How the solutions work · counted by a rules engine
What a typical promotion solution looks like
Sample: 7,271 promotion puzzles (5% of all 146,245).
3.5% need 1 solver move, 28.2% need 2 solver moves, 34.4% need 3 solver moves, 18.1% need 4 solver moves, 15.7% need 5 or more solver moves. Median rating: 1063 for the shortest solutions, 2084 for the longest.
52.7% open with a pawn move. The first move captures in 22.9% and gives check in 35.5%; 13.4% end in checkmate, 25.4% involve a sacrifice, 52.2% have White to move.
22.9%first move captures
35.5%first move gives check
13.4%end in checkmate
25.4%involve a sacrifice
How many moves does the solver need?
1 solver move
3.5% · median rating 1063 2 solver moves
28.2% · median rating 1257 3 solver moves
34.4% · median rating 1554 4 solver moves
18.1% · median rating 1699 5+ solver moves
15.7% · median rating 2084 Which piece plays the key move?
What does the solver win?
Captures nothing along the line
44.6% Most valuable capture: rook
26.3% Most valuable capture: queen
11.1% Most valuable capture: pawn
10.2% Most valuable capture: bishop
4.4% Most valuable capture: knight
3.4% Material balance along the whole line, counting every capture by both sides (pawn 1, minor piece 3, rook 5, queen 9):
No material gained (mating or positional)
81.1% 3–4 points (about a minor piece)
4.8% 5–8 points (a rook or more)
6.3% 9 or more points (a queen’s worth)
1.7% How much is left on the board?
28 or more pieces on the board
0.1% How it is counted: every puzzle in the sample is replayed move by move with a chess rules engine. A sacrifice means a piece that is captured on the very next ply and was worth more than what it captured itself (pawn 1, minor piece 3, rook 5, queen 9). Sample of 7,271 puzzles. Percentages are shares of the sample.
Positions and move sequences come from real rated games (CC0 data). Engine evaluations, where shown, are stored evaluations of the position (CC0).
Background reading
Promotion (chess)
In chess, promotion is the replacement of a pawn with a new piece when the pawn is moved to its last rank. The player replaces the pawn immediately with a queen, rook, bishop, or knight of the same color. The new piece does not have to be a previously captured piece. Promotion is mandatory when moving to the last rank; the pawn cannot remain as a pawn. Promotion to a queen is known as queening; promotion to any other piece is known as underpromotion. Promotion is almost always to a queen, as it is the most powerful piece. Underpromotion might be done for various reasons, such as to avoid stalemate or for tactical reasons related to the knight's unique movement pattern. Promotion or the threat of it often decides the result in an endgame.
Rules
When a pawn is promoted, it is removed from the board, and the new piece is placed on the square the pawn moved to. The promotion may be to any other piece (except king) regardless of whether the original piece has been captured. Consequently, a player might have two or more queens, or three or more rooks, bishops, or knights. In theory, a player could have as many as nine queens, ten knights, ten bishops, or ten rooks, though these are highly improbable scenarios.
Representation of promoted pieces
Most chess sets come with only the 32 pieces used in the starting position. Some chess sets come with an extra queen of each color, but this does not accommodate the possibility of having three or more pieces of the same type. When multiple sets are available, promoted pieces are borrowed from other sets if required. Under FIDE rules, a player may stop the clocks and summon the arbiter to provide a piece for promotion. Under US Chess Federation rules and in casual play, an upside-down rook may designate a queen. However, according to FIDE arbiter guidelines, such a move is treated as a legal promotion to a rook (not an illegal move, which would incur a time penalty).
History
Promotion first existed in chaturanga, an ancestor of chess created in the 6th century. In chaturanga, a pawn is promoted upon reaching the last rank of the board. Historians dispute what the pawn can be promoted to. Some sources state that a pawn can be promoted only to a mantri, an early form of the queen only able to move one square diagonally, with the idea being that a foot soldier that advanced all the way through the enemy lines was promoted to the lowest rank of officer. Others claim that the pawn, if the piece is available for promotion, is promoted to the piece initially positioned on the file on which the pawn stands, except if the pawn stands on the king's file, in which case it is promoted to a mantri. If the piece is unavailable, the pawn remains unpromoted on its square. Chaturanga was introduced to the Middle East as shatranj around the 7th century. In shatranj, a pawn can be promoted only to a fers (equivalent to chaturanga's mantri). As chaturanga and shatranj spread to the western world and eastern Asia, as well as several other regions of the world, the promotion rule evolved. (See Regional games of the chess family section for more information.) After the queen gained its modern identity and abilities in the 15th century, replacing the farzin or ferz, some players objected to the fact that a king could have more than one queen via promotion. One old set of chess rules says, "A promoted pawn became a ferz, with the move of the queen." In Italy, in the 18th and early 19th centuries, a pawn could be promoted only to a captured piece; if none of the promoting player's non-pawn pieces were captured, the pawn remained inactive until a piece became available, whereupon the pawn immediately assumed that piece's role. Philidor did not like the possibility of having two queens; in all editions of his book (1749 to 1790), he stated that a promotion could only be to a piece previously captured. Lambe also stated this rule in a 1765 book. A player could thus never have more queens, knights, rooks, or bishops on board than the number the player starts with. The restricted promotion rule was applied inconsistently. Jacob Sarratt's 1828 book gave unrestricted promotion. By Sarratt's time, unrestricted promotion was popular, and according to Davidson, it was universal by the mid-19th century. However, Howard Staunton wrote in The Chess-Player's Handbook, originally published in 1847, that Carl Jaenisch said that the restricted promotion rule was still in force in northern Europe, Russia, Scandinavia, and Germany. and this wording was used as late as 1862 for the third and final reprint.
1862 British Chess Association rule
Under Law XIII of the 1862 "Code of Laws of the British Chess Association", a pawn reaching its last rank had the option to remain as a pawn instead of being promoted. In his 1889 work The Modern Chess Instructor, Wilhelm Steinitz, the first World Chess Champion, endorsed this rule, explaining its purpose by referring to the position diagrammed, which he cited from Johann Löwenthal's Book of the London Chess Congress, of 1862. 1.Bxg2? loses quickly after 1...Ra1+ 2.Bf1 Rb1, putting White in zugzwang, so the pawn must capture the rook. If White plays 1.bxa8=Q? or promotes to rook, bishop or knight, Black wins with 1...gxh3, whereupon 2...h2# is unstoppable. Instead, White draws by 1.bxa8=P!!, when 1...gxh3 or 1...Kxh3 stalemates White, and other moves allow 2.Bxg2, with a drawn endgame. Steinitz wrote, "We approve of the decision of the London Chess Congress, of 1862, although the 'dummy' pawn rule was denounced by some authorities." The broad language of Law XIII appears to allow promotion to any piece of either color. This led to the whimsical joke chess problem illustrated. White is to play and checkmate in one move. No solution is possible under modern-day rules, but with Law XIII in effect, the surprising solution is 1.g8=BlackN#!!, when the newly promoted knight blocks its own king's flight square. Other amusing problems have been created involving promotion to a white or black king, which Law XIII also appears to allow. Howard Staunton vigorously opposed the 1862 rule when it was proposed, but the tournament committee passed it by a large majority of votes. It did not catch on, however. Philip Sergeant wrote: A correspondent in the May 1865 Chess World ... did not exaggerate when he wrote that the B.C.A. Code had been very generally rejected by British amateurs, and emphatically condemned by the leading authorities of America, Germany, and France. In particular, the absurd "dead Pawn" rule, against which Staunton had made his protest in 1862, had failed to win acceptance. The British Chess Association code was superseded by the "Revised International Chess Code" of the London 1883 international chess tournament, under which promotion is mandatory.
Strategy
The ability to promote is often the critical factor in endgames and thus is an important consideration in opening and middlegame strategy. A far-advanced pawn can threaten to be promoted and thus be a valuable asset. Almost all promotions occur in the endgame, but promotion can happen at any point in the game. Due to the pawn's ability to be promoted, having an extra pawn can often be a decisive advantage. In general, a pawn is more valuable the farther advanced it is, as it is closer to promotion. As a result, it is often beneficial to place a pawn in enemy territory; even if it does not control any important squares, it may still be useful, as it forces the opponent to ensure that it is not promoted. A passed pawn is a pawn that no enemy pawns can stop from reaching promotion. A passed pawn is highly valuable in the endgame, where few enemy pieces remain to prevent it from being promoted. A pawn race is a situation in which each side tries to promote a passed pawn before their opponent. Usually, the first player to promote wins unless their opponent can promote immediately afterward.
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