Vizzini

3D Chess

Musings on 3D Chess

Introduction

Chessboards

Piece Movement

Game Variations

Conclusion

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Musings on 3D Chess

Table of Contents

  1. Introduction

  2. Chessboards

  3. Piece Movement
    4. 3.1.   Straight Line Piece Moves
    3.2.   Knight Moves
    3.3.   Pawn Moves
    3.4.   Piece Movement - Upright, Varying
    3.5.   Piece Movement - Cant, Constant
    3.6.   Piece Movement - Slant, Constant
    3.7.   Piece Movement - Skew, Varying
  4. Game Variations

  5. Conclusion

3.4.   Piece Movement - Upright, Varying

This chessboard configuration is the most straightforward extension of 2D chess into 3D. See Artemis Chess and Raumschach Chess as examples.

Piece 2D 3D Upright, Varying Comments
Vectors Vectors Illustration
Rook (±n,0)
(0,±n) 		(±n,0,0)
(0,±n,0)
(0,0,±n) 		Travels through alternating color cells. Ends on a cell of either color.
Bishop (±n,±n) (±n,±n,0)
(±n,0,±n)
(0,±n,±n) 		Travels through same color cells. Ends on a cell of the starting color.
Mace (a.k.a. Unicorn) n/a (±n,±n,±n) Triagonal move. Travels through same color cells. Ends on a cell of the starting color.
Queen (±n,0)
(0,±n)
(±n,±n) 		(±n,0,0)
(0,±n,0)
(0,0,±n)
(±n,±n,0)
(±n,0,±n)
(0,±n,±n)
(±n,±n,±n) 		Combines the moves of the Rook, Bishop, and Mage. Makes all possible straight line moves. Ends on a cell of either color.
King (±1,0)
(0,±1)
(±1,±1) 		(±1,0,0)
(0,±1,0)
(0,0,±1)
(±1,±1,0)
(±1,0,±1)
(0,±1,±1)
(±1,±1,±1) 		Moves the same as a Queen but only for a distance of one. Ends on a cell of either color.
Knight (±1,±2,0)
(±2,±1) 		(±1,±2,0)
(±2,±1,0)

(±2,0,±1)
(0,±2,±1)

(±1,0,±2)
(0,±1,±2) 		Travels through alternating color cells. Ends on a cell the opposite of the starting color.
Pawn First Move (White) +(0,1)
+(0,2) 		+(0,1,0)
+(0,2,0)
+(0,0,1)
+(0,0,2) 		Travels through alternating color cells. Ends on a cell of either color.
Pawn Normal and Attack (White) Normal:
+(0,1)
Attack:
+(±1,1) 		Normal:
+(0,1,0)
+(0,0,1)
Attack:
+(±1,1,0)
+(0,1,1) 		Normal: Travels to an opposite color cell. Ends on a cell the opposite of the starting color.
Attack: Travels to a same color cell. Ends on a cell of the starting color.
Pawn First Move (Black) -(0,1)
-(0,2) 		-(0,1,0)
-(0,2,0)
-(0,0,1)
-(0,0,2) 		Travels through alternating color cells. Ends on a cell of either color.
Pawn Normal and Attack (Black) Normal:
-(0,1)
Attack:
-(±1,1) 		Normal:
-(0,1,0)
-(0,0,1)
Attack:
-(±1,1,0)
-(0,1,1) 		Normal: Travels to an opposite color cell. Ends on a cell the opposite of the starting color.
Attack: Travels to a same color cell. Ends on a cell of the starting color.
n integer in [1,∞], in practice limited by the chessboard dimensions
a.k.a. also known as
n/a not applicable
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