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Rook and pawn versus rook endgame
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Supporters of the minimum wage claim it increases the standard of living of workers, reduces poverty, reduces inequality, boosts morale and forces businesses to be more efficient. Critics of the minimum wage claim it actually increases poverty, increases unemployment (particularly among low productivity workers), and is damaging to businesses.
Queen and pawn versus queen endgame
The rook and pawn versus rook endgame is of fundamental importance to chess endgames (Keres 1973:100), (de la Villa 2008:123–25), (Emms 2008:16), (Burgess 2009:94), (Nunn 2009:106) and has been widely studied (Nunn 1999:6), (Minev 2004:58). Precise play is usually required in these positions. With optimal play, some complicated wins require sixty moves to either checkmate, win the defending rook, or successfully promote the pawn (Speelman, Tisdall & Wade 1993:7). In some cases, thirty-five moves are required to advance the pawn once (Thompson 1986).
The play of this type of ending revolves around whether or not the pawn can be promoted, or if the defending rook must be sacrificed to prevent promotion. If the pawn promotes, that side will have an overwhelming material advantage. If the pawn is about to promote, the defending side may give up his rook for the pawn, resulting in an easily won endgame for the superior side (a basic checkmate). In a few cases, the superior side gives up his rook in order to promote the pawn, resulting in a won queen versus rook position (see Pawnless chess endgame#Queen versus rook).
The queen and pawn versus queen endgame is a chess endgame in which both sides have a queen and one side has a pawn, which he is trying to promote. It is very complicated and difficult to play. Cross-checks are often used as a device to win the game by forcing the exchange of queens. It is almost always a draw if the defending king is in front of the pawn (Nunn 2007:148).
Karsten Müller and Frank Lamprecht say that this endgame occurs quite frequently but Mark Dvoretsky says that it occurs quite seldom (Müller & Lamprecht 2001:316), (Dvoretsky 2006:250). This is the second most common "piece and pawn versus piece" endgame, next to the rook and pawn versus rook endgame (Nunn 2007:148).
The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame. Those who write about chess theory, who are often but not necessarily also eminent players, are referred to as "theorists" or "theoreticians".
"Opening theory" commonly refers to consensus, broadly represented by current literature on the openings. "Endgame theory" consists of statements regarding specific positions, or positions of a similar type, though there are few universally applicable principles. "Middlegame theory" often refers to maxims or principles applicable to the middlegame. The modern trend, however, is to assign paramount importance to analysis of the specific position at hand rather than to general principles.
In chess and chess-like games, the endgame (or end game or ending) is the stage of the game when there are few pieces left on the board.
The line between middlegame and endgame is often not clear, and may occur gradually or with the quick exchange of a few pairs of pieces. The endgame, however, tends to have different characteristics from the middlegame, and the players have correspondingly different strategic concerns. In particular, pawns become more important as endgames often revolve around attempting to promote a pawn by advancing it to the eighth rank. The king, which has to be protected in the middlegame owing to the threat of checkmate, becomes a strong piece in the endgame. It can be brought to the center of the board and be a useful attacking piece.