
Is it really possible to checkmate with two knights and king against a
Theoretically, the checkmate is possible, but you can not do it in practice unless the weaker side allows you to. This is related to a drawback in the way knight moves.
There is a mating position with this but no extra tempo to do it in
What are the ...
Here's a simpler way to see why it's winning for black: You're right that the queen cannot checkmate the king by itself, but it can stalemate the king [*] (an example pointed out by Ionut Deaconu) and that's all we need here as that would force the bishop to move. Once the bishop moves it's clear that material loss is unavoidable as either the bishop [**] or ...
Honestly it's rude to ask your opponent to resign in any position. The one exception may be them deliberately letting their clock run to 0 in a completely lost position, but in this case they're being deliberately malicious and you can't really hope to reason with them.
Even though you're absolutely justified in thinking your opponent should resign, that ...