3-Player Chess I

Setup

The board is (supposed to be) an equilateral triangle, with 'square' spaces; there are 10 spaces along each edge.

An (admittedly rather awkward) ASCII representation would be:

.....
.....\
.....\\
.....\\\
.....\\\\
..........
..........
..........
..........
..........
where spaces connected by slashes are considered adjacent

The pieces are set up as shown here:

kcsp.
cgdp.\
sdrp.\\
ppp..\\\
.....\\\\
..........
ppp....ppp
sdrp..prds
cgdp..pdgc
kcsp..psck
Pieces are represented by their initials as given below; each player has a camp of 15 pieces in a corner

'forward' for a given player is towards the edge opposite the player's camp; on a player's central diagonal, either possible direction may be regarded as forward

N.b. A diagonal move cannot cross the centre, as all 3 cells surrounding it are orthogonally adjacent
N.bb. This shape of board was selected because it can be emulated by simply ignoring one quarter of a 10x10 board and warping the rest accordingly, as in the ASCII diagram

Pieces

The Pawn

The pawn moves as an orthodox chess pawn, i.e. one step straight forward without capturing, or one step diagonally forward to capture.
It does not have an initial two step capability, and thus there is no en-passant capture
It is written as mfWcfF in Betza's funny notation

The promoted pawn moves one step straight or diagonally forward whether or not it is capturing
It may also move one step in any orthogonal direction without capturing or one step in any diagonal direction to capture
It is written as fKmsbWcbF (I think) in funny notation and is referred to as a goldsteward by Charles Gilman's 'Man and Beast' classification

The Draught

The draught moves one step in any diagonal direction without capturing; to capture, it jumps over a diagonally adjacent piece, which is captured. It cannot capture by displacement
It is also capable of (though not required to) making multiple consecutive captures
Additionally, for ease of developing what would otherwise be a nearly useless piece, it may make a noncapturing dabbabah or knight leap provided it has not yet been moved
I am unsure how to describe this in funnny notation due to its overtaking capture; In MAB the basic version (without multiple capture or the first-move privelege) is called a twice-pawned overtaking ferz; It may also be referred to as a checker/chequer/etc.

The promoted draught moves as a bishop, and captures by overtaking; it must land on the next square
It is also capable of making multiple captures; however, all but the first must be legal captures for an unpromoted draught
Again, due to the overtaking capture, I cannot describe it in funy notation; The MAB name is late-overtaking bishop

If multiple capture is deemed too powerful for these pieces, I suggest keeping the multiple leaps but capturing only the last piece leapt

N.b. This draught, with promotion, is taken from the version of draughts I grew up with; I am aware that it is different from the better known one played hereabouts...
N.bb. It may be notworthy that due to the topology of the board, neither the draught nor the unpromoted star (see below) is colourbound

The Star

The star jumps two spaces either orthogonally or diagonally, ignoring intervening pieces
It is notable for its 'star triumph' capture (taken from 4-handed Chaturanga) whereby if it moves such that it forms a 2x2 square with three other stars, it captures all 3 others
A star can in this way capture stars even if they are promoted; it may capture an additional piece by piece by displacement, and in the (extremely unlikely) event that it completes a 3x2 rectangle (such that it is in the middle) it captures all five others; it captures stars on its own side in addition to opponents
Other than the star triumph rule, it is notated in funny notation as DA and is better known as an alibaba

The promoted star moves as a normal star wih the additional ability to move as a king; when moving as a king, the star triumph rule does not apply
Star triumph aside, this piece is also known as a KDA in funny notation, a pasha in MAB, or a mastodon elsewhere, among others

The Chariot

The chariot moves as an orthodox rook

The promoted chariot gains a single diagonal step in addition to its normal move
This is variously known as an RF in funny notation, a chatelaine in MAB, a dragon king in shogi, and probably other things besides

N.b. The choice of the name 'chariot' rather than the more common 'rook' is in part an aesthetic choice, with 'rook' in the chess context originally coming from a word for 'chariot', as well as the continued use of the term in xiang qi, but also to avoid an initial conflict with 'rose' (see below)

The Griffin

The griffin (also spelt griffon, gryphon, etc.) moves as it does in Alfonso X's Grande Acedrex, i.e. one step diagonally followed by a rook's move away from the starting square; the funny notation is t[FR]

The promoted griffin gains an additional single orthogonal step; I cannot find an MAB name for this; the funny notation is Wt[FR]

The Rose

The rose's move comprises one to eight steps. Its first step can be to any adjacent square, like the King's move. The second step must be diagonal if the first step was orthogonal, or orthogonal if the first step was diagonal, and must otherwise continue the direction of the first step as far as possible (that is, the second step must involve a course change of 45° compared to the direction of the first step). On the second step, the Rhinoceros will always be a Knight's move away from its original position; on its third and subsequent steps, it continues making the same angular course change from the preceding step as it made from its first step to its second step.
It is NOT the commonly known circular knightrider; rather it is the piece variously known as circular king or qK by Betza, rhinoceros in John Savard's Leaping Bat Chess, or curved double rhino in MAB; a friend of mine refers to it as a primrose
The rose may not make a null move
Additionally, to prevent such a powerful piece coming out too early, the rose may not start its movement diagonally if all orthogonally adjacent spaces are occupied, and vice versa

The promoted rose gains a noncapturing two-space orthogonal leap, i.e. it is a qKmD

N.b. The topology of the board means that in some positions the rose's path may not be a closed ring; getting used to this is part of the strategy

The King

The king moves as in orthodox chess, i.e. one step orthogonally or diagonally. Its royal restriction is not quite as stringently enforced as in orthodox chess; see below

The promoted king moves as an orthodox queen, with the added ability to capture by 'illumination', i.e. it may, rather than moving, capture all unprotected (including protection by the third player) pieces it threatens

N.b. capture by illumination is taken from my interpretation of Tanigasaki Jisuke's Kokusai Sannin Shogi

Rules

Turns

Turn order

The first and second players to move are decided arbitrarily (perhaps play should begin clockwise starting from the youngest player?)
Subsequent turn order is as follows (conditions are evaluated in ascending order (from 1.-10.) and next player is decided by first condition that applies to 1 and only 1; a player cannot have 2 consecutive turns)

A moves after C if:
1. B cannot move
2. B passed his turn
3. A’s king was captured and A can capture either opposing king
4. B’s king was captured and B cannot capture either opposing king
5. A’s king is threatened
6. 6 consecutive turns (3 each; resets if A passes his/her turn) have passed between B and C without A having a turn
7. A threatens C’s king
8. One of A’s pieces was captured
9. 2 consecutive turns have passed between B and C without A having a turn

N.b. the flexible turn order rules are intended to account for the problems of fixed turn order where it is possible, for instance, for a player to discover an opponent's check on the third player and for the second player to capture the third's king without the third being able to do anything about it; they also reduce the first-move advantage

The Cubes

All players except the one who makes the first move begin with a cube
On his/her turn a player may relinquish his cube to the player without a cube in return for making 2 moves
The player may not use the cube to win, or if his/her king is threatened
The player must move 2 different pieces (including drops)
The cubes are optional

N.b. the cubes are borrowed from the Chess Variant Pages' Luo Tuo Qi; they are, also intended to minimise the first turn advantage

Other

A player may pass his/her turn; affects turn order as above; the player to whom the turn is passed may not pass; If he/she does so, he/she forfeits the game
A player may not pass more than twice consecutively; to do so is a forfeit
A player may forfeit; he/she cannot win and play continues as if he/she is passing at every opportunity
The pieces of a player who has forfeit are still subject to capture; in particular, capturing his/her king still grants a win
The kō rule applies (i.e. no repeated positions are permitted – how strongly this is enforced may depend on the context of the game)

Promotion

The promotion zone consists of the back two ranks, opposite the player's camp
A piece which ends its turn in the promotion zone is promoted; promotion is to one kind of piece only, as in Shogi

N.b. the two-rank promotion zone is to compensate for the otherwise excessive effort required to promote the star

Drops

As in Shogi, captured pieces are brought to the capturer’s side to be kept ‘in hand’ and may be dropped instead of making a move
Promoted pieces are demoted on capture
A piece may not be dropped in the promotion zone or on the home square (the King’s starting space)
Pieces must be dropped on empty spaces; a drop cannot capture (exception: a star dropped on an empty space to form a 2x2 square captures by triumph; see above)
Dropped pieces are considered not to have moved
A dropped piece may not place an enemy king under threat

N.b. Drops are optional; if they are to be used, it may be better to play with Shogi-style pieces, which, for the sake of being able to distinguish whose they are, always face forward (see above)

Winning

If a player to whom the turn is passed forfeits, the last player to move wins
If a player forfeits without being passed to, he/she loses and play continues as if he is passing at every opportunity
In the event that a king is captured, turn order is as above; only king-capturing moves are permitted once a king is captured
If only 1 king is captured, the capturer wins
If 2 kings are captured, the last player with a king wins
If all 3 kings are captured, the game is a draw
If a player succeeds in reaching either opponent’s home square and is not displaced by his/her next turn, he/she wins