Huygens (chess piece)
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The huygens is a variant chess piece that jumps prime numbers of squares in orthogonal directions. It is typically played on large gameboards, or versions of infinite chess.
Movement[edit]
Description[edit]
In its most basic form, the huygens jumps any prime number of squares (2, 3, 5, 7, 11, 13...) in orthogonal directions, but in game rules it is usually restricted to jumps of five or more (5, 7, 11, 13...). The minimum jump restriction is added to make the huygens a long jumper rather than a close-range attacker. It is used on large or unbounded gameboards.[1] The fact that it makes jumps of prime numbers introduces some interesting features to the piece, and the games it is used in.
Since it jumps prime numbers of squares, other pieces that jump such as the knight, dababba, and hawk, are required to make an innefficient maneuver when chasing the huygens. Since a prime number is not a multiple of any other number (other than 1 and itself), another jumper which attacks a huygens cannot do so again unless it makes a non-full-length jump, or moves in a path which is not the straightest path towards the huygens.
The huygens also leads to another interesting aspect in the study of chess. Mathematical studies have shown that the game of chess is decidable, both when played on a normal 8×8 board, and also an unbounded gameboard. Although neither of these games has been solved, there does exist a decision tree with finite depth and finite vertices that will show whether the game is a draw, a win for white, or a win for black. However, it has been suggested that by adding the huygens to the set of chess pieces, this conclusion needs to be re-examined. Since the huygens jumps prime numbers of squares, and the complete set of prime numbers is unknown, the game of chess when played with the huygens on an infinite gameboard may be undecidable. That is, any algorithm or mathematical method to solve the game cannot be completed, because it requires using the set of prime numbers, and this set is unknown, and there is no method to compute it. Nevertheless, despite this distinction, the huygens by itself does not change the game very much in a practical way (other than how the game is changed with the introduction any other variant chess piece). Whether the huygens is used or not, the game of chess, especially when played on an infinite chessboard, is complex enough that the difference is not noticed in normal play.[2][3][4]
Value[edit]
The piece value of the huygens may depend significantly on the set of other pieces that are on the board and their locations. The huygens can jump arbitrarily far, something even a queen cannot always do (a queen slides, so can be blocked by other pieces). But in most game setups, there are usually no pieces starting very far from the "a1-h8" area (the normal 8×8 chess playing area), and there's little reason for pieces to move far from this. Therefore, the huygens gains little benefit from the infinite number of squares it attacks. With this in consideration, one study has shown that when played with other pieces starting in a zone of 18 files and 20 ranks, a huygens with a shortest allowed jump of 5 squares, will have about nine useful squares which it attacks, leading to an estimated value slightly superior to a bishop, or about 3.5 pawns.[5][6]
References[edit]
- ↑ Chess on an Infinite Plane with Huygens Option game rules example.
- ↑ The Mate-in-n Problem of Infinite Chess Is Decidable Dan Brumleve, Joel David Hamkins, Philipp Schlicht.
- ↑ Transfinite Game Values in Infinite Chess C.D.A Evans, Joel David Hamkins.
- ↑ On the Fundamentals of Human Chess Forum discussing a theoretical omniscient chess player, and the effect of adding a huygens gamepiece.
- ↑ Winboard Forum Forum discussing FairyMax chess-playing computer program and a chess piece equation to estimate piece values.
- ↑ The Chess Variant Pages Description of the huygens and its piece value
See also[edit]
External links[edit]
- Trappist-1 A sample chess variant with the huygens at The Chess Variant Pages
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