17 Oct '07 11:30

What is the “shortest” possible game of chess ending in checkmate?

Although the shortest possible game would be a forfeit in which no moves have been played (Fischer-Spassky, Reykjavik 1972, World Championship Game 2, for example) and the shortest game between Grandmasters is the famous Fischer-Panno game in 1970 in Palma de Majorca, there are three further ways to define the term “shortest.” One of the ways to define the word is by time on the clock. Another way is to define it by the fewest number of moves. With this definition, the shortest possible game ending in checkmate is the famous fool’s mate which is occasionally seen in children’s tournaments:

1. f3 e6, 2. g4 Qh4#. There are variations: White’s first move could be 1.f4, not 1.f3; White’s first and second moves may be transposed; and Black’s first move could be 1. ... e5, not 1. ... e6.

However, let us consider the geometrical length of each move, since the word “short” can be a measure of distance too. Using this notion, we define the “length of a move” as the distance between the centres of the starting and ending squares of each move.

Therefore, assuming that each square is one unit of length, the length of a king’s vertical or horizontal move is 1, as is a queen’s vertical or horizontal move of one square, a rook’s move of one square, or a pawn’s move of one square. However, a king’s diagonal move, or a queen’s diagonal move of one square, or a bishop’s move of one square, or a pawn’s capturing move, is, according to the Pythagorean theorem in geometry, √2. The knight’s move is √5. Therefore, in the fool’s mate, the total length of all the moves is (1 + 1 + 2) + 4√2 = (4 + 4 √2) = ca. 9.65685, or (1 + 1 + 2) + √32 = (4 + 4√2), which is exactly the same thing.

However, the fool’s mate is not the “shortest” possible game geometrically. With this in mind, the intention of the question concerns the geometrical length of each move. What is the “shortest” possible game of chess ending in checkmate?

Answer: The shortest possible game of chess, ending in checkmate, with the minimal possible length of moves is:

1. d3 e6, 2. Qd2 Ke7, 3. Qe3 e5, 4. Qxe5#. There is one variation which does not alter the answer: Black’s second and third moves may be transposed.

Although this game has more moves than the fool’s mate, the total length of all the moves is (4 x 1) + √2 + (1 + 2) = (7 + √2) = ca. 8.4142 which is about 1.24 units shorter than the fool’s mate and is therefore the “shortest” possible game of chess that ends in checkmate.

Unfortunately, the knowledge of these details does absolutely nothing to help one play the game better.

Although the shortest possible game would be a forfeit in which no moves have been played (Fischer-Spassky, Reykjavik 1972, World Championship Game 2, for example) and the shortest game between Grandmasters is the famous Fischer-Panno game in 1970 in Palma de Majorca, there are three further ways to define the term “shortest.” One of the ways to define the word is by time on the clock. Another way is to define it by the fewest number of moves. With this definition, the shortest possible game ending in checkmate is the famous fool’s mate which is occasionally seen in children’s tournaments:

1. f3 e6, 2. g4 Qh4#. There are variations: White’s first move could be 1.f4, not 1.f3; White’s first and second moves may be transposed; and Black’s first move could be 1. ... e5, not 1. ... e6.

However, let us consider the geometrical length of each move, since the word “short” can be a measure of distance too. Using this notion, we define the “length of a move” as the distance between the centres of the starting and ending squares of each move.

Therefore, assuming that each square is one unit of length, the length of a king’s vertical or horizontal move is 1, as is a queen’s vertical or horizontal move of one square, a rook’s move of one square, or a pawn’s move of one square. However, a king’s diagonal move, or a queen’s diagonal move of one square, or a bishop’s move of one square, or a pawn’s capturing move, is, according to the Pythagorean theorem in geometry, √2. The knight’s move is √5. Therefore, in the fool’s mate, the total length of all the moves is (1 + 1 + 2) + 4√2 = (4 + 4 √2) = ca. 9.65685, or (1 + 1 + 2) + √32 = (4 + 4√2), which is exactly the same thing.

However, the fool’s mate is not the “shortest” possible game geometrically. With this in mind, the intention of the question concerns the geometrical length of each move. What is the “shortest” possible game of chess ending in checkmate?

Answer: The shortest possible game of chess, ending in checkmate, with the minimal possible length of moves is:

1. d3 e6, 2. Qd2 Ke7, 3. Qe3 e5, 4. Qxe5#. There is one variation which does not alter the answer: Black’s second and third moves may be transposed.

Although this game has more moves than the fool’s mate, the total length of all the moves is (4 x 1) + √2 + (1 + 2) = (7 + √2) = ca. 8.4142 which is about 1.24 units shorter than the fool’s mate and is therefore the “shortest” possible game of chess that ends in checkmate.

Unfortunately, the knowledge of these details does absolutely nothing to help one play the game better.