# Millennium 3D Chess

3D rendering of starting position

Millennium 3D Chess is a three-dimensional chess variant created by William L. D'Agostino in 2001 which employs three vertically stacked 8×8 boards, with each player controlling a standard set of chess pieces;[1][2] the inventor describes his objective as "extending the traditional chess game into a multilevel environment without distorting the basic game."[3]

## Rules

Millenium 3D Chess retains almost all the rules of standard chess, with additions made for the extra dimension.[4]

The three board levels are denoted 1, 2 (the middle board), and 3. Moves are recorded in the same manner as chess, using algebraic notation, with the only difference that each square is prefaced by its level number; the white and black armies begin, in standard formation, on boards 1 and 3 respectively.

For example, in standard chess, White's king starts on square e1 and Black's king starts on square e8. In Millennium 3D Chess, White's king starts on 1e1 and Black's king starts on 3e8.

All pieces can always move as normal whilst staying on the same board. Additionally, every piece is able to move between boards; each piece's additional permitted movement in the third dimension is extrapolated from its traditional movement as follows:

• Kings can move one square up or down in addition to their regular movement.
• Knights' L-shaped move can involve moving one or two steps up or down. As in standard chess, the knight is the only piece able to "jump" over other pieces.
• Bishops can move up or down one or two boards, as long as it also moves the same number of squares in a diagonal direction.
• Rooks can move vertically up and down while not moving in the other two dimensions. Additionally, a rook can move an equal number of squares vertically as it does in one of the lateral dimensions.
• A queen moves as the bishop and rook combined.
• Pawns can move one square up or down whilst staying in the same position laterally, or they can advance one square and additionally move one board up or down. A pawn's first move can, optionally, be two squares vertically, or two squares forward and two squares vertically. Pawns can capture diagonally forwards on boards immediately above and below. En passant rules allow capture on the square passed through on a two-step first move, but a pawn cannot be captured en passant if its first move is two squares vertically only. Promotion requires the pawn to reach the opponent's back rank and starting board, i.e. white promotes at rank 8 of board 3, and black promotes at rank 1 of board 1.

1 2 3
Diagram of initial setup

1 2 3
Movement of the rook and knight

1 2 3
Movement of the bishop and queen

1 2 3
Movement of the pawn and king. Squares marked × are capturing moves for the pawns.

## Example games

George Davis vs. William D'Agostino, corr. 2006:
1. N2g3 B2b7 2. B3e3 N3c6 3. N2b3 B2g7 4. N2a5 Q1b6 5. N3c5 Qx1b2 6. Nx3b7 Q3b4 7. N3c5 Q3e1+ 8. Q2e1 Q3c3+ 9. K2f1 Qx1a1 10. Q2c1 B2a6+ 11. 2e2 Qx1a2 12. N2c7 R2h7 13. N1e7+ K2e8 14. N1c6 R1c8 15. Nx3c7 Rx1c2 16. Q2c7 Q2b1+ 17. K1g1 N3e5 18. Q1d7+ K2f8 19. B2f4 Q2d1 20. Bx3e5 Q3e1+ 21. K2g1 Qx3e5 22. Q2e7+ K1g7 23. Qx3d7 B2d4+ 24. 2e3 R2c1+ 25. K1g1 Q3g3+ 26. 2g2 R2f1+ 27. Nx2f1 B3e3+ 28. 2f2 Qx2f2# 0–1

## References

1. ^ Pritchard (2007), p. 227
2. ^ Smith, L. Lynn (Summer 2003). Handscomb, Kerry (ed.). "Space Chess for the Millennium". Abstract Games. No. 14. Carpe Diem Publishing. pp. 20–21. ISSN 1492-0492.
3. ^ D'Agostino, William L. "Millennium 3D Chess". webspace.webring.com. Retrieved 15 August 2018.
4. ^ D'Agostino, William L. "MILLENIUM THREE DIMENSIONAL (3D) CHESS RULES" (PDF). Retrieved 15 August 2018.

Bibliography