David's personal notes from "Rethinking the Chess Pieces" (Soltis)

SECTION ONE: PIECE VALUES

1) Pawn equals one, Knight equals three

Two minor pieces are worth more in the middlegame than a Rook and pawn(s).
The value of pieces changes according to the availability of targets.
Two pieces often beat one. Even Knight+Knight v Queen is usually a draw
As pieces are traded off, a strong pawn centre means less and less.
Endgame value is what counts in chess, unless the game is over in the midgame.
The fewer pieces are on the board, the less their value is dependent on their location.
A Knight is frequently more active, more threatening, in short, more significant than a Bishop in the first ten or so moves of a game. That may sound trivial, but it is quarter of a 40-move game.
Rooks, on the other hand, wait in the wings. Their chart value is largely potential until move 15 and often well beyond that.
The more powerful the piece, the more it appreciates in mobility (and thus value) as the game goes on.
With a Rook each, Bishop beats Knight. With a Queen each, Knight may beat Bishop.
A sacrifice of the exchange may be sound when you have three minor pieces left, but quite unsound when you have only one.
In most Queen+Rook v RR positions, the second player should avoid trading Rooks. Two Rooks coordinate very well against a Queen and Rook.
Piece imbalances emphasize pawn structure.
Two Rooks generally beat a lone Queen, so it pays for the player with the Rooks to swap off any other pieces as quickly as possible.

2) Mobility and targets

Piece value begins with mobility
When you have a choice between recapturing with a piece or with the Rook-pawn, recapturing with the Rook pawn is usually best. Not only does it increase the Rook's mobility, but the pawn with which the capture was made now has two possible captures instead of one. However, this may hamper the ability to force a passed pawn in the endgame.
No player seeks to make his Bishop bad. "Badness" comes when he has other things on his mind.
Even in the endgame, when pieces normally have their greatest range and material values are clearest, there are sacrifices to improve mobility.
Getting a Rook to the seventh rank is worth a pawn
Making a Bishop good is often worth a pawn.
Sacrifices have the common aim of increasing the effectiveness of other pieces - if possible, suddenly.
Ordinarily, Rook and three pawns are no match for a Queen.
When your opponent makes one or more pieces bad, he is giving you chances to force matters, through extraordinary measures, to reach a more favourable position.
The badness of heavy pieces is temporary, based on pawn structure and piece placement that is bound to change.
Mobility alone doesn't decide games. Mobility plus targets does.
Even in a relatively open position, NN can outplay BB when the Bishops don't have targets.
Basic decisions should weigh both mobility and the presence of targets.

3) Board range

Short-range pieces benefit greatly from a smaller battleground (such as when part of the board is taken out of the game by the pawn structure).
A trade of Rooks is normally advantageous to the player with an exchange advantage.
With targets limited to one wing, long-range pieces are less significant.
When is a Knight stronger than a Bishop? In open positions, say the books, but they should add "if there is play on both sides of the board".
Giving up a Bishop for a Knight can be a serious error in a game with action on both wings. Trading a Knight for a Bishop can be just as great an error in a one-wing game.
The average Bishop is equal in value to the average Knight when there are four pawns each on the board.
Under normal conditions, a Rook ending with four Kingside pawns against three is not a win.
The King is a superb defender when the action is limited to a small chunk of terrain.
The chief reason Rooks belong behind passed pawns is that when it is placed behind the pawn, every move made by the pawn increases the Rook's field of action, and, on the contrary, when it is placed in front, every move of the pawn will diminish the range of the Rook.
A board is generally two small for two Queens to be used harmoniously. Should you find yourself with two Queens, it pays to look for a chance to sacrifice one of them for what would normally be considered insufficient compensation.

4) Cooperation and redundancy

When a piece can execute a double attack, one piece beats two. When the pieces cooperate to attack a single target, then two beat one.
Players often think that once they capture the enemy Queen for insufficient compensation, the win is very easy. It usually isn't, because in the absence of double attacks, the Queen needs the assistance of a second piece.
The huge value we place on our Queen is only justified when there are opportunities for a double attack.
In Queen v pieces endings, the Queen can suffer as a result of otherwise equal exchanges (minor piece for identical piece, or pawn for pawn), because there are fewer targets to attack.
Cooperation reaches its highest form in combinations and mating attacks.
True attacks are realized with many coordinated pieces, and rarely one or two.
There are three basic ingredients to evaluation: force, freedom of action, and coordination.
In Queen v Knight+Bishop endings, the minor pieces can form a fortress, protecting the King who resides in the corner. The job of the minor pieces is not to block checks, so much as to block the advance of the enemy King.
Two Knights can defend each other, but in the pawnless ending they shouldn't, as it destroys their mobility.
Defending with two Knights against a King, the King should protect the Knights and not allow them to be attacked by the enemy King.
In equal material endings, often the only winning idea is creating a numerical superiority in some portion of the board.
When one player has two Rooks and his opponent has one Rook, such as in exchange-up positions or when two minor pieces have been given up for a Rook and pawn, it is usually in the first player's interest to swap Rooks.
Knights can be redundant when they both have only one good square to occupy.
Pawns should be placed on squares of the opposite colour to that of your Bishop, in Bishops of opposite colours endgames.
When all the pawns are on on wing on exchange-up endgames, the defender should try to draw by establishing a fortress.

5) The personalities of the pieces

Some piece functions, such as blockading, are best performed by less valuable pieces, the less valuable the better. So if you are headed for an ending in which you need to blockade a pawn, trading Knights rather than Rooks may be disastrous.
A King separated from an enemy Knight by one diagonal square is safe from checks for three moves.
If a Knight attacks a Bishop, the Bishop can be advanced or retreated one square in order to restrict the activity of the Knight.
Stronger pieces attack weaker pieces more easily than vice versa.
In endgames of Rook+Bishop v Rook+Knight, the first player often enjoys two advantages. First, his Bishop can attack the Rook more easily than the enemy Knight can attack his Rook. Second, his Rook can attack the Knight much more easily than the enemy Rook can attack his Bishop.
MInor pieces usually cannot force the win of anything, in the opening, midgame, or ending, until its targets are frozen on squares. But a Bishop's ability to attack distant pawns early in the game helps it serve as a scout that can test the intentions of enemy pawns.
A pieces offensive value increases sharply if it can deliver double attacks.
Chess is a game of double attack.
The most powerful weapon in chess is the turn to move.
The Queen can also perform triple and even quadruple attacks, and so on, when it captures on a square that opens up more lines.
Exercise: Queen v two Bishops (no Kings). The Queen wins if she can capture a Bishop within 20 moves. The Bishops win if they both survive 20 moves.
The Knight is a poor defender because it cannot move, and still protect what it defends. This is often also true of the King.
Bishop endings are often dominated by maneuvering rather than forcing moves, whereas endings with Knights (and all pure pawn endings) are more about calculation.
A Bishop's role as defender helps explain why Bad Bishops aren't always so bad. A Bad Bishop lacks mobility, which is another way of saying attacking power. But Bad Bishops do a good job of protecting pawns.
In practice, the stronger piece does the supporting, and the lesser piece makes the capture. "Strongest in the rear".
When the target is a King, though, often a Rook-Queen-Rook battery is best. "Strongest in the middle".
Restriction: All pieces restrict the movements of enemy pieces by guarding vacant squares that they have in common.
It is one of the greatest assets of a Bishop that it can perform long-range restriction.
Restriction is usually a double-edged battle. A piece doing the restricting is, in turn, restricted by the other pieces, simply because they have the square(s) in common.
Since both pieces do some restriction, it is vital to look for the dominated pieces to look for the opportunity to switch roles and become the dominator.
Bishops are wonderful at running Knights out of moves.
Heavy pieces naturally restrict the most.
The best policy in Queen+pawn v Queen is often to centralize the Queen and use the King to chaperone the pawn to glory. This is because the centralized Queen restricts its opposite number, and takes away many potential checking squares, allowing progress to be made.
Exercise: A Knight of each colour on the board. No Kings. White moves first, and wins if he can "check" the enemy Knight within 15 moves.
One good reason that a Knight is so good at blockading is that once it is forced to give way and allow the pawn to advance, it can usually find a way to give itself up to prevent promotion. This is one reason why Knight+pawn v Knight is typically drawn, but Queen+pawn v Queen is often won.
Dissimilar pieces are best at blockade-breaking since they can attack the blockader without being exposed to capture.
In many endings, the Rook must be flexibly placed in order to be able to check on either files or ranks. This is a key principle in Rook v Rook endgames when one side has a Rook-pawn + Knight-pawn duo.
One of the unique failings of a Knight is its inability to lose a move. (as per Nimzowitsch, "The Knight's unequivocal nature favours Zugzwang")
In Knight v pawn, the pawn cannot avoid capture if it goes to the same colour square as the Knight each turn.

SECTION TWO: MATERIAL IMBALANCES

6) Transactions

Trades are useful when they serve to open a file for use, destroy a defender, or serve to avoid the loss of time.
The question of tempo plays an essential part in every exchange
If you have a material edge, trade pieces, not pawns.
When behind in material, trade pawns, not pieces.
If you have a positional endue, pieces should be exchanged only when it brings concrete advantages
Trade only those pieces that do not contribute to a positional advantage
Don't trade well-placed pieces for ill-placed ones.
Trades of material change the relative values of the material remaining on the board
With pawns on only one side of the board, the value of a Rook is diminished.
An exchange that is favourable in an even position may be harmful in a pawn-up position
In Bishop+Knight v Bishop+Knight endings, trading dissimilar pieces increases the defender's drawing chances
Consider the material that'll be left on the board, not the material that goes off it.
Giving up a Rook for a piece and a pawn à la Capablanca is not an equal transaction. But it is what remains on the board - the extra pawn that can be promoted - that matters.
In most cases, sacrifices serve to increase already existing advantages
Black must sacrifice in some positions or he will be positionally squashed
Sacrificing the exchange is cheaper than a pawn in the early stage of a game
The cut-off for how much to sacrifice on purely intuitive grounds seems to be a Rook
When giving up the Queen for two minors, the sacrificer must have all four, or a least three, minors after giving up the Queen.

7) The Exchange

The bottom line to any exchange sacrifice is how it affects the other pieces that stay on
The material difference of the exchange may seem great but it is essentially one pieces against another. For that reason, the most effective way of winning an exchange-up endgame is often the conversion to a more tangible edge, such as an extra pawn.
Creating a passed pawn is at least equal to having an extra pawn (and this may be borne in mind when doing exchange calculations)
If there were no endgames in chess, then the sacrifice of the exchange, especially for an outpost Knight, might be as common as the minority attack or Bishop x Knight to double pawns.
The exchange sacrifice can be used to free a pawn majority
It is the minor pieces that matter the most when you sacrifice the exchange; either the enemy minor that is captured, or its opposite number, your piece, that remains on the board.
A common theme in the exchange sacrifice is eliminating an opponent's DSB to the benefit of one's own.
The exchange sacrifice can be justified when the Rooks can't behave like Rooks.
Sacrifices can not only open files (ranks, diagonals), but can also close them.
When you win the exchange, it is vital to keep your Rooks active.
Rxe6 to take out the LSB and weaken light squares is a thematic sacrifice akin to Rxc3 to screw with Queenside pawn structure in the O-O-O Sicilians.
Exchange sacrifices that disrupt the enemy pawns can leave the sacrificer in the enviable position of being the only one who can change the pawn structure.
Inability to change the pawn structure often makes the heavy pieces look stupid, just as it enables the minor pieces to look brilliant.
Sacrificing the exchange can also be sound when it wins the Bishop pair advantage.
A Queen (or Rook) swap generally helps the player who is up the exchange.
Only when there are 10 pawns or fewer will the side who is up the exchange have significant chances against the other.

8) Queen v Pieces

Queen v two pieces is a battle between two principles: cooperation v double attack.
Queen v two pieces: in most general terms, the pieces have the edge if the coordinate well and find targets. The Queen has the edge if it can use checks and forks.
The Queen must be able to act like a Queen to have any chance against the pieces.
The pieces carry with them a higher calculating burden.
The player with the Queen assumes a greater calculating burden only under one major condition: if he is the one who initiates the imbalance and is betting that the pieces won't coordinate well before he can inflict damage. Then he has to be sure that he can exploit the window of opportunity.
Giving up the Queen for pieces requires attention not only to the attacking possibilities of the pieces, but also to their capability of defending one another from attack by the Queen.
The Queen usually has more ways of winning than the pieces, but the pieces have more ways of drawing.
To draw, the Queen is usually limited to perpetual checks. The pieces, however, can also blockade a pawn, form counterplay by ganging up on a target, or cobble a fortress.
A sacrifice of a Queen for two minors, unless it leads to a mating attack or a powerful bind, requires pawns and positional assets thrown in. As little as two extra pawns and good open lines can be sufficient, provided at least one pawn is potentially an outside passer. Add any more compensation to the two pieces and two pawns, and the advantage turns sharply in favour of the pieces.
Practical rule of thumb: three minors, unless grossly uncoordinated, are adequate compensation for a Queen, even for a Queen plus a pawn. Two minor pieces need pawns and other goodies to balance the Queen.
As for Queen v Rook + minor, if it reaches an ending, the Queen will win, but not without difficulty. The Rook and piece needs one and a half pawns to balance the Queen.
A Rook and a piece coordinate very well in defence and in the creation of a fortress, regardless of the number of pawns.
Queen v Rook and two minors is very favourable to the pieces, by about +2.
For the Queen to have any chance against Rook and two minors, it must have pawns that restrict the pieces or threaten to promote.
The chart-based claim of Queen+pawn being equal to two Rooks is only true with no minor pieces on the board. With two or more minors each, the Queen needs no pawn to equal the Rooks.
In Queen v two Rooks, the player with the Rooks should look to swap any remaining minor pieces.
With the Queen, keep as much material as possible on the board.
When a player has a material edge, but few or no pawns, the outcome hinges on King vulnerability.

9) Bishops v Knights v pawns

The future belongs to him with the Bishops. The Bishops will improve in range as the board is trimmed of traffic.
A Knight may be superior to a Bishop when it stands on a central square and protected by a pawn.
Pawn trades not only add value to a Bishop but also devalue the Knight
Three reasons to trade BxN for positional play: To create a pawn majority on one wing (as in the Ruy), to create exploitable targets (as in the Winawer), or to leave enemy pawns static on and unable to favourably change the centre (as in the Four Knights Game).
Bad Bishops are not nearly as bad as their reputation. Bad Bishops protect good pawns.
Whenever the possibility arises of exchanging off an opponent's Bishop, Remember that piece values depend on targets, not just mobility. A Bad Bishop may be key to the enemy's defences, and merit being taken off.
The drawing power of opposite-coloured Bishops in the endgame is notorious. One side's Bishop enjoys superb powers of blockade and restriction from a distance.
In the middlegame, Bishops of opposite colours usually increase the chances of an attack being successful; the defender can't defend with his Bishop what the other Bishop attacks, of course, but also the defender cannot ease pressure by trading Bishops.
In middlegames with Bishops of the opposite colour, the player with the initiative is effectively a piece up. This is especially clear when there are Queens and Rooks on the board to fuel the attack, but no Knights to provide defence.
Once no player has the two Bishops, Bishops and Knights can become much more equal.
Knights decrease in value whenever pawns are swapped.
The two Bishops vs Bishop and Knight advantage is significant, and is magnified by swaps of major pieces.
A pawn that has advanced to the sixth rank plays the role of a piece
A Knight generally draws against two pawns, and often loses against three isolated pawns.
A Bishop does a much better job of defending against pawns, isolated or connected, than a Knight.
If the enemy King is committed to stopping pawns on one wing, his minor piece often loses the battle against King and pawns on the other. A Bishop will typically fare better than a Knight in this regard.
A player with a piece against three pawns will generally have a winning advantage if he also holds the two Bishops.
In the case of piece against pawns, it is important for the player with the piece to stop the pawns from a advancing.

10) Rook v two minors

A Rook is rarely sufficient compensation for two pieces. It needs something else thrown into the transaction. The break-even point is a pawn and a half.
Giving up the pieces for a Rook and one pawn is generally bad in the opening though roughly even in the ending.
Two pawns (and two pieces) for the Rook offer excellent winning chances if Queens are then traded.
Giving up the pieces creates a sharp situation that offers greater winning chances to both players than other imbalances. It can be the pragmatic choice for a player who would otherwise be slightly inferior.
If it is a one-pawn difference, the numerical advantage of the pieces comes into play.
When the two pieces cooperate against a target defended by the Rook, they can reverse the imbalance.
It is often worth a pawn for the player with the Rook to reach an endgame.
It is worthwhile for the player with the pieces to give up a pawn (or even, sometimes, two!) to avoid reaching an endgame, should the opportunity arise to make a sacrifice that achieves that.
When the Queens are already off the board, the big question is who benefits by a swap of Rooks. It has been said that the trade generally favours the player with the remaining Rook. This makes sense because it reduces his redundancy and deprives his opponent of the best piece to restrain passed pawns. In addition, when the surviving Rook can cut off the enemy King along files and ranks, a trade can decisively pave the way for his unopposed King.
The side with the Rook will be better off if the minor pieces cannot coordinate
The side with the Rook will be better off if that side holds the initiative. If the player with the Rook loses the initiative, he'll probably lose the game as well.
The side with the Rook will benefit from there being pawns on both wings. A Rook may enjoy greater range than minor pieces, but it won't matter if it doesn't have targets. It performs best if there are two theatres of action; pawns to push and / or attack on both wings.
The pieces generally have drawing chances in this kind of ending because of the possibility of sacrificing a piece for a dangerous pawn - but the ending can be very difficult.
The pieces can do a remarkable job of taking points of penetration away from the Rook.
Two Bishops and a Knight will generally dominate against a Rook pair, or even a Rook pair and a pawn, if the minor piece coordination is good.

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