Mathematichess
Mathematichess is a new chess variant created for both chess lovers and mathematicians. It is played on a 13x13 board and involves unique rules that incorporate mathematical concepts.
This game is a combination of Chess, Go, Rummy, and maths. The objective of the game is to control the empty squares that give value points to the owner. The value of a square depends on the number and type of pieces surrounding it.
Setup
The initial setup is a 13x13 empty board. Each player has 9 Kings, 9 Queens, 9 Treasurers, 9 Rooks, 9 Bishops, 9 Knights, 9 Guards, 9 Pawns, and 9 Farmers, with values from 9 to 1 in the order listed.
The game has two stages:
- In the first stage players take turns placing their pieces anywhere on the board until all pieces are on the board.
- In the second stage players battle for controlling the empty squares.
Each player has 81 pieces. When all pieces are on the board seven empty squares should remain. The empty squares are the focus of the game.
Pieces
Each piece has a certain numerical value from 1 to 9. There are four types of moves:
- Sliding (one square orthogonally or diagonally, or both).
- Jumping (like a Knight, or one square diagonally, or orthogonally, or both).
- Pushing (pushing an entire line, or column, or diagonal).
- Substituting (swapping places with nearby pieces).
Only the Knight retains its original move from classic chess. Pieces have to move differently from classic chess due to the crowded board.
All piece movements are only allowed towards an empty square.
Sliders:
- Farmers are the lowest pieces with a value of one. They move one square diagonally.
- Pawns have a value of two. They move one square orthogonnaly in any dirrection.
Jumpers:
- Guards have a value of three. They jump one square diagonally or orthogonally. They can jump over both friendly or enemy pieces.
- Knights have a value of four. They jump like in the classic chess on an empty square.
Pushers:
- Bishops have a value of five. They can push an entire diagonal towards an empty square.
- Rooks have a value of six. They can push an entire line or colum towards an empty square.
- Treasurers have a value of seven. They can push an entire line, column, or diagonal towards an empty square.
Substituters:
- Queens have a value of eight. They can substitute any piece close to an empty square through a Queen like move, by jumping over pieces on their way. The substituted piece will take the Queen's original place. Queens cannot jump over Kings, or empty squares.
- Kings have a value of nine. They can substitute any nearby piece close to an empty square by swaping places.
Terminators:
- At any stage of the game each player is allowed to choose a Terminator among its own pieces.
- The choosen Terminator is removed from the board in order to create an additional empty square.
- Once removed from the board Terminators don't play any further role into the game.
- Each player is only allowed one Terminator move per game.
- After both Terminator moves are played the board should have 9 empty squares.
Rules
There is no castling, no en passant, no promotions, no check, and no check mate. Also, there is no capturing of pieces. The battle is arround the empty squares. Each empty square represents a territory whose value is given by the value of the pieces surrounding it. The objective of the game is to control as many territories as possible.
Pieces surrounding a territory (one square away orthogonally or diagonally) are called Settlers. The value of a teritory is given by the value of its Settlers.
Each teritory can have 8 Settlers in the centre of the board, 5 Settlers on a side, and 3 on a corner. Players are allowed to join territories (two or three, or more empty squares) if they can control them.
There are two types of territories:
- Sovereign (a teritory where a player has a numerical advantage).
- Shared (a teritory where the black/white pieces are on a 50/50 ratio).
The value of a territory is calculated as following:
- Pieces controlling the sides have their value multiplied.
- Pieces controlling the corners have their value added.
- On a Sovereign territory the value of the opponent's pieces are also considered as belonging to the player controlling that territory.
- On a Shared territory each player only counts the value of his own pieces.
Pieces controlling the sides of a territory (First Class Settlers) are more important than the pieces controlling its corners (Second Class Settlers).
Kings and Queens represent the Royals. If at least two Royals of the same color become Settlers of the same territory in a Sovereign territory belonging to the owner of that color, that color can no longer be invaded by the enemy. A "Secured Territory" (that can no longer be invaded) also freezes its own Settlers. They can no longer be pushed or substituted by the opponent. This rule only applies if both Royals are (First Class Settlers) controlling the sides, not the corners, of that territory.
Players get additional points for controlling Sovereign territories with pieces of the same kind (all Kings, or all Queens etc). A territory controlled by pieces of the same kind is called a Homogeneous territory. For example, if the white player has 5 Knights controlling a territory, the value of that territory is also multiplied by the value of a single Knight (four). If a player controlls a Sovereign territory but his own Knights plus the enemy Knights also form a majority, that is still considered a homogenous territory, and its value is multiplied by half the value of a single Knight.
Territories where no pieces of the same kind have a numerical advantage are called "Diverse territories". Diverse territories do not get extra points as in the case of Homogeneous territories.
Since the game has so manny possible territorial compositions, the game may end by agreement between the two players, but not before both Terminator moves have been played.
A game cannot end in the first stage.
Here are some possible game endings:
- The first player to create 4 Sovereign territories wins by getting an additional 5000 points.
- The first player to create a Homogenous territory wins by getting an additional of 5000 points.
- The first player to create two Royal territories (where Royals have the majority) wins by getting 5000 additional points.
- etc.
At the end of the game each player calculates the value of his own Sovereign territories, and adds the value of his pieces from the Shared territories.
Players may also decide the winning conditions and the value of the additional (bonus) points.
This 'user submitted' page is a collaboration between the posting user and the Chess Variant Pages. Registered contributors to the Chess Variant Pages have the ability to post their own works, subject to review and editing by the Chess Variant Pages Editorial Staff.
By Florin Lupusoru.
Last revised by Florin Lupusoru.
Web page created: 2023-05-07. Web page last updated: 2024-01-04