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3-player Honeycomb Chess

Introduction

My variant Honeycomb Chess was designed to extend standard Chess to 3 dimensions with full-strength (or as a subvariant, double-strength!) pieces while retaining the original automatic rule that diagonal and Knight moves always take a piece forward or backward. For 2 players the geometry achieves that very effectively, with pieces inheriting most of their character from 2 dimensions. The drawback is the difficulty extrapolating a geometry with hex boards as ranks to more than 2 players. As ranks and files are not interchangeable by rotation, you cannot have two pairs of players playing across each other as in my own Fivequarters, or a player starting in each corner of a uniformly enlarged board as in 4 Armies.

2d Hex variants can often be extrapolated to 3 players. My own hex variants for 2 or 3 players on the same board (and page) include first Anglojewish Chess, from which the name of the Finch below derives, and more recently Hexgi and AltOrth Hex Chess. As this depends on players being in 3 of the 6 directions away from the centre, applying it to 3 dimensions means rotating the board. This replaces the change-of-rank rule for Bishops and Knights with a change-of-level rule, so there is still some restriction on these. This change now reflects the 2d change-of-file rule, which as a bonus restores the ratio of capturing to noncapturing Pawn moves to that of FIDE Chess.

Since posting this variant I have gone on to use a smaller board with this geometry (but for only 2 players) for Lengthleaper Hex Chess, and larger ones (with 4 players) for the second and third variants in my Armies of Faith series.

Setup

This variant reverses 2-player Honeycomb's 8 triangles of side 5 cells to 5 triangles of side 8 cells, to retain 8 ranks for each pair of players. This raises the number of cells by half from 120 to 180, maintaining both piece density (each player has as many pieces as in 2-player variants) and four-step range of diagonal moves. Levels are lettered from a-e, as these are no longer ranks. The 36 columns (too many to be covered by single letters) are numbered in the following order:

88 78 68 58 48 38 28 18
77 67 57 47 37 27 17
66 56 46 36 26 16
55 45 35 25 15
44 34 24 14
33 23 13
22 12
11

Columns dividing by 3 exactly are purple on levels a/c/e and yellow on levels b/d.
Columns dividing by 3 with remainder 1 are orange on levels a/c/e and blue on levels b/d.
Columns dividing by 3 with remainder 2 are green on levels a/c/e and red on levels b/d.
Individual cells have the level letter interposed between the column digits.

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In the basic variant corner columns contain the pieces RQKQR, like a 5-file version of the back ranks of John Groeneman's Half Chess, with Queens on their own colour. The two columns adjacent to each corner have the same player's BNFNB, where F is a Finch physically represented by an inverted Rook. The three remaining columns adjoining each of those pairs are filled with Pawns. The third army can be represented by both armies of a third set distinguishable from the two identical sets.

This diagram applies to levels A and E:

This diagram applies to levels B and D:

This diagram applies to level C:

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In 3-player Wildhoney Chess corner columns become (from top to bottom) RQKGR, where G is a Gnu. The adjacent columns become BCNCB, where C is a Camel. For this version it may be best to use three easily distinguishable sets, one for each army, with e.g. White pieces representing KQBBRP and Black ones representing -GCCNP.

This diagram applies to levels A and E:

This diagram applies to level B:

This diagram applies to level C:

This diagram applies to level D:

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Pawnless subvariants of both are also possible for the same reason as Half Chess, the shortness of the second-rank pieces' moves on the board. These would not however save on physical pieces, as they would still require the back ranks of three FIDE sets.

Pieces

Pieces common to both variants:
The PAWN always moves to an adjacent column. Red Pawns increment their column by 1 or 11, Yellow Pawns increment by 10 or decrement by 1, and Blue Pawns decrement by 10 or 11. Vertically, Pawns move to an adjacent level when capturing and otherwise remain on the same level, corresponding to how 2d Pawns move relative to files. Pawns have 2 noncapturing and 4 capturing moves on inner levels and 2 of each on Rook levels, twice the FIDE numbers of moves. Each player starts with 15 Pawns.
The ROOK moves any distance through empty intermediate cells along Hex orthogonals within levels, cycling through the level's three colours, or along columns between levels, alternating between the column's two opposite colours. These add up to 8 directions, twice the FIDE number, falling to 7 from a Rook level, 6 from a rectangular face, 5 from the edge of a Rook level, 4 from a corner column, and 3 from a vertex. Each player starts with 2 Rooks.
The BISHOP moves any distance through empty intermediate cells along square diagonals, always changing level and column at the same rate, as it does file and rank in 2d, and cycling through all six colours in the obvious spectral order. There are up to 12 such directions, 3 times the FIDE number, falling to 8 from a rectangular face, 6 from a Rook level, 4 from an edge, and 2 from a vertex. It cannot start and end a move on the same column or level, and can reach the entire board. Each player starts with 4 Bishops.
The QUEEN combines the Rook and Bishop moves. This gives up to 20 directions, falling to 14 from a rectangular face, 13 from a Rook level, 9 from the edge of a Rook level, 8 from a corner column, and 5 from a vertex. Each player starts with 2 Queens in the basic variant and 1 in the Wildhoney one.
The KING moves in the same directions as the Queen but only by one step per move. Each player starts with 1 King, and must hang on to it!
The KNIGHT moves either 2 columns (in the same direction) and 1 level or 1 column and 2 levels. From a centre cell (3c5, 3c6, 4c6) it has 24 destinations, but this number drops rapidly as it approaches a face. It cannot be blocked. It cannot start and end a move on the same column or level, although unlike in FIDE Chess it can lose the move in 5 moves. It always moves to a cell of a different, but not opposite, colour. Each player starts with 4 Knights in the basic version and 2 in the Wildhoney version.
Pieces specific to the basic variant:
The FINCH is a curved Rook, which makes a 60° turn left or right between each step of its move, but not mixing the two in one move. It is blocked by intervening pieces on the circuit, though not on the cell being encircled. For example the Red Finches can make their first move along the circuit 1c2-1c3-2c4-3c4-3c3-2c2 once the 1c3 and 3c3 Pawns are clear of it, even if the 2c3 Pawn is unmoved. The Finch alternates between cells of the two colours other than that of the cell being encircled. As there are no orthogonals at 60° to columns, Finches moving between levels can only do so one step straight up or down. Each player starts with 2 Finches in the basic variant.
Pieces specific to the Wildhoney variant
The CAMEL moves either 3 columns (in the same direction) and 1 level or 1 column and 3 levels. On a large enough hex-prism board it too would have 24 destinations but on this one the best that it can manage is 18, from the middle of a Queen level (3b5, 3b6, 4b6, 3d5, 3d6, 4d6). It cannot be blocked. It cannot start and end a move on the same column or level, or an even number of levels apart. It always moves to a cell of an adjacent or opposite colour. Both the last two characteristics reflect its inability to lose the move, although like the Bishop it does lose its 2d and cubic colourbinding. Each player starts with 4 Camels in the Wildhoney version.
The GNU combines the Knight and Camel moves. On a large enough board it would have 48 destinations but on this one the best that it can manage is 36 (24 Knight + 12 Camel) from the centre cells. It cannot be blocked. It can triangulate in a Camel move and two Knight ones. Each player starts with 1 Gnu in the Wildhoney version.

Rules

Play proceeds in anticlockwise order starting with Red. As Pawns start on what is effectively their third rank there is no initial double-step move and therefore no En Passant. As this variant is both 3d and 3-player it will come to no surprise to those who know my variants that there is no Castling!

Pawns that have no further move are promoted to another capturable piece from the relevant variant's array.

A player is checkmated when their King is threatened by the player about to move. The first player checkmated loses and their pieces are recruited by the checkmating player. Whichever remaining player checkmates the other wins.

Notes

The basic version inverts half the Rooks for Finches ro make "Rook level" unambiguous and ensure that all longest-range pieces are at the back. Descriptive notation may qualify Queens (basic) and Rooks (both) as upper/lower, Finches (basic) and Knights (Wildhoney) as left/right, Bishops (both) Knights (basic) and Camels (Wildhoney) as upper/lower left/right, and Pawns by the corner-column piece followed by left/centre/right.

In these variants the hex diagonal and hybrid diagonal are not used. As with the 2-player version, double-strength subvariants are also possible in which hex diagonals are treated the same as orthogonals, hybrid diagonals the same as standard diagonals, and obliques extrapolated from there. This version has the same effect on most pieces as it does for two players except that Pawns gain the hex-diagonal forward noncapturing move, as well as capturing moves along the two forward hybrid diagonals above and below it, to become Pawnouts. Note that the double-strength counterpart of the Finch is termed a COHEN as of February 2008.



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By Charles Gilman.
Web page created: 2006-04-13. Web page last updated: 2016-03-08