Chess Variants/Infinite Chess

thumb|Starting position of the most basic version of infinite chess Introduction Infinite Chess refers to a family of chess variants played on a board of infinite size. History Standard chess is played on a board of eight by eight squares, but the history of chess includes chess variants played on boards of many sizes. For example, the game of Courier chess, played in Germany in the 12th century, was played on a board of 12 by 8 squares, and the medieval game of Tamerlane chess was played on a board of 10 by 11 squares. In addition, the many variants of shogi, the Japanese cousin of chess, were played on board of varying sizes - the largest of these being taikyoku shōgi, which was played in the mid-16th century and features a 36 by 36 board with 402 pieces per player. The basic idea of chess on an infinite board has been proposed several times throughout the 20th and early 21st centuries. The first known reference to such a variant was by Hungarian mathematician Dénes Kőnig in 1927 - in an essay about the graph theory theorem now known as Kőnig's lemma, Kőnig included a footnote about a variant of chess played on an infinite board. Several other people proposed different version of infinite chess over the following decades, both as a model for mathematical study and an actual, playable game. Most recently, Internet user Naviary created an online version of infinite chess in 2022. Rules As its name suggests, infinite chess is played on a board that is unbounded and stretches infinitely in all directions. The infinite size of the board makes algebraic notation untenable, so squares are instead labelled using an XY coordinate system - for example, in the diagram above the white king starts on square (-3, 1). There are many different versions of infinite chess, which mainly differ in the exact movement of the pieces and which exact pieces are used. This page will cover four of the most notable versions. Kőnig's infinite chess As already stated above, this was the first version of infinite chess as proposed by Dénes Kőnig. Rules are the same of the standard game with one exception - the rooks, bishops and queen can only move up to seven squares in one move. Converse's infinite chess This version of infinite chess was proposed by Tim Converse of the University of Chicago, although the exact years of the variant's proposal is unknown. Unlike Kőnig's variant, the bishops, rooks and queen are allowed to move as many squares as they want provided there are no obstructions in their path. Ji's infinite chess Chinese chess player Jianying Ji proposed this version of infinite chess in December 2000. Compared to Converse's variant it makes three changes to the rules: The knights are replaced with nightriders. The nightrider moves like a knight, but it may keep making knight jumps in the same direction until it reaches an obstacle. A pawn promotes when it reaches a rank beyond which there are no enemy pieces. After a piece moves, the player must be able to draw an 8 by 8 square of squares which contains both the piece they moved and at least one enemy piece. If they cannot do this, the move is illegal. Chess on an infinite plane thumb|326x326px|Starting position of chess on an infinite plane Proposed by one V. Reinhart in 2017, chess on an infinite plane is one of the more complex versions of infinite chess. Unlike other infinite chess variants it does not reuse the standard game's opening setup - it instead adds additional pieces for both variety and to hopefully give one player enough material to force a checkmate in the endgame. Additional pawns are also added - some of these are position in special rearward formations called "jäger units" that can create the threat of additional promoted pieces. The variant includes two each of the following new pieces: Chancellor - combines the move of the rook and the knight. It can slide forward, backward or sideays like a rook or jump like a knight, but not both in one move. Guard - moves like a king, but is not royal and can capture and be captured just like any other piece. Hawk - jumps two or three squares forward, backward, sideways or diagonally. The pawns promote at rank 8 (for White) and rank 1 (for Black). There is also no castling for 50-move rule. All other rules are the same as the standard game. Sub-variants Chess on an infinite plane has two major sub-variants: Trappist-1 adds a new piece called the huygens. The huygens may jump X squares forward, backward or sideways, where X may be any prime number larger than three. They are initially positioned to protect the rearmost pawns in the jäger units. Formation chess grants each player a large number of knights, usually twelve or more. If four knights join together into a 2x2 square formation, they gain the collective ability to move as a queen. The formation must stop if it reaches an obstacle, and it that obstacle is an enemy piece the formation may capture that piece, but no others. If the formation is broken up or one knight is captured, the other three knights immediately resume their normal movement powers.