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Man and Beast 15: Strengthened Across the Board

MAB 04: Generalised Generals, MAB 07: When Beasts Collide, and MAB 11: Long-nosed Generals cover pieces mixing symmetric moves in one kind of direction with forward-only (FO) moves in another. MAB 09: Mighty Like a Rose and MAB 13: Straight and Crooked Moving consider pieces that need not keep to a direction within a move. MAB 12: Alternative Fronts extends mixtures of moves further, combining forward moves with, for example, backward but not sideways ones or vice versa. This article considers pieces based on rethinking what constitutes a direction.

The acknowledgments, overview, and glossary to the series can be found here. Established pieces have a link to their Piececlopedia page. The images used in this series, and indeed in most of my pages, can be found here.


One obvious question in rethinking directions is "What happens at the board's edge?" Two alternatives, on a rectilinear board at any rate, to the conventional answer that the direction ends there are to wrap round to the opposite edge and to reflect off at the appropriate angle. Often this is applied to every piece on a board, but it can be applied individually. As the latter is rare I shun short names in favour of prefix words.

A piece continuing on the opposite edge is WRAPAROUND. If specific to a particular pair of edges it is RANK-WRAPAROUND or FILE-WRAPAROUND - or in 3d RANK-WRAPAROUND, FILESTACK-WRAPAROUND, or LEVEL-WRAPAROUND. On boards with odd numbers of files File Wraparound unbinds colourbound pieces, for example playing Shogi with a FILE-WRAPAROUND BISHOP, and enables colourswitching pieces to lose the move, for example playing Xiang Qi with a FILE-WRAPAROUND MAO. An all-file-Wraparound version of Wildebeest Chess has examples both ways but a FILE-WRAPAROUND CAMEL still cannot lose the move as it still switches between odd and even ranks. Eleport Xiang Qi's FILE-WRAPAROUND STEPPING ELEPHANT remains bound to alternate ranks. Rank-Wraparound and fully Wraparound symmetric pieces generally require a departure from traditional board-edge - and even from corner - camps. Wraparound occasionally allows a Rook to avoid a blocking piece, or a Cannon to make use of one or even hop an enemy to then capture it.

An all-Rank-Wraparound variant with many more ranks than files is usually depicted with files as concentric rings. Often each player has FO-piece analogues equally divided between clockwise and anticlockwise. If these need distinguishing they can be referred to as the symmetric piece preceded by CLOCK- and ANTICLOCK-, a convention established with Turn Qi's CLOCKWAZIR and ANTICLOCKWAZIR punning on Wazirs being wise.

A piece returning from a board edge in a different Straight direction is REFLECTING. This can itself be prefixed with Rank or File but these are in turn subdivisible. FRONT-REFLECTING, BACK-REFLECTING, LEFT-REFLECTING, and RIGHT-REFLECTING - and in 3d TOP-REFLECTING and BOTTOM-REFLECTING - pieces reflect off only one boundary. Only full Reflecting allows continuous loops. Usually they change direction at the Straight direction's last cell, preserving binding and switching. An alternative is to reflect beyond the last cell, which I term SWITCH-REFLECTING. Where a standard REFLECTING BISHOP follows a diagonal to its end cell and turns 90° (even on a cubic board, never 60°) to continue along the diagonal sharing that cell, a SWITCH-REFLECTING BISHOP makes two 45° turns with a single orthogonal step in between. Likewise where in 3d a REFLECTING UNICORN turns 110° on an edge orthogonal or 70° elsewhere on a face, a SWITCH-REFLECTING UNICORN splits the turn with one step along the orthogonal and the SD respectively. These steps unbind Switch-Reflecting pieces. Contrast a REFLECTING KNIGHT which can move a single step along the orthogonal adjoining the edge one, with a SWITCH-REFLECTING KNIGHT which can move a single diagonal step between the edge orthogonal and its neighbour. Elliards Xiang Qi has a SWITCH-REFLECTING STEPPING ELEPHANT. Reflecting of any kind never affects Rooks, but can again allow a Cannon to hop an enemy and then capture it. FO pieces (or rotations thereof) can have only reflections preserving their allowed directions, allowing a FILE-REFLECTING MITRE but not a Rank-Reflecting or fully Reflecting one. The REFLECTING QUEEN, REFLECTING INFANTA, REFLECTING INQUISITOR, REFLECTING DUCHESS, REFLECTING EMPRESS, REFLECTING MARSHAL et cetera are reflecting only as regards non-orthogonal moves.

To make up for their lack of use for Reflecting, symmetric orthogonal pieces (Wazir apart) can be REFRACTING, a move pioneered in Chess in the Round. Either instead of the Straight move (EXCLUSIVELY REFRACTING) or as well (INCLUSIVELY REFRACTING, the default), such pieces move at a constant distance from the edge (including along it), turning 90° at what on n by n boards are long diagonals. As with Wraparound this gives continuous loops. A piece that can go from an edge to the long diagonal and then turn 90° toward the other nearest edge is CONTRAREFRACTING and a piece that can do both DOUBLE-REFRACTING. FO orthogonal pieces can Refract only on a corner-camp board, and between the 2 forward directions. On a cubic board a Refracting, Contrarefracting, or Double-Refracting piece can treat any plane as a normal square-cell board. On this latter geometry symmetric diagonal pieces (Ferz apart) can also Refract, turning 60° so that one set of planes resembles frames of a film of the 2d orthogonal move. So can pieces mixing long enough moves in both kinds of direction such as a REFRACTING QUEEN, REFRACTING INFANTA, REFRACTING INQUISITOR, et cetera. Even FO diagonal pieces can do this if they always refract from one forward diagonal to another. A REFRACTING (or other versions) BISHORANKER can Refract between 2 forward or 2 backward directions but not from one to the other.

To avoid making these pieces overstrong, they may be limited to a set number of reflections. The ONE-REFLECTION BISHOP is the archetype for this, and there can also be TWO-REFLECTION, ONE-SWITCH-REFLECTION, ONE-REFRACTION, ONE-WRAPAROUND, and many other such kinds of, pieces. Finally in this section, a piece can wrap around one kind of edge and reflect off the other. Of particular note are Rank-Wraparound File-Reflecting FO pieces, which prefix I shorten to RAFFISH.


Rotatability can strengthen FO pieces. The square-cell board has RIGHT-YAWING pieces always rotating 90° clockwise (unsuffixed-dexter-coward-sinister-unsuffixed), LEFT-YAWING ones always rotating 90° anticlockwise (unsuffixed-sinister-coward-dexter-unsuffixed), REVERSING ones always rotating 180°, DUAL-YAWING pieces rotating 90° in either direction, or mix two or more types in the same game. 90° turns can also strengthen rankers and filers. Cubic boards add UP-PITCHING pieces always rotating 90° upward (unsuffixed-chief-coward-base-unsuffixed), DOWN-PITCHING ones always rotating 90° downward (unsuffixed-base-coward-chief-unsuffixed), or DUAL-PITCHING ones rotating 90° up or down.

Another issue is when rotation happens. The commonest rule is OPTIONAL rotation in place of a normal move, allowing a piece to progress as far as the player wants (if not captured first) before turning another way. Another approach is automatic END-OF-MOVE rotation. This actually weakens a single-rotation-type Point (FO Wazir) or Dabchick (FO Dabbaba), and has an ambivalent effect on other single-rotation-type short-range pieces. On the other hand, an end-of-move single-rotation-type Wing (FO Rook) has almost the freedom of an optional single-rotation-type Point. It most strengthens multiple-rotation-type pieces. Optional rotation still gives these the advantage of not having to guess the most advantageous rotation as many moves in advance, but end-of-move rotation still gives them that of not rotating at the expense of a normal move.

Some pieces can turn by odd as well as even multiples of 45°, the former switching them to a dual move. These are DUAL-INCLUSIVE versions of the normal rotating pieces. Antoine Fourrière pioneered such pieces with a Dual-inclusive Yawing Bishop in Polypiece 43 , and a Dual-inclusive Yawing Cannon in Bilateral Chess and Jacks and Witches. The DELTA of Gabriel Vicente Maura's abstract variant Omega Chess is a Dual-inclusive Yawing Wing. The ALPHA and LAMBDA of my Beyond Omega are a Dual-inclusive Yawing Backing and Veering Helmrider respectively. The MU, a Dual-inclusive Yawing full Helmrider, which I so term as the letter is crowned by angles pointing in two directions rather than the one of Alpha, Delta, and Lambda - has yet to be used in a variant. Rotary and Tournoy have a Dual-inclusive Yawing Rook, Princess, Rookranker, Superwing, and Hawker but with different names for the same pieces. Pieces that can turn no more than 45° from their array direction are termed PIVOTED pieces. Hex pieces turn by multiples of 60° (so far): in Larry Lynn Smith's Stations the CRUISER, CUTTER, DESTROYER, DREADNAUGHT, and FIGHTER are rotatable forms of the Glinski board's Rookfiler, Rookranker, Forerook, Brigarider, and Wing.

Pieces' directions can also depend which cell they are on. The QUERQUISITE is an Ace restricted to moving as the piece whose FIDE file it occupies. The ZELIG of Zelig Chess is a Querquisite modified by a restriction on how many pieces with each move a player can have on the board. The COHEIR created for Paired-Linepiece Tunnelchess is an MAB 01 Heir restricted to move between different types of file. Take the Brain and Fergus Duniho's offshoot thereof, Storm the Ivory Tower, use more complex pieces abandoning distinctions between orthogonal and diagonal to give restricted-by-cell versions of orthogonal+diagonal compounds. Take the Brain's BRAIN, NUMSKULL, and NINNY are restricted forms of the King, Queen, and Prince. Storm the Ivory Tower adds a restricted Alibaba called a FUDDY-DUDDY, a restricted Tank called a CLODHOPPER, and restricted Moo called a YAHOO. This takes one step in a direction marked on the cell followed by a 45° turn and a step in a dual direction. For a Fagin, Harlequin, Trilby, Double Rhino, Gorgon, and Falcon with their first step similarly restricted I suggest the names BUMBLE, STOOGE, DUNCE, RAMPAGER, GOBLIN, and BIRDBRAIN. Compounds include Brain+Fuddy-duddy=BRAINBOX, Ninny+Fuddy-duddy=NITWIT, Ninny+Dunce=NINCOMPOOP, Fuddy-duddy+Dunce=FUSSPOT, and Ninny+Fuddy-duddy+Dunce=LOONDOG.

In theory restricted forms of mixed-range pieces could move differently along marked diagonals than along marked orthogonals. There could also be a mixture of marked-direction pieces and unmarked-direction pieces in the same game, or even compound pieces making moves of one range along marked and another along unmarked directions.


Some very powerful pieces can be formed by not distinguishing between directions at all, be they radial or oblique. Most who use the coprime leaper in all square-board directions term it a WIZARD, and its rider a WITCH - which is not simply a go-anywhere piece as non-coprime moves can be blocked. As with Champion, Dragon, Lion, Scorpion, and the like these pieces do not have a monopoly of their names. The Wizard can be split into subcompounds making just the colourswitching and just the colourbound - but rankswitching, at least in 2d - leaps. These I respectively term COLOURWIZARD and RANKWIZARD. Their riders the COLOURWITCH and RANKWITCH are probably less interesting, although the latter is colourbound. The TIGER, COLOURTIGER, and RANKTIGER are Hopping forms of the Witch and its two halves.

Every-direction mixed-range pieces include Colourwitch+Rankwizard=COLOURWAGON and Rankwitch+Colourwizard=RANKWAGON - wagon deriving from the first letter of Wizard and Witch combined with the end of Dragon - Colourwitch+Ranktiger=TIGRESS and Rankwitch+Colourtiger=SABRETOOTH, and Colourtiger+Rankwizard=COLOURWAGONHOPPER and Ranktiger+Colourwizard=RANKWAGONHOPPER. In Lewis Carroll's Pig Tale the birds teach "tigresses to smile".

Paradoxically this lack of distinction of directions can be counterbalanced by restricting it to those directions at least as forward as the forward standard diagonals. For the FO versions of the Wizard, Witch, and Tiger I suggest the terms ENCHANTER, ENCHANTRESS, and TIGERCUB, with the same further restriction of the prefixes Colour- and Rank-. Tigercub extends to TIGRESSCUB and SABRETOOTHCUB, while the FO versions of the -wagon pieces substitute -CART. Prefixing these names with Gold- and Silver- extend to the whole of the Colour- or Rank- piece so that Colourwizard+Rankenchanter=GOLDENCHANTER, Rankwitch+Colourenchantree=SILVERENCHANTRESS, Colourwitch+Rankenchanter=GOLDCOLOURCART, Rankwitch+Colourtigercub=SILVERTIGRESSCUB, et cetera.


Before reaching 3d-specific interpretations, it is worth noting an interpretation of forward on Glinski-orientated hex boards emulating square-board ranks. On a typical convex hex board the same-rank directions are the inward half-forward and outward half-backward orthogonals. At the middle file they switch from half-forward to half-backward, forming a chevron shape. Files remain the straight forward/backward orthogonals. The analogues to the square-board diagonals are the remaining orthogonal axis and the inward forward and outward backward hexc diagonals. A stelliform board such as my Flatstar uses swaps the outward and inward radials. These definitions give analogues to all square-board pieces, but these require new names as standard orthogonal pieces could theoretically exist alongside them, and standard diagonal pieces on a hex-prism board - and as a reminder that as each player has their own ranks enemy pieces do not interact like square-board ones. Only pieces moving only along a file - the Point, Wing, Dabchick, Poker, Cannonball, Pandacub, Wazirranker, Rookranker, Dabbaranker, et cetera - are genuinely identical.

I pioneered names for symmetric and FO pieces in my Chevron Ranks variants. The Wazirfiler analogue I term WASTREL for its weakness and the full Wazir one, Wazirranker+Wastrel, WARRANT after warrant officers. Both names also echo the start of Wazir. The Ferz and Cross analogues are INSPECTOR and INVESTIGATOR, after kinds of public and private detective respectively. The Princeling analogue I term SERGEANT, the position below warrant officer in the army and inspector in the police and marked by chevron insignia. Note that a SERGECOWARD shares only its move along a file with an enemy Sergeant, and an INVESCOWARD none at all with an enemy Investigator. For the Prince and King analogues I enhance Wazir to WARLORD and Xiang Qi's General to GENERALISSIMO. In Gyokugi I add analogues to Shogi generals, drawing on some of the longer-named jewels with Wazirranker+Investigator=AMETHYST, Inspector+Point=SAPPHIRE, and Warrant+Investigator=EMERALD. These add a blue tint to the red of Copper, white of Silver, and yellow of Gold. For movement diagrams I show the entire board with examples both left and right of the centreline. The numbers 1 and 2 represent destinations specific to them respectively, and 3 represents destinations common to both. Here are those of the Wastrel, Warrant, Inspector, Investigator, Sergeant, Warlord, Generalissimo, Amethyst, Sapphire, and Emerald:

Glinski-level 3d boards add the interhex orthogonal to Warrant directions and the diagonals directly above all Warrant directions to Inspector (including Mitre moves to Investigator) ones. The long-range version of the Warlord is the WARLADY. Those of other capturable pieces simply suffix the first five letters with -RIDER, with the FO Warlady the SERGERIDER. Note that for these pieces change on the middle file such as from half-forward to half-backward orthogonal happen even in mid-move. Thus a two-step move between the files flanking the middle one is, for a WARRARIDER or WASTRRIDER, to a Viceroy rather than Dabbaba destination, and for a INSPERIDER or INVESRIDER, to a Sennight rather than Eunuch-Dabbaba hunter one. Here are the movement diagrams for the six:

The use of Warlady allows a distnction between Inspector+Wazirranker=WARLORANKER and Insperider+Rookranker=WARLARANKER, and between Inspector+Wastrel=WARLOFILER and Insperider+Wastrrider=WARLFILER. For a Warrarider, Insperider, AMETHRIDER, EMERARIDER, or SAPPHRIDER restricted to making two, one or two, more than one, and any odd number of, steps I use MAB 12's Moor- suffixes: -DEMON, -POTENTATE, -MISER, and -SWITCHER, and a requirement for some or all moves to have an intervening piece by -HOPPER. The same restrictions are already defined on the Wing in MAB 06: The Heavy Brigade. On the Invesrider they give the INCUBUS, INSPESUBJECT, INSET, INUIT, and INVESHOPPER in allusion to its first two letters and on the Wastrrider the DAYDREAMER, WASSAILER, PROMENADER, PASSEGIATA, and WASTRHOPPER in reference to other kinds of idler. on the Wrlady they apply the suffixes to Warlo-. Adding remaining Generalissimo moves to full riders follows Ryu Shogi practice with WARRADRAGON, INSPEDRAGON, AMETHDRAGON, EMERADRAGON, and SAPPHDRAGON. The compounds Warrant+Dabchick, Inspector+Incubus, Warrademon+Point, and Inspedemon+Investigator are WARRAPIG, INSPEPIG, WARRAMASTER, and INSPEMASTER. Here are the movement diagrams for the Warrademon, Warradragon, Inspedemon, and Inspedragon:


An extension specific to cubic 3d boards with 6x6 or more files in a face-to-face orientation is that of my STOCK pieces. Stock radials are two groupings analogous to square-board radials in a very similar manner to the Glinski-McCooey use of hex radials. The starting point is forward moves, of which the orthogonal is judged an analogue to its 2d manifestation, but the 4 nonstandard diagonals (ND) analogues to the square-board standard diagonals. The actual forward SDs I then divide between the 2 groups - those keeping the same distance from the edge files as orthogonal analogue and those moving in or out as diagonal analogues.

As the new FO pieces are enhancements of orthogonal and ND pieces, but not of SD pieces, I prefix the unenhanced pieces. The STOCKPOINT can move to 3 cells on the next rank. The STOCKSALTIRE can move to 1 from a corner file but 3 from any other edge file and 6 from an interior file. The compound of Stockpoint and Stocksaltire is the familiar Conqueror (Point+Cross+Saltire). Long-range versions are slightly more complex as their SD moves turn corners to maintain their constant or changing distance from the edge files. The STOCKWING's SD move turns like an Exclusively Refracting Mitre of the article's first section, the STOCKHORN's like an Exclusively Contrarefracting Mitre. Thus their compound the STOCKCOUNTESS differs from the Conqueress (Wing+Mitre+Horn) in that its Mitre element is Exclusively Double-Refracting. The STOCKVIRAGO and STOCKRAM differ still more from MAB 01 FO pieces in mixing one-step moves on some forward diagonals with Exclusively Refracting or Contrarefracting moves on others.

The Ferz and Bishop analogues, the STOCKVICEROY and STOCKUNICORN, add to the forward moves corresponding backward ones. So do Wazirranker and Rookranker analogues the STOCKWAZIRRANKER and STOCKROOKRANKER. The compound Stockwazirranker+Stockviceroy is the Archdranker but Stockrookranker+Stockunicorn=STOCKDUCHERANKER differs from the Empreranker in its SD moves. Less obvious is adding in same-rank moves for Wazir and Rook analogues. As each sideways 2d Rook destination is halfway between the corresponding forward and backward Bishop destinations, so I add in the destination halfway between each pair of forward ND or inward/outward SD destinations. This gives all 4 same-rank SDs but only 2 same-rank orthogonals, any inward one Exclusively Contrarefracting, the other 2 being jumping-on-the-spot anaolgues. This adds Stock moves to MAB 12's Fwazir and Brook to give the STOCKFWAZIR and STOCKBROOK. The latter's name, shared with a tributary of Tolkien's Brandywine, inspired the name of the plain Brook. This time all four compounds differ from non-Stock ones: Stockfwazir+Stockviceroy=STOCKGDUKE by having same-rank orthogonals unlike the Archdranksman but fewer than the full Archduke, Stockbrook+Stockunicorn=STOCKGDUCHESS for the same reason relative to the Empreranksman and Empress but also in its forward and backward diagonals being Exclusively Refracting or Contrarefracting, and Stockbrook+Stockviceroy=STOCKMVICEREINE and Stockunicorn+Stockfwazir=STOCKHBESIEGER still more so.


Knight analogue the STOCKNSEXTON has the moves of the Nsexton (Sextoranker+Ninjafiler) plus those Nightranker moves taking it 1 layer in or out and those Nightfiler moves taking it 2 layers in or out. Its FO version is the STOCKSHOVEL, a Shovel (FO Sexton) that can also make those Helm (FO Knight) moves taking it one layer in or out. The STOCKUELF. STOCKLFENCER, STOCKWNIMEL, et cetera work in similar ways.


A more drastic expansion is to Planar pieces. These have appeared from time to time but Gavin Smith's Prince names them. My own Gutenschach expanded on these pieces, naming new pieces along the same lines. My approach to planar pieces differs from his in starting from not the Straight FIDE pieces, but Crooked linepieces alternating between steps in two directions. This opens up the option of making any number of steps between turns. This would give a colossally powerful piece even on a 2d board, so it needs damping down a bit. Therefore the usual rule for multi-path pieces that they can reach a destination if at least one path is clear and not if all are blocked is reversed. In other words they can reach a destination if all paths are clear and not if at least one is blocked.

Mr. Smith termed his pieces the Base, Scientist, and Reporter. Base is a problematic name due to its use as a suffix in MAB 12, so in Gutenschach I term this piece the FOUNDATION. The double meaning of the subterranean substructure keeping a building stable and an institution such as a college or hospital still fits the theme. It extrapolates the Girlscout, and so always moves in a rectilinear plane. The Scientist turns out to be a compound piece. Its components are the THEORIST, which extrapolates the Boyscout and so also always moves in a rectilinear plane, and the TECHNICIAN, which extrapolates the Longboyhexer and so always moves in a plane that is a hex array of cells of one Bishop binding. The REPORTER extrapolates the Longrangescout and so always moves in a plane at 45° to two rectilinear ones and 90° to the other. Prince features two compounds of two of these pieces: Foundation+Reporter=NETWORK and of course Theorist+Technician=SCIENTIST. Gutenschach adds Foundation+Theorist=STUDY, Foundation+Technician=LABORATORY, Theorist+Reporter=REVIEWER, and Technician+Reporter=PRINTER. Scientist compounds in Prince are effectively triple compounds: Foundation+Theorist+Technician=UNIVERSITY and Theorist+Technician+Reporter=SPY. Gutenschach adds Foundation+Theorist+Reporter=LIBRARY and Foundation+Technician+Reporter=PRESS.

To extrapolate from pieces alternating two kinds of direction I devised the HEALER extrapolating the Rhino, the ATTENDANT extrapolating the Tapir, the ENGINEER extrapolating the Navvy, and the TACTICIAN extrapolating the Thug. The Healer moves in rectilinear planes and the other three in the same planes as the Reporter. Gutenschach uses these together with their double and triple compounds. The former are Healer+Attendant=APOTHECARY, Healer+Engineer=SURGEON, Healer+Tactician=PHYSICIAN, Attendant+Engineer=PLANNER, Attendant+Tactician=EXPLORER, and Engineer+Tactician=STRATEGIST; the latter Healer+Attendant+Engineer=HOSPITAL, Healer+Attendant+Tactician=ROUND, Healer+Engineer+Tactician=CONSULTANT, and Attendant+Engineer+Tactician=AMBASSADOR.

Since seeing Larry Smith's Li Qi use the Foundation, Theorist, and Study on a square board it has occurred to me that the next stage will be to use similar pieces on a hex board. For these I have devised names based on the honeycomb pattern of hex boards: the MESH extrapolating the Longgirlhexer and the FORAGER extrapolating the Longrangehexer. For their compound I combine the names to give MESSENGER.


The next article, MAB 16: Diverging Further, covers pieces of the kind described here which are also divergent.

Theoretically another piece has the name Ninny, an extrapolation of MAB 12's Hinny with a subset of the Parvenu's move comprising leaps 11 forward and 1 sideways, 5 forward and 6 sideways, 1 backward and 11 sideways, and 6 backward and 5 sideways. However that piece cannot be used on a board smaller than 12x12, nor can Take the Brain's Ninny on a board without directions marked on the cells, so ambiguity can be avoided.

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By Charles Gilman.
Web page created: 2008-05-17. Web page last updated: 2016-05-20