The first variant that I posted on these pages, the 3d
Tunnelchess, has a weakness. Having only 16 cells at each end limits total army strength, and the shortest dimension of 4 restricts Bishops and Unicorns. Having seen the unbalance of the 5³ board and unwieldiness of the 8³ board I settled on a 6³ board for further two-player cubic-board games. This page's variants have symmetric pieces on the back ranks. On the second rank I originally considered a mixture of Pawnlike pieces from Man and Beast 02: Shield Bearers but have now switched to the Stockbroker first devised for my offshoot Courier Leapale. There is no initial double move and, as is usual in my three-dimensional and/or four-player variants, there is no Castling.
To identify cells, I recommend ranks numbered 1-6, levels lettered u-z (the first character of the cell), and the remaining dimension lettered a-f (the middle character, before the rank number). Extending Tunnelchess file groupings, files divide into an Outer Frame of files ua, uf, za, zf; an Outer Wall of files ub-ue, va-ya, vf-yf, zb-ze; an Inner Frame of files vb, ve, yb, ye; an Inner Wall of files vc, vd, wb, we, xb, xe, yc, yd; and a Tunnel of wc, wd, xc, xd. In Leapale the Inner Frame and Wall inherit the Frame and Wall rôle from Tunnelchess. In Unionschach and Sachsenschach the Outer Frame has the Rooks, the Outer Wall the minor pieces, the Tunnel the three-component compounds, and remaining files the two-component compounds. This terminology also helps explain how Stockbrokers move.
UNIONSCHACH
Unionschach has a back rank exclusively of radial pieces. The above diagram shows the top 3 levels. The 4th level is the mirror image of the 3rd, and the 5th and 6th the same as the 2nd and 1st respectively.
The ROOK, BISHOP, and QUEEN are the familiar linepieces of FIDE Chess.
The UNICORN is the additional piece from Raumschach.
The DUCHESS, GOVERNOR, and EMPRESS are the Rook, Bishop, and Queen with the Unicorn move added.
The EMPEROR is a King that can also make a 1:1:1 move. These names are more fully explained in my piece article Man and Beast 01: Constitutional Characters.
They are in the same numbers as Pawnless Tunnelchess: two imperial couples and four of everything else. This has the advantage that four standard sets, two each of two distinguishable sizes, can be used using all Pawns and small Knights as Stockbrokers, small linepieces as themselves, small Kings as the remaining Queens, large Knights as Unicorns, large linepieces as their own compounds with the Unicorn, and large Kings as Emperors. Promotion requires the usual improvisations. The name is because the arrangement suggests the Union Jack, the flag of Britain.
SACHSENSCHACH
Sachsenschach has the same arrangement of radial pieces, but with 2 to 4 kinds of coprime oblique leaper filling the 8 empty back-rank cells. The example shown has 
2:1:0 KNIGHTS on the top level, 
2:1:1 SEXTONS above and 
2:2:1 NINJAS below the Bishops, and 
3:1:0 CAMELS on the bottom level, giving a neat balance of pieces with the Bishop's binding (Sexton, Camel) to unbound ones (Knight, Ninja) and biaxial (Bishop, Knight, Camel) to triaxial (Unicorn, Sexton, Ninja). Substituting 3:2:0 ZEBRAS, 3:2:1 FORTNIGHTS, 3:2:2 FENCERS, and 3:3:2 LECTURERS respectively gives a similar effect with longer leaps. A further alternative would be to have just two kinds of oblique leaper, one between all Rooks and Bishops and the other between all Rooks and Unicorns; this could bring in the 
3:1:1 ELF which shares the Unicorn's binding. For the origin of piece names not having their own links see my article Man and Beast 05: Punning by Numbers. Its good extrapolation of the FIDE piece mix may make Sachsenschach my best family of face-to-face 3d variants, especially now that it uses Stockbrokers. A disadvantage is the need for a fifth set, though with only 72 of the 80-piece total. On the other hand this allows all Stockbrokers to be Pawn-shaped, oblique leapers Knight-shaped, and spare pieces ready for promotions. The name is a pun on sax=sex=six. The first equation refers to the names of Saxon colonies in southern Britain: Essex and Middlesex around London, Sussex on the Channel coast to the south, and Wessex to the west of that. The second is Latin-English translation.
LEAPALE
Leapale starts with the Simple Tunnelchess, Intermediate Tunnelchess (the example above as it is rotationally symmetric, with lower levels extrapolated as with the Unionschach diagram), or Paired Piece Tunnelchess back rank and adds 4 each of 5 types of coprime oblique leaper symmetrically around the outside. Leapale is leaper-heavy, no bad thing in a 3d variant, and especially useful if the Elf is to be used. This is a more diverse family of variants than Sachsenschach, as the three sets of inner-file radial pieces differ in strength. The name is from Leapale Road in the heart of Guildford, the town on the river Wey where Lewis Carroll ended his days. It is also a fitting name for a variant first submitted in 2004, this millennium's first leap year (and most recently updated in 2008, its second), although the honour of first variant alluding to 2004 goes to Ken Franklin's Leap Chess, and it is fitting having the leapers "outside the pale" of the nobility-filled Tunnelchess file ends. Guildford is, like the Runnymede of Magna Carta Chess, in my native county of Surrey, whose own name means "southern part of a kingdom", that is, of the Middlesex of Saxon times. I have since added a page for the related but Courier-influenced Courier Leapale in which the Stockbroker first appeared.
THE FRONT RANK
All this page's variants have a front rank filled with STOCKBROKERS. This piece is an enhancement of the Broker of Man and Beast 02: Shield Bearers, hence its name. Like Brokers they can move one step directly forward without capturing, or capture one step in any of the Unicorn's forward directions, but the Stockbroker can also move one step in the Bishop's forward directions. This last kind of move must be noncapturing when staying within the Tunnel, within the Inner Wall and Frame, or within the Outer Wall and Frame; it must be capturing when moving between two of these three groupings. Stockbrokers are, in terms of ratios of capturing to noncapturing moves and moving between inner and outer files, the closest extrapolation of the 2d Pawn to a 3d face-to-face variant with more than 5x5 files.
The simplest promotion rule is to any capturable back-rank piece, but there are other options. To avoid the temptation to always promote to Empress, that choice could be restricted to require a capturing arrival on the far rank. Another approach is to allow promotion to Empress only at the end of the Tunnel, two-piece compounds at the end of the Inner Wall/Frame, and simple pieces at the end of the Outer Wall/Frame.
Last modified: Thursday, March 27, 2008
