hirosi Kano wrote on Fri, Apr 21, 2023 03:23 AM UTC:
What is my proposed Material Cost?
All pieces or units used in Chess, Shogi, etc. have a concept called Material Cost.
Material Cost can be thought of as the cost of summoning a unit.
In general, the higher the Material Cost, the more powerful the piece.
For example, Pawn costs 1 material.
Queen costs 16 materials.
Introduce the calculation method.
Place a piece in the central diamond-shaped square, the Central Zone(CZ), d4 of [7x7] chess pattern map, and apply the squares that it controls.
If the CZ is Colored Square, it can calculate with other Colored Squares (x 1/2) and non-Colored Squares (x 1).
For example, in the case of King, it controls one step orthogonally and diagonally square from CZ.
So, the calculation is here.
(1×4)+(0.5×4)=6
It becomes 6 materials.
Summarize the Material Costs of other Chess and Shogi pieces in a table.
The size of the map used to calculate the cost is different for Leaper and Rider.
Leaper is a piece that jumps, and Rider can be thought of as a piece that goes straight ahead without jump.
Leaper: Knight
Riders: Queen, Bishop, Rook
The Leaper applies on [7×7] map, and the Rider on [11×11] or [13×13] maps.
One step squares orthogonally and diagonally from CZ are dominated by Blank Leaper(○: ×1) squares every on [7×7], [11×11] and [13×13] maps, never in Rider squares(Ⓡ).
Riders on [11×11] are Queen, Bishop, Rook, Dragon Horse, Dragon King, Archbishop, Chancellor and so on.
Riders on [13×13] are Nighrider, Rose, and so on.
About the calculation method in more detail
Pawn motion is divided into movement only and capture only.
The calculation method in this case is calculated using the following rule table.
What is my proposed Material Cost?
All pieces or units used in Chess, Shogi, etc. have a concept called Material Cost.
Material Cost can be thought of as the cost of summoning a unit.
In general, the higher the Material Cost, the more powerful the piece.
For example, Pawn costs 1 material.
Queen costs 16 materials.
Introduce the calculation method.
Place a piece in the central diamond-shaped square, the Central Zone(CZ), d4 of [7x7] chess pattern map, and apply the squares that it controls.
If the CZ is Colored Square, it can calculate with other Colored Squares (x 1/2) and non-Colored Squares (x 1).
For example, in the case of King, it controls one step orthogonally and diagonally square from CZ.
So, the calculation is here.
(1×4)+(0.5×4)=6
It becomes 6 materials.
Summarize the Material Costs of other Chess and Shogi pieces in a table.
The size of the map used to calculate the cost is different for Leaper and Rider.
Leaper is a piece that jumps, and Rider can be thought of as a piece that goes straight ahead without jump.
Leaper: Knight
Riders: Queen, Bishop, Rook
The Leaper applies on [7×7] map, and the Rider on [11×11] or [13×13] maps.
One step squares orthogonally and diagonally from CZ are dominated by Blank Leaper(○: ×1) squares every on [7×7], [11×11] and [13×13] maps, never in Rider squares(Ⓡ).
Riders on [11×11] are Queen, Bishop, Rook, Dragon Horse, Dragon King, Archbishop, Chancellor and so on.
Riders on [13×13] are Nighrider, Rose, and so on.
About the calculation method in more detail
Pawn motion is divided into movement only and capture only.
The calculation method in this case is calculated using the following rule table.
Colored Square (×1/2)
non-Colored Square (×1)
△(Move, no caputure) (×1/2)
×(Capture, no move) (×1/2)
○(Blank Leaper) (×1)
Ⓛ(Leaper) (×1)
Ⓡ(Rider) (×1/2)
In the case of Pawn.
Pawn moves one step strait forward and captures one step forward diagonally.
So, Pawn Calculation is here.
0.5+(0.5×0.5×2)=1
So the Pawn costs 1 material.
Next, I will introduce how to calculate the Bishop.
Calculating with [11×11],
(0.5×4)+(0.5×0.5×16)=6
So the Bishop costs 6 materials.
Complete Symmetry Correction (Knight only)
Knight have Complete Symmetry and corrects (-2) of Material Cost.
example)
Knight=(1×8)-2=6
Pawn=1
King=6
Queen=16
Bishop=6
Knight=6
Rook=10
Pawn(Shogi)=1
King(Shogi)=6
Gold General=5
Silver General=3
Horse Cavalry=2
Lance=2.5
Bishop(Shogi)=6
Dragon Horse=10
Rook(Shogi)=10
Dragon King=12