In chess, the exchange is the material difference of a rook for a minor piece (i.e. a bishop or knight).
The value of the exchange (i.e. the difference between a rook and a minor piece) has been considered for decades.
Siegbert Tarrasch put its value as 1½ pawns in the endgame, but not for the opening or the first part of the middlegame.
That is widely accepted today, but Jacob Sarratt, Howard Staunton, and José Capablanca felt that the exchange was worth two pawns.
[5][6] Max Euwe put the value at 1½ in the middlegame and said that two pawns are more than sufficient compensation for the exchange.
If the pawns are not passed, the side with knight has good drawing chances if its pieces are well-placed.
Sometimes the exchange can be sacrificed purely on long term positional objectives, as frequently demonstrated by former world champion Tigran Petrosian.
[22] In the tenth game from the 1966 World Chess Championship between defending champion Tigran Petrosian and challenger Boris Spassky contained two exchange sacrifices by White.
In a 1994 game between World Champion Garry Kasparov and Alexei Shirov,[25] White sacrificed a pure exchange (rook for a bishop) with the move 17.
Black returned the exchange on move 28, making the material equal, but White had a strong initiative.
In most chess positions, a bishop is worth slightly more than a knight because of its longer range of movement.
As a chess game progresses, pawns tend to get traded, removing support points from the knight and opening up lines for the bishop.
Traditional chess theory espoused by masters such as Wilhelm Steinitz and Siegbert Tarrasch puts more value on the bishop than the knight.
[29] Occasions when a knight can be worth more than a bishop are frequent, so this exchange is not necessarily made at every opportunity to do so.
Many of the Classicists of the late nineteenth and early twentieth century claimed that two bishops versus rook and knight were equivalent.
Today, the view is that a pair of bishops shouldn't be underestimated, but the rook and knight are still superior.
A pair of active bishops is frequently adequate compensation for a pawn - or even the exchange in a middlegame position.
[32] More recently, John Watson has stated that from his study of this endgame that an unusually large proportion of queen and knight versus queen and bishop endings are drawn, and that most decisive games are characterized by the winning side having one or more obvious advantages (for example, having a knight against a bad bishop in a closed position, or having a bishop in a position with pawns on both sides of the board, particularly if the knight has no natural outpost).
Most decisive games were won because of a significant advantage from the middlegame and only a limited number of positions show an inherent superiority for one over the other.