Most basic first - this rule is the reason that King vs King is an immediate draw. Neither side has a piece to check with, let alone checkmate with. A position that is a draw because neither side can win is called a "dead position".
Playing against a bare king, a bishop or a knight is insufficient to checkmate with, and therefore K+B v K and K+N v K is ...
White has a lot of compensation for the sacrificed exchange, specifically:
more space: the white central pawns are perfectly placed to limit the movement of the black knight and bishop
play on the dark squares: black has considerably weakened the dark squares on the king side and does not have a dark-squared bishop anymore; White can easily take advantage ...
RemcoGerlich's answer is quite exhaustive, but I would like to add that unsymmetric theoretically drawn positions can arise. These are situations where one player may still checkmate, but the other cannot, e. g.
[FEN "kq6/8/KB6/8/8/8/8/8 b - - 0 1"]
You will not find a mating position for white but it is quite clear that black still may. Of course, this ...
While it's a gambit by Black, what about Tal's gambit? Black is scoring 55% in 228 grandmaster and elite correspondence games after 1 e4 c5; 2 f4 d5; 3 exd5 Nf6. I'd call Black doing better than 50% in that many top games an advantage. (And 55% is better than Black's score in any of the main non-gambit responses to 2 f4.)
The queen does a good job when there are a lot of weaknesses to attack, especially if the opponent's king is out in the open, so there are a lot of options for double attacks.
The pieces are generally stronger if they can coordinate and the king is still relatively safe. Earlier in the game that's usually the case.
If you feel that if you could change seats with your opponent and play his side and win then your decision was correct. He was good enough to get such a big advantage. If you could win from his position then, likely, so can he.
If, on the other hand, you don't know how you would win if you could swap positions, then don't resign. It could be that he doesn't ...
This answers your question by showing the pull White has. White's advantage is real. But I think it is important to notice how resilient a defender can be. This is a great example of how difficult it can be to win a "won" game. I am pretty sure Stockfish could beat me from either side of the board.
The following is Stockfish 6 playing each side of the board,...
The game is draw when a position is reached from which a checkmate cannot occur by any possible series of legal moves
Is a good summary in itself. It is not just how much material e.g. white has, black's material is also important. For example, let's say white has a K+N and black has K and h-pawn. Black's time runs out. Black loses on time, ...
Read the article "Evaluation of Material Imbalances" by GM Larry Kaufman:
The Evaluation of Material Imbalances.
He says about the bishop pair:
The bishop pair has an average value of half a pawn (more when the
opponent has no minor pieces to exchange for one of the bishops),
enough to regard it as part of the material evaluation of the
Games 61/62 of the 17th TCEC season featured such a gambit:
1. d4 Nf6 2. Bg5 c5 3. d5 Qb6 4. Nc3
White gambits the b2-pawn. After 4...Qxb2 5. Bd2, Stockfish evaluated the position as +0.61 for White. In the reverse game, Leela gave White a +0.49 advantage after the same moves.
The standard value for a piece that we learn early on (Queen=9 pawns, Rook=5 pawns, Bishop,Knight=3 pawns) is often a very good guidepost for people to make proper trades and find good tactical sequences. However, it should not be taken for granted that a rook will always be better than a bishop. Let's look at one extreme example:
You can play the Queen's gambit if you go for 3.Nf3, actually offering your opponent a chance to stick to the pawn later on, so even if it's not a "real gambit" at move 2, you can turn it into one later on. The position often gives white a small advantage.
Another interesting possibility is the From's Gambit (1.f4 e5 fxe5 d6 exd6 Bxd6) which is often said ...
Only a general answer can be given for this:
Generally the exchange of R+P (sometimes an extra pawn) for a Bishop and Knight favors the player who has the Bishop and Knight afterwards due to the simple fact that the Minor Pieces are much stronger during the middlegame than the Rook. You have two attacking pieces vs. one attacking piece. The side with the ...
One interesting forced mate which nobody has mentioned is K+N+N v K+P.
Provided the pawn is not far advanced the side with the 2 knights drives the opposing king towards a corner. At a certain point when the driving can be completed by K+N the other knight blockades the pawn. The K+N finish driving the opposing king into a corner, building a prison, say a1+...
As a general rule, two Rooks tend to be stronger than a Queen. Typical endgames like 2R+5P vs Q+5P are much better for the rooks who will coordinate to attack the opponent's weakest pawn.
However, some factors can favor the queen:
Open kings : the queen is very strong in direct mating attacks. It can checkmate with minimal support, fork king and ...
Let's assume that the material is equal, except that one player has a pair of Rooks while the other player has a Queen. In what situations is the Queen stronger than the pair of Rooks?
Since everything else is symmetrical, she can be stronger only if two rooks are not well coordinated and there is a presence of pawns on both wings. This gives you a chance ...
The side with the Queen will be stronger when the player with the two Rooks has a lot of weak pawns and/or squares. Yet, the balance in a Queen versus two Rooks situation depends a lot on the position. Thus, a rule of thumb is to prefer the Queen when it has a lot of weak squares and pawns to attack.
What follows is basically a partial answer that is heavy on explanation, plus a pointer for using it to obtain a fuller answer if so desired.
Suppose we start with a blank 64-square chessboard and ask how many different positions we can make by placing down just 2 white knights. A quick answer is that it is 64*63 = 4032 positions, because we can place the ...
On average, two bishops are better than two knights, but there are plenty of exceptions (e.g., a closed position where the bishops don't have room to operate).
On average, two rooks are better than a queen, but there are plenty of exceptions (e.g., when the player with the rooks has a bunch of weak pawns that are easy for the queen to attack).
Congratulations on a fine win. I see you have dominated the center with your knight which is backed up by doubled rooks on an open file. Your king is in a safe position, compared to black's drafty King position. Black's queen is passive though not poorly placed. One of black's rooks is still in the box and is undefended. It's vulnerable. The other rook is ...
If you don't count forfeits (including time forfeits) then yes, the two possibilities for losing a game are resignation or checkmate. There may be other reasons for resignation than material or positional inferiority, however.
In 2017, GM Hou Yifan resigned after 5 moves in protest over perceived manipulated pairings. (The pairings were later analyzed ...
By material, white is down three pawns. (R+P vs B) -3
White has the bishop pair, which is ~pawn 1
White has more space ~ 1/2 pawn 1/2
White has great lead in development ~pawn 1
Black's king stuck in the middle ~pawn 1
So the positional advantages outweigh the material deficit.
Black's best ...
As a general rule of thumb I would say
Knight + Bishop = Rook + 2 pawns
Following factors influence evaluation of this material imbalance
Static position of King
Whether Queens are present
Number of open files
Strong positions for light pieces thanks to pawn structure
Rook + passed pawns or non-passed pawns
Rook + blocked pawns or non-blocked pawns
Usually you want to open the center up for the bishops so that you can attack on both sides of the board. Or you can try to exchange bishop for knight in order to obtain a more permanent pawn structure weakness like doubled pawns or isolated pawns to attack later in the game.
A lot depends on whether there are other pieces involved and the pawn structure.
If you mean positions with Q alone vs three minor pieces then relative king safety comes into play. The side with the Q tries to expose the opponents king and harass it.
The Q alone side may need to create connected passed pawns to make progress since the pieces should easily ...
A variation of the Caro Kann, Advance: Tal Variation called Caveman Variation is a "gambit" where White can gambit mere pawns, or whole pieces, but probably will mate. If Black should go for the rook, the imbalance most often is 2 rooks + 2 pawns for the queen in a structure that favors the queen.
1. e4 c6 2. d4 d5 3. e5 Bf5 4. ...
Imagine the position
[fen "5K1k/8/8/3BN3/8/6n1/6nb/5b1r b - - 0 59"]
and you (=white) to move. There is a simple win for white in two moves.....
But of course in 99.9% of all such positions you are lost...
So never give up using generic principles but on the result of analysis of the concrete position...
Chess is a dynamic game and so the pieces get their values according to the position on the board at the time and what they are doing. This is fluid and subject to change.
That said, as a general rule the rook side of the equation is worth more in the endgame and vice versa in the late opening or early middlegame.
I have seen expert players on several ...