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Stockschach

Introduction

Some time ago I invented the "Stockbroker" piece as a Pawn analogue for face-to-face 3d variants, but with a ratio of capturing to noncapturing moves comparable to the 2d Pawn. Mostly I used it with highly conventional symmetric 3d pieces, starting with Courier Leapale and following it with Blocschach. A more dramatic departure was Brookschach, with its pieces mixing subsets of the Rook and Bishop moves. As my affection for this piece grew I began substituting it for the original Pawn analogues of my earlier face-to-face cubic-board variants.

In the meantime I expanded the "stock" enhancement of plain 3d pieces, as part of my piece article Man and Beast 15: Strengthened Across the Board. The names are also explained there. Briefly I start with the same radial analogues as Messrs. Glinski and McCooey used in their hex variants - substituting the root-3 diagonal for the root-2 one - but then replace same-rank orthogonals with same-rank diagonals and carve up the remaining root-2 diagonals between the two. This amounts to Pawn-Broker-Broker-Stockbroker, Rook-Rook-Brook-Stockbrook (the B stands for Bishop), Bishop-Unicorn-Unicorn-Stockunicorn, and Queen-Duchess-Gduchess-Stockgduchess (the G stands for Governor). A similar approach leads to Knight-Sexton-Nsexton-Stocknsexton (the N stands for Ninja), but it does not involve any piece also existing on the hex 2d board.

When it came to deploying them in a variant it struck me as obvious to use the physical form of the original square-board pieces. As 6² is equal to (5x7)+1 and 8² to (9x7)+1, it suddenly became obvious what proportions to use them in. The FIDE back rank has a King and 7 capturable pieces, so a Stockschach one would have one royally-restricted piece and five (in the 6³ case) or 9 (in the 8³ case) times the number of everything else. That way the variants can be played with 5 and 9 FIDE sets respectively, and it matters not how many are identical!

Setup

Stockschach 216 has 6 ranks numbered 1 to 6, 6 filestacks - vertical stacks of files - lettered a-f, and 6 levels lettered u-z. Each player's back rank is filled as follows:
  a    b    c    d    e    f
 ---- ---- ---- ---- ---- ----
|Sbrk|Sucn|Snsx|Sucn|Snsx|Sbrk|u
 ---- ==== ==== ==== ==== ----
|Sucn#Snsx|Sbrk|Sgds|Sucn|Snsx|v
 ---- ---- ==== ==== ---- ----
|Snsx#Sbrk#Sgds|Eprr#Sgds#Sucn|w
 ---- ---- ---- ---- ---- ----
|Sucn#Sbrk#Sgds|Sgds#Sbrk#Snsx|x
 ---- ---- ==== ==== ---- ----
|Snsx#Sucn|Sbrk|Sbrk|Snsx#Sucn|y
 ---- ==== ==== ==== ==== ----
|Sbrk|Snsx|Sucn|Snsx|Sucn|Sbrk|z
 ---- ---- ---- ---- ---- ----

Stockschach 512 has 8 ranks numbered 1 to 8, 8 filestacks - vertical stacks of files - lettered a-h, and 8 levels lettered s-z. Each player's back rank is filled as follows:

  a    b    c    d    e    f    g     h
 ---- ---- ---- ---- ---- ---- ---- ----
|Sbrk|Snsx|Sucn|Sbrk|Sbrk|Snsx|Sucn|Sbrk|s
 ---- ==== ==== ==== ==== ==== ==== ----
|Snsx#Sucn|Snsx|Sucn|Snsx|Sucn|Snsx#Sucn|t
 ---- ---- ==== ==== ==== ==== ---- ----
|Sucn#Snsx#Sgds|Sbrk|Sgds|Sbrk#Sucn#Snsx|u
 ---- ---- ---- ==== ==== ---- ---- ----
|Sbrk#Sucn#Sbrk#Sgds|Eprr#Sgds#Snsx#Sbrk|v
 ---- ---- ---- ---- ---- ---- ---- ----
|Sbrk#Snsx#Sgds#Sgds|Sgds#Sbrk#Sucn#Sbrk|w
 ---- ---- ---- ==== ==== ---- ---- ----
|Snsx#Sucn#Sbrk|Sgds|Sbrk|Sgds#Snsx#Sucn|x
 ---- ---- ==== ==== ==== ==== ---- ----
|Sucn#Snsx|Sucn|Snsx|Sucn|Snsx|Sucn#Snsx|y
 ---- ==== ==== ==== ==== ==== ==== ----
|Sbrk|Sucn|Snsx|Sbrk|Sbrk|Sucn|Snsx|Sbrk|z
 ---- ---- ---- ---- ---- ---- ---- ----

In both variants, each player's second rank is filled with their Stockbrokers.

Pieces

The STOCKBROKER is the Pawn analogue. It moves one step along any of the 9 forward radials with the restriction that the move must be:
(1) noncapturing if orthogonal (from Point via Broker);
(2) noncapturing if SD and to a file the same distance in/out - crossing file boundaries marked ---- and | but not ==== and #;
(3) capturing if SD and to a file further in or out - crossing file boundaries marked ==== and # but not ---- and |;
(4) capturing if ND, including "cutting a corner" with no change in distance in/out (from Saltire via Broker).
For examples of how its moves break down in individual files, see Brookschach or Courier Leapale for Stockschach 216 and Blocschach or Gutenschach for Stockschach 512.

The STOCKBROOK (Sbrk) is the Rook analogue. It moves any distance through empty intermediate cells along any:

type of radialStockschach 216 exampleStockschach 512 example
(1)file (from Rook via Brook)za1-za2-za3-za4-za5-za6za1-za2-za3-za4-za5-za6-za7-za8
(2)same-filestack diagonal crossing level boundaries marked ----,
but not those marked ====
yb2-xb3-wb4-vb5
(but not zb1 or ub6)
yb2-xb3-wb4-vb5-ub6-tb7
(but not zb1 or sb8)
(3)same-level diagonal crossing filestack boundaries marked |,
but not those marked #
yb2-yc3-yd4-ye5
(but not ya1 or yf6)
yb2-yc3-yd4-ye5-yf6-yg7
(but not ya1 or yh8)
(4)"refracting" diagonal switching from (2) to (3) or vice versayc1-yb2-xb3-wb4-vb5-vc6
xb1-yb2-yc3-yd4-ye5-xe6
yc1-yb2-xb3-wb4-vb5-ub6-tb7-tc8
xb1-yb2-yc3-yd4-ye5-yf6-yg7-xg8
(5)same-rank diagonal (from Bishop via Brook)za1-yb1-xc1-wd1-ve1-uf1za1-yb1-xc1-wd1-ve1-uf1-tg1-sh1
(6)same-rank orthogonal crossing level boundaries marked ====,
but not those marked ----
zd1-yd1-xd1
(but not wd1)
zd1-yd1-xd1-wd1
(but not vd1)
(7)same-rank orthogonal crossing filestack boundaries marked #,
but not those marked |
wa1-wb1-wc1
(but not wd1)
wa1-wb1-wc1-wd1
(but not we1)
(8)"contrarefracting" orthogonal switching from (6) to (7) or vice versazc1-yc1-xc1-xb1-xa1zc1-yc1-xc1-xb1-xa1

The STOCKUNICORN (Sucn) is the Bishop analogue. It moves any distance through empty intermediate cells along any:

type of radialStockschach 216 exampleStockschach 512 example
(1)root-3 diagonal, commonly called triagonal (the plain Unicorn move)za1-yb2-xv3-wd4-ue5-vf6za1-yb2-xv3-wd4-ue5-vf6-tg7-sh8
(2)same-filestack diagonal crossing level boundaries marked ====,
but not those marked ----
zd1-yd2-xd3
(but not wd4)
zd1-yd2-xd3-wd4
(but not vd5)
(3)same-level diagonal crossing filestack boundaries marked #,
but not those marked |
wa1-wb2-wc3
(but not wd4)
wa1-wb2-wc3-wd4
(but not we5)
(4)"contrarefracting" diagonal switching from (2) to (3) or vice versazc1-yc2-xc3-xb4-xa5zc1-yc2-xc3-xb4-xa5

The STOCKGDUCHESS (Sgds) is the Queen analogue. It is the compound of the Stockbrook and Stockunicorn.

The STOCKNSEXTON (Snsx) is the Knight analogue. It makes unblockable leaps with the following coordinates:

coordinatesexample
12 forward/backward, 1 up/down, 1 left/right (from Sexton via Nsexton)xa1-yb3
22 forward/backward, 1 up/down through boundary marked ==== (but not ----)zc1-yc3
32 forward/backward, 1 left/right through boundary marked # (but not |)xa1-xb3
41 forward/backward, 2 up/down, 2 left/right (from Ninja via Nsexton)xa1-zc2
51 forward/backward, 2 up/down through boundaries marked ==== (but not ----)zc1-xc2
61 forward/backward, 2 left/right through boundary marked # (but not |)xa1-xc2
71 forward/backward, 1 up/down through boundary marked ====, 1 left/right through boundary marked # ya1-zb2

The EMPEROR (Eprr) is the King analogue. It makes one step in any of the 26 radial directions. There is of course one Emperor aside, and it must be kept out of Check.It is the only piece that can move orthogonally through boundaries marked ---- and |, a decision that I made in conjunction with Castling (see below).

A STOCKCHATURANGA can be devised by replacing Stockunicorns with leaping STOCKEUNUCHS leaping exactly two steps along the same lines, and Stockgduchesses with STOCKVICEROYS moving exactly one step along Stockunicorn lines. The Stockviceroy adds selected Ferz moves to the plain Viceroy. The Stockeunuch adds a smaller selection of Elephant moves but also a few Sexton ones to the plain Eunuch.

Rules

Stockschach 216 has no double-step initial move, En Passant, Castling, or Cathedralling. So does Stockchaturanga of either size.

Stockschach 512 Stockbrokers have an optional initial double-step noncapturing move. The two steps need not be in the same direction - and in some cases cannot be - but must be valid noncapturing moves as if each step were a whole move. Immediately after making such a move they may be captured En Passant by an enemy Stockbroker as if it had made only the first step, if such a piece is so placed to do so.

An unmoved Stockschach 512 Emperor can Castle with an unmoved Stockbrook at either end of either of its within-rank orthogonals, or Cathedral with one at either end of its long diagonal. The Emperor moves 2 steps toward the Stockbrook, and the Stockbrook moves to the middle of the Emperor's path. There must be no intervening piece and no part of the Emperor's move may be in Check.

In either Stockschach a Stockbroker reaching the far rank must be promoted to a Stockbrook, Stockunicorn, Stockgduchess, or Stocknsexton. Stockchaturanga extrapolates promotion from the relevant stage of Chaturanga's evolution.

Check, Checkmate, and Stalemate are as usual.



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By Charles Gilman.
Web page created: 2008-10-04. Web page last updated: 2010-01-06