A princess is a fairy chess piece that can move like a bishop or a knight. It cannot jump over other pieces when moving as a bishop, but may do so when moving as a knight. The piece has acquired many names and is frequently called archbishop or cardinal; it may also be called simply the bishop+knight compound. Chess moves in this article use NB as notation for the princess.
Movement
The princess can move as a bishop or a knight.
History and nomenclature
The princess is one of the most simply described fairy chess pieces and as such has a long history and has gone by many names. A generic name would be the bishop+knight compound. The name archbishop was introduced by José Raúl Capablanca in his large variantCapablanca Chess. He originally called it the chancellor, but later changed the names and the rook+knight compound became known as the chancellor. Both of these names refer to higher ranks than the bishop in the Roman Catholic Church, but archbishop does so more obviously to most people, and thus became more popular. In fact, the name archbishop has been used for other augmented bishops as well, such as the "reflecting bishop" and the bishop+king compound. A similar approach was taken by Christian Freeling, the inventor of Grand Chess, who named it the cardinal. Both archbishop and cardinal are popular names for the bishop+knight compound. The name princess is more widely used among problemists. By analogy with the queen, which is a rook+bishop compound, it was decided that the three basic combinations of the three simple chess pieces should all be named after female royalty. Since the bishop+knight compound is obviously weaker than the rook+knight compound, the name princess was used for the bishop+knight compound and the rook+knight compound was called the empress. The princess was first used in Turkish Great Chess, a large medieval variant of chess, where it was called the vizir. It was introduced in the West with Carrera's chess, a chess variant from 1617, where it was called a centaur, and has been used in many chess variants since then.
Value
Ralph Betza rated the princess as about seven points, intermediate between a rook and a queen, noting that it was "a weak Queen" and that its value was increased by its 12 different directions of movement versus 8 directions for queen. However, all three of his alternate armies for that game are actually stronger than the standard FIDE army which they were supposed to equal, reflecting the general tendency for players to undervalue pieces which they are unfamiliar with; Larry Kaufman commented that this is particularly true for the princess, which is significantly more valuable than most players predict. Computer self-play studies show that a single pawn is enough to compensate the difference between queen and princess on an 8×8 board, and that on 10×8 boards princess plus pawn even have a light advantage over queen. This implies that the princess is worth approximately eight pawns. This appears somewhat surprising, as the value difference of the non-bishop-components is closer to two pawns, implying an unusually large synergy between the bishop and knight move. Although princess versus rook is usually a draw, so is queen versus princess. King and princess versus king is a forced win for the side with the princess; checkmate can be forced within 17 moves. In comparison, the queen requires 10 moves and the rook requires 16. A princess can checkmate a lone king without the aid of its own king in a position where the enemy king is the corner and the princess is two spaces diagonally away from it, but this cannot be forced. These assymptions tend to be confirmed by a mathematecal approach used in Musketeer Chess to determine relative piece value of Archbishop was estimated to 770 centipawns on an 8x8 Board.
Symbol
Both white and black symbols for the princess were added to version 12 of the Unicode standard in March 2019, in the Chess Symbols block: ? U+1FA50 WHITE CHESS KNIGHT-BISHOP ? U+1FA53 BLACK CHESS KNIGHT-BISHOP
