hirosi Kano wrote on Thu, Aug 3, 2023 05:16 PM UTC:
Material cost is the cost of pieces, or used in a specific situation by summoning unit for some card games.
If one of material costs is higher than another piece, this one is more powerful, but heavier than another.
Another way of saying, one which has a low material cost, it is more light and movable, and easy to exchange for higher costs.
For example, material costs(Material Cost) of knight is 6. ,the pawn have 1 material.
How is calculating material costs mathematically.
Let’s suppose a checked board in your hands. Adjust it to 7×7 squares.
Put a piece you want calculate on the d4 central.
You can analyze movements of the piece to a part. And you can apply this movements into each squares, (ranks and files).
These motion elements are parted into Leap, Ride, Hurdle, Capture only and Move only.
In particularly, the special ability which have various pieces, for example warp, is regarded as special ability elements, these are stood for a letter .
The following list are symbols of the elements.
Ⓛ: Leap
Ⓡ: Ride
☐: Hurdle
×: Capture only
△: Move only
A: Capture without move
B: Muti-capture without move
C: Copy
I: Imitate
P: Push
R: Reverse
S: Sky
T: Turn around
X: Stop
Y: Warp
All elements are able to calculate, a pawn with one step orthogonal capture and one step diagonal move, in this situation pawn cannot move double step at the initial movement, which have △ in d3 and × in c3, e3. So, the following expression is made up.
Pawn=(△)•(d3)+(×)•(c3)+(×)•(e3)
A king moves one step orthogonally and diagonally, it means Ⓛ in c3, c4, c5, d3, d5, e3, e4, e5.
Next, I want explain for calculation of material cost about Rider.
In general, rider is known as a series of same direction leaps as far as the board will allow, each of which must be to an empty spaces.
Well, which the initial step of rider is the some of Leap or Ride, et cetera.
It is possible that both Leap and Ride. In case of general rider; bishop and rook, the initial step is Leap. In case of circular rider; rose, the initial step is Ride.
As well, rider that move by crawling under ground; bishop, rook or queen, and another type of rider that move by interval jumping; nightrider, exist.
The first type of rider is calculated by 11×11 squares checked board, and second type of rider is by 13×13.
Super Symmetry Correction; SSC, for the type of Knights and Nightrider.
Knight and nightrider have 9 symmetries and this is maximum numbers.So, you can correct these material costs.
Material cost is the cost of pieces, or used in a specific situation by summoning unit for some card games. If one of material costs is higher than another piece, this one is more powerful, but heavier than another. Another way of saying, one which has a low material cost, it is more light and movable, and easy to exchange for higher costs. For example, material costs(Material Cost) of knight is 6. ,the pawn have 1 material.
How is calculating material costs mathematically.
Let’s suppose a checked board in your hands. Adjust it to 7×7 squares.
(a1,a3,a5,a7,b2,b4,b6,c1,c3,c5,c7,d2,d4,d6,e1,e3,e5,e7,f2,f4,f6,g1,g3,g5,g7)=|A|
(a2,a4,a6,b1,b3,b5,b7,c2,c4,c6,d1,d3,d5,d7,e2,e4,e6,f1,f3,f5,f7,g2,g4,g6)=|B|
+—+—+—+
|c1|b1|a1|
+—+—+—+
|c2|b2|a2|
+—+—+—+
|c3|b3|a3|
+—+—+—+
|A| and |B| are an assembly element.
Put a piece you want calculate on the d4 central. You can analyze movements of the piece to a part. And you can apply this movements into each squares, (ranks and files). These motion elements are parted into Leap, Ride, Hurdle, Capture only and Move only.
In particularly, the special ability which have various pieces, for example warp, is regarded as special ability elements, these are stood for a letter .
The following list are symbols of the elements.
Ⓛ: Leap Ⓡ: Ride ☐: Hurdle ×: Capture only △: Move only A: Capture without move B: Muti-capture without move C: Copy I: Imitate P: Push R: Reverse S: Sky T: Turn around X: Stop Y: Warp
All elements are able to calculate, a pawn with one step orthogonal capture and one step diagonal move, in this situation pawn cannot move double step at the initial movement, which have △ in d3 and × in c3, e3. So, the following expression is made up.
Pawn=(△)•(d3)+(×)•(c3)+(×)•(e3)
A king moves one step orthogonally and diagonally, it means Ⓛ in c3, c4, c5, d3, d5, e3, e4, e5.
King=(Ⓛ)•(c3)+(Ⓛ)•(c4)+(Ⓛ)•(c5)+(Ⓛ)•(d3)+(Ⓛ)•(d5)+(Ⓛ)•(e3)+(Ⓛ)•(e4)+(Ⓛ)•(e5)
Next, I want show a list of the operation process numbers.
(|A|)=1/2 (|B|)=1 (Ⓛ)=1 (Ⓡ)=1/2 (☐)=1/2 (×)=1/2 (△)=1/2 (A)=1/2 (B)=1 (C)=1 (I)=1/2 (P)=1/2 (R)=1 (S)=1/2 (T)=1 (X)=1 (Y)=1
Next, I want explain for calculation of material cost about Rider.
In general, rider is known as a series of same direction leaps as far as the board will allow, each of which must be to an empty spaces.
Well, which the initial step of rider is the some of Leap or Ride, et cetera. It is possible that both Leap and Ride. In case of general rider; bishop and rook, the initial step is Leap. In case of circular rider; rose, the initial step is Ride.
As well, rider that move by crawling under ground; bishop, rook or queen, and another type of rider that move by interval jumping; nightrider, exist. The first type of rider is calculated by 11×11 squares checked board, and second type of rider is by 13×13.
(A1,a3,a5,a7,a9,a11,b2,b4,b6,b8,b10,c1,c3,c5,c7,c9,c11,d2,d4,d6,d8,d10,e1,e3,e5,e7,e9,e11,f2,f4,f6,f8,f10,g1,g3,g5,g7,g9,g11,h2,h4,h6,h8,h10,i1,i3,i5,i7,i9,i11,j2,j4,j6,j8,j10,k1,k3,k5,k7,k9,k11)=|A|
(a2,a4,a6,a8,a10,b1,b3,b5,b7,b9,b11,c2,c4,c6,c8,c10,d1,d3,d5,d7,d9,d11,e2,e4,e6,e8,e10,f1,f3,f5,f7,f9,f11,g2,g4,g6,g8,g10,h1,h3,h5,h7,h9,h11,i2,i4,i6,i8,i10,j1,j3,j5,j7,j9,j11,k2,k4,k6,k8,k10)=|B|
The central is f6.
I want to explain the calculation for rook.
Ⓛ in e6, f5, f7, g6. Ⓡ in a6, b6, c6, d6, f1, f2, f3, f4, f8, f9, f10, f11, h6, i6, j6, k6
Rook=(Ⓛ)•{(e6)+(f5)+(f7)+(g6)}+(Ⓡ)•{(a6)+(b6)+(c6)+(d6)+(f1)+(f2)+(f3)+(f4)+(f8)+(f9)+(f10)+(f11)+(h6)+(i6)+(j6)+(k6)}
Super Symmetry Correction; SSC, for the type of Knights and Nightrider. Knight and nightrider have 9 symmetries and this is maximum numbers.So, you can correct these material costs.
(SSC)=-2
Pawn=1 King=6 Queen=16 Bishop=6 Knight=6 Rook=10