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.
Here is an example diagram for the game.
Two pieces had been removed from the board (see the Terminator move). The result is 7 simple territories and a double territory.
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 direction.
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 his 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 (Settlers) 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).
By their composition, territories can also be homogeneous and mixed. A territory becomes homogeneous if pieces of the same kind form the majority of the group (Settlers) controlling it. Homogeneous territories give a huge advantage to its owner because of the extra points it brings.
The value of a territory is calculated as following:
- Pieces controlling the sides have their value doubled.
- Pieces controlling the corners retain their original value.
- The values of all pieces controlling a territory are added together giving the overall value of that territory.
- Two, or more pieces of the same kind ( two or three, or more Knights, two or three, or more Rooks etc.) controlling a territory have their values multiplied first (before being added to the overall value of the group).
- On a Sovereign territory the values 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 pieces of the same kind and 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, but its own owner can still move pieces around to increase its value. This rule only applies if both pieces are (First Class Settlers) controlling the sides, not the corners, of that territory.
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 300 points.
- The first player to create a Homogenous territory wins by getting an additional of 300 points.
- The first player to create one, or two Royal territories (where Royals have the majority) wins by getting 300 additional points.
- The first player to reach a certain number of points on the board.
- 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.
Explaining the points calculation:
1) The e11-e12 territory is a Sovreign territory controlled by the white player, because it has 5 out of 6 First Class Settlers (in this case the 3 Bishops and the two Queens). Black can no longer move here.
Points calculations:
Queens have the value of 8.
Bishops have the value of 5.
(8*2)+(8*2)=32
(5*2)+(5*2)+(5*2)=30
The value of the black Night passes to the white player.
4*2=8
32+30+8=70
The value of the pieces controlling the corners is simply added together.
Knight =4
Rook = 6
King = 9
Farmer = 1
4+6+9+1 = 20
20+70 = 90.
Now, the 3 Bishops are majority of the First class settlers.
Bishops have a value of 5.
The value of this territory is then multiplied by the value of a Bishop (because they are the majority First Class Settlers controlling it).
90*5 = 450 The final value of this teritory as for now.
This should remain the final value, unless the white player can move by substitution the King from c13 to d13, and then to e13, further increasing the value of this territory.
2) F2 territory is a Royal territory because 7 out of 8 pieces are Royals. The three Queens from e1, f1 and g1 only have a single First Class Settler -- the Queen from f1. Since the three black Queens controlling the same territory have 2 First class Settlers, the Queens from e2 and g2, they should receive additional points (according to how the players agree on this).
Notes
I realised that there are some problems defining a Sovereign territory and which player gets the points. For example, the territory from h5 has two white First Class Settlers. The two Kings bring the most points to that territory, but they are in numerical disadvantage. I still have to decide whether the quality of Settlers is more important than the numerical advantage.
Another problem is the deffinition of a Homogeneous territory. For example, the f2 territory has 3 white Queens, 3 black Queens, 1 black King, and a white Bishop. Two of the black Queens are First Class Settlers, meaning that they controll it, although the ratio of black to white pieces is 4 to 4. This would still make a Royal territory because the royal pieces are more than half. Also, the black has 4 royal pieces, vs 3 white royals. I think the condition for a Homogeneous territory should be at least half pieces of the same kind, and of the same color. For example, if the black player had 4, instead of three Queens for that territory. In such case, the black player would have to get additional points equivalent to the value of its homogeneus pieces (the Queens, in this case).
I am looking forward some feedback to help me decide on this.
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By Florin Lupusoru.
Last revised by Florin Lupusoru.
Web page created: 2023-05-07. Web page last updated: 2024-01-04