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3D-chess FAQ file. Information on the classic 5x5x5 three dimensional chess game. (5x(5x5), Cells: 125) [All Comments] [Add Comment or Rating]
David Paulowich wrote on Fri, Jul 9, 2010 01:31 PM UTC:

The colorbound piece mentioned in yesterday's comment is also called a HIPPOGRIFF in the 6x6x6 variant Monster 3D Chess. Smith says that it 'leaps to the opposite corner of a 2x2x3 area'.

Charles Gilman wrote on Thu, Jul 8, 2010 05:52 PM UTC:
'In fact, a move from Ea5 to Cb4, one square along a 2-D diagonal and then two cells vertically, is a move that no piece in this game can make. A new 3-D, knightlike piece would have to be invented for that.'
It had been. There is no general consensus on its name, but problematists call it a Sexton.

David Paulowich wrote on Fri, Jun 29, 2007 01:13 AM UTC:

Checkmate on 5x5x5: Starting with King and 3 Rooks versus a lone King, the White King can make its way onto the central cell (Cc3) without much difficulty. The Black King is now restricted to the 98 cells on the six faces of the playing area. It should be possible to then force a position with the lone King trapped on one face, for example level 'A'. The following (Zillions tested) checkmate in 14 moves looks fairly convincing.

	*	*	*
(Black King Ab2)
(White King Cc3)
(White Rook Ba5)
(White Rook Be5)
(White Rook Be1)
1. Rook Be1 - Ba1
1. King Ab2 - Ac2
2. Rook Be5 - Ae5
2. King Ac2 - Ad3
3. Rook Ba5 - Be5
3. King Ad3 - Ac2
4. Rook Ae5 - Ab5
4. King Ac2 - Ac3
5. Rook Ba1 - Be1
5. King Ac3 - Ac4
6. Rook Ab5 - Ab1
6. King Ac4 - Ac3
7. Rook Be1 - Ae1
7. King Ac3 - Ac4
8. Rook Ae1 - Ad1
8. King Ac4 - Ac5
9. Rook Ad1 - Ad3
9. King Ac5 - Ac4
10. Rook Ab1 - Ab3
10. King Ac4 - Ac5
11. King Cc3 - Cc4
11. King Ac5 - Ac4
12. Rook Be5 - Be2
12. King Ac4 - Ac5
13. Rook Be2 - Ae2
13. King Ac5 - Ac4
14. Rook Ae2 - Ac2
	*	*	*

Checkmate on 6x6x6: If we somehow reached the position given above, can White still force a similar checkmate? Note that the Black King is trapped inside a 5x5 area on level 'A' and should not be allowed to escape.

David Paulowich wrote on Thu, Jun 21, 2007 10:56 PM UTC:Excellent ★★★★★

Piece Values on 5x5x5: I am using the name Alicorn for the piece in Raumschach with triagonal movement and Unicorn for a piece combining the moves of Alicorn and Ferz (called a Ferzicorn by David Moeser in 2001). Wizard combines the moves of Alicorn and Bishop, this piece was used in Jim Aikin's Five Up (2001). Narwhal combines the moves of Alicorn and Rook. 'Alicorn' is the name for the horn of a unicorn, centuries ago narwhals were the main source of fake alicorns. Favourite combines the moves of Bishop and Rook, some 3D variants use it to replace the Raumschach Queen, which combines the moves of Alicorn and Bishop and Rook. Setting the value of a Knight equal to 30 points, Zillions thinks the Pawn is worth around 11 points in Raumschach.

Alicorn=15, Rook=25, Bishop=30, Knight=30,
Unicorn=40, Narwhal=50, Wizard=55, Favourite=60, Queen=80.

Zillions tends to simply add the values of component pieces together, giving 30 + 25 + 15 = 70 for the Queen, while I believe that 80 points is a more reasonable value. Using the Queen as a benchmark, I have estimated values for Unicorn, Narwhale, Wizard and Favourite. Note that the Unicorn and Wizard can visit all 125 cells, unlike their components. Use these numbers until something better turns up - and remember that the original Zillions calculations were based on a game with Kings that moved to all 26 adjacent cells. A final note: Zillions assigned 9 points to Pawns that move straight up (Black Pawns move down) in a 5x5x5 variant I was testing - but that value may have been influenced by the fact that the Favourite was the strongest piece in the game.

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