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64 triangles

Introduction

```Dave McCooey told about his chess "our goal was to create the closest hexagonal equivalent to the real game of chess as possible".
Now, i want to do the same with triangle chess. Maybe, better triangle games are possible, and they may be even closer to standart chess. But now it's probably closest equivalent to standart chess (but, maybe, not the best trinagle chess game).```

Setup

```Board is equilateral triangle, with 64 cells, 8 on each side.
Here is empty board, black triangles are marked with "=" (on other diagrams board is not colored):

/\
/= \
----
/\  /\
/= \/= \
--------
/\  /\  /\
/= \/= \/= \
------------
/\  /\  /\  /\
/= \/= \/= \/= \
----------------
/\  /\  /\  /\  /\
/= \/= \/= \/= \/= \
--------------------
/\  /\  /\  /\  /\  /\
/= \/= \/= \/= \/= \/= \
------------------------
/\  /\  /\  /\  /\  /\  /\
/= \/= \/= \/= \/= \/= \/= \
----------------------------
/\  /\  /\  /\  /\  /\  /\  /\
/= \/= \/= \/= \/= \/= \/= \/= \
--------------------------------

There are five possible opening setups, 3 for 2-player game, 2 for 3-player game. For one player, there are 2 setups: corner and side.

3 Players, corners setups:

/\
/Q \
----
/\K /\
/B \/R \
--------
/\R /\B /\
/N \/P \/N \
------------
/\P /\P /\P /\
/P \/P \/P \/P \
----------------
/\  /\  /\  /\  /\
/P \/  \/  \/  \/P \
--------------------
/\P /\  /\  /\  /\P /\
/N \/P \/  \/  \/P \/N \
------------------------
/\R /\P /\  /\  /\P /\B /\
/B \/P \/P \/  \/P \/P \/R \
----------------------------
/\K /\B /\P /\  /\P /\R /\K /\
/Q \/R \/N \/P \/P \/N \/B \/Q \
--------------------------------

Three players, side setups:

/\
/  \
----
/\  /\
/N \/N \
--------
/\P /\P /\
/R \/  \/R \
------------
/\P /\  /\P /\
/Q \/P \/P \/Q \
----------------
/\B /\P /\P /\B /\
/B \/K \/  \/K \/B \
-------------------
/\P /\P /\  /\P /\P /\
/R \/P \/  \/  \/P \/R \
------------------------
/\P /\  /\P /\P /\  /\P /\
/N \/  \/P \/K \/P \/  \/N \
----------------------------
/\  /\P /\P /\B /\P /\P /\  /\
/  \/N \/R \/B \/Q \/R \/N \/  \
--------------------------------

Two players, corner setup vs side setup:

/\
/Q \
----
/\K /\
/B \/R \
--------
/\R /\B /\
/N \/P \/N \
------------
/\P /\P /\P /\
/P \/P \/P \/P \
----------------
/\  /\  /\  /\  /\
/  \/  \/  \/  \/  \
--------------------
/\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \
------------------------
/\  /\  /\P /\P /\  /\  /\
/  \/  \/P \/K \/P \/  \/  \
----------------------------
/\  /\P /\P /\B /\P /\P /\  /\
/  \/N \/R \/B \/Q \/R \/N \/  \
--------------------------------

Other two are same as three player, but without one of player's pieces.

The best setups are probably where pieces of all (2 or 3) players starts in corners. Games with side setups was not tried.```

Pieces

```Piece, wich usually called "rook" in other triangle chess variants is actually not rook, but crooked rook. In my triangle chess, rook moves along triangles, wich shares sides, always turning left or right, but not both in same move. It's not allowed to make null moves (if you want, you an play game with null moves):

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/  \/  \/  \
------------
/\  /\  /\  /\
/  \/  \/  \/  \
----------------
/\  /\* /\* /\  /\
/  \/* \/* \/* \/  \
--------------------
/\  /\* /\R /\* /\  /\
/  \/  \/* \/* \/  \/  \
------------------------
/\  /\  /\* /\* /\  /\  /\
/  \/  \/  \/* \/  \/  \/  \
----------------------------
/\  /\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------

Optional replacement for rook is crooked rook, wich alternates left and right turns, but it looks like moving along straight line, this piece is often called "rook" in other triangle games:

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/* \/  \/* \
------------
/\* /\  /\* /\
/  \/* \/* \/  \
----------------
/\* /\* /\* /\* /\
/* \/* \/CR\/* \/* \
--------------------
/\  /\  /\* /\  /\  /\
/  \/  \/* \/* \/  \/  \
------------------------
/\  /\  /\* /\* /\  /\  /\
/  \/  \/* \/  \/* \/  \/  \
----------------------------
/\  /\  /\* /\  /\* /\  /\  /\
/  \/  \/* \/  \/  \/* \/  \/  \
--------------------------------

Bishop steps to cell, wich shares corner with starting cell and same-colored (sides of these two triangles are parallel, see also unicorn bellow), may continue moving in same direction. It's bound to board's half. Also note that it's path partially overlaps with crooked rook's path.

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/  \/  \/  \
------------
/\* /\  /\* /\
/  \/  \/  \/  \
----------------
/\  /\* /\* /\  /\
/  \/  \/  \/  \/  \
--------------------
/\* /\* /\B /\* /\* /\
/  \/  \/  \/  \/  \/  \
------------------------
/\  /\  /\* /\* /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \
----------------------------
/\  /\  /\* /\  /\* /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------

Queen, of course, moves as rook or bishop. If you replaced rook with crooked rook, you also may optionally replace queen with crooked rook and bishop compound.

King moves as queen, but only one step away. There is no castling.

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/  \/  \/  \
------------
/\  /\  /\  /\
/  \/* \/* \/  \
----------------
/\  /\* /\* /\  /\
/  \/* \/K \/* \/  \
--------------------
/\  /\  /\* /\  /\  /\
/  \/  \/* \/* \/  \/  \
------------------------
/\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \
----------------------------
/\  /\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------

Pawns moves without capturing one rookwise forward, captures one bishopwise forward. Promotes when they are in position, where it will not be possible to move anymore (note that pawns of corner setup can promote on 8 different cells, pawns of side setup only on one sell, in corner). For double step and other rules, see below.
Here are two examples (pawns from corner setup):

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/  \/  \/  \
------------
/\  /\  /\  /\
/  \/  \/  \/  \
----------------
/\  /\  /\c /\  /\
/  \/  \/m \/  \/  \
--------------------
/\  /\  /\P /\c /\  /\
/  \/c \/  \/m \/  \/  \
------------------------
/\  /\m /\  /\  /\  /\  /\
/  \/P \/c \/  \/  \/  \/  \
----------------------------
/\  /\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------

Knight's move is like rook's step, then bishop's step outwards. Or like two rook's step, when another roo's step not in usual direction. Or like exactly 3-step leaping crooked rook (same as on square board!). It can jump in one of 6 triangles:

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/  \/  \/  \
------------
/\* /\  /\* /\
/  \/  \/  \/  \
----------------
/\* /\  /\  /\* /\
/  \/  \/N \/  \/  \
--------------------
/\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \
------------------------
/\  /\  /\* /\* /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \
----------------------------
/\  /\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------```

Rules

```Pawns, wich have not moved yet, may not capture opponent's pawns, wich also have not moved.

Initial multiple pawn step is possible only in "corner vs side" setup and only for side player: pawns may make up to 3 non-capturing forward steps, until they reaches marked cells:

/\
/Q \
----
/\K /\
/B \/R \
--------
/\R /\B /\
/N \/P \/N \
------------
/\P /\P /\P /\
/P \/P \/P \/P \
----------------
/\  /\  /\  /\  /\
/* \/* \/* \/* \/* \
--------------------
/\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \
------------------------
/\  /\  /\P /\P /\  /\  /\
/  \/  \/P \/K \/P \/  \/  \
----------------------------
/\  /\P /\P /\B /\P /\P /\  /\
/  \/N \/R \/B \/Q \/R \/N \/  \
--------------------------------

En-passant is possible.
All other rules are usual.
Check, checkmate, stalemate rules in 3-player variants may be taken from other multiplayer variants.

Here is another one variant, Grand triangle chess, played on diamond-shaped board. Can be played with two chess sets on two triangle boards.

/\
/K \
----
/\Q /\
/D \/S \
--------
/\U /\U /\
/R \/B \/R \
------------
/\N /\B /\N /\
/J \/G \/G \/J \
----------------
/\G /\G /\G /\G /\
/P \/G \/A \/G \/P \
--------------------
/\P /\P /\A /\P /\P /\
/  \/  \/P \/P \/  \/  \
------------------------
/\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \
----------------------------
/\  /\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------
\  /\  /\  /\  /\  /\  /\  /\  /
\/  \/  \/  \/  \/  \/  \/  \/
----------------------------
\  /\  /\  /\  /\  /\  /\  /
\/  \/  \/  \/  \/  \/  \/
------------------------
\  /\  /\P /\P /\  /\  /
\/P \/P \/A \/P \/P \/
--------------------
\P /\G /\A /\G /\P /
\/G \/G \/G \/G \/
----------------
\J /\G /\G /\J /
\/N \/B \/N \/
------------
\R /\B /\R /
\/U \/U \/
--------
\D /\S /
\/Q \/
----
\K /
\/

D - duchess;
S - princess;
U - unicorn;
J - ninja;
A - archer;
G - girl.

All normal pieces, expect king, moves as in previous game (rook and it's moves in compounds still may be replaced with crooked rook).
King now can step to ANY adjecent triangle (there are total 12 of them). Now king can move to same cells as rook, but is not blockable! To differ it from king of previous game, it can be called "emperor".

New piece is unicorn. It steps to adjecent cell, wich is not bishopwise or rookwise adjecent (this kind of movement further will be called "triagonal"), may continue moving in this way, turning left or right, but not both on same move. As rook, it moves along circle (yes, null moves are not allowed).

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/  \/* \/  \
------------
/\* /\  /\* /\
/  \/  \/  \/  \
----------------
/\  /\  /\  /\  /\
/  \/* \/  \/* \/  \
--------------------
/\* /\  /\U /\  /\* /\
/  \/  \/  \/  \/  \/  \
------------------------
/\  /\  /\  /\  /\  /\  /\
/  \/* \/  \/* \/  \/* \/  \
----------------------------
/\  /\  /\* /\  /\* /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------

It's bound to board's quarter and it also unable to go to corner (or out of corner). Here is alternative board coloring (corner cells are also colored, though unicorns can not go here):

/\
/, \
----
/\= /\
/  \/+ \
--------
/\+ /\  /\
/, \/= \/, \
------------
/\= /\, /\= /\
/  \/+ \/  \/+ \
----------------
/\+ /\  /\+ /\  /\
/, \/= \/, \/= \/, \
--------------------
/\= /\, /\= /\, /\= /\
/  \/+ \/  \/+ \/  \/+ \
------------------------
/\+ /\  /\+ /\  /\+ /\  /\
/, \/= \/, \/= \/, \/= \/, \
----------------------------
/\= /\, /\= /\, /\= /\, /\= /\
/  \/+ \/  \/+ \/  \/+ \/  \/+ \
--------------------------------

Duchess is compound of rook and unicorn. Princess is compound of bishop and unicorn.

Ninja and archer are leapers, like knight, other pieces don't obstruct thier path.
Ninja steps diagonally, when triagonally outwards (as knight, can reach one of 6 cells and it's colorswitching):

/\
/  \
----
/\  /\
/  \/  \
--------
/\* /\* /\
/  \/  \/  \
------------
/\  /\  /\  /\
/  \/  \/  \/  \
----------------
/\  /\  /\  /\  /\
/  \/  \/J \/  \/  \
--------------------
/\* /\  /\  /\  /\* /\
/  \/  \/  \/  \/  \/  \
------------------------
/\  /\* /\  /\  /\* /\  /\
/  \/  \/  \/  \/  \/  \/  \
----------------------------
/\  /\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------

Archer steps orthogonally, when triagonally in same direction or triagonally, when orthogonally in same direction (also can reach one of 6 cells, but this time it's colorbound, like bishop):

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/  \/* \/  \
------------
/\  /\  /\  /\
/* \/  \/  \/* \
----------------
/\  /\  /\  /\  /\
/  \/  \/A \/  \/  \
--------------------
/\  /\  /\  /\  /\  /\
/  \/* \/  \/  \/* \/  \
------------------------
/\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/* \/  \/  \/  \
----------------------------
/\  /\  /\  /\  /\  /\  /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------

Girl is another pawn-like piece, moves without capturing 1 orthogonally forward, captures 1 triagonally forward. Promotion rules are same.

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/  \/  \/  \
------------
/\  /\  /\  /\
/  \/  \/  \/  \
----------------
/\  /\  /\  /\  /\
/  \/  \/  \/  \/  \
--------------------
/\  /\  /\  /\c /\  /\
/  \/m \/c \/  \/  \/  \
------------------------
/\  /\G /\  /\  /\m /\  /\
/  \/  \/m \/  \/G \/  \/  \
----------------------------
/\  /\  /\  /\  /\  /\c /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------

There is no castling.
Pawn and girl can make any number of non-apturing moves towards center line (any combination of orthogonal forward directions may be used during this move), can be captured en-passant by pawn-like piece of either kind. Stalemated or bared player loses.

Optional rule: when piece captures one of opponent's compound pieces, it promotes. Pieces with rook's moves promotes to pieces with crooked rook moves, piece with unicorn's moves promotes to pieces with crooked unicorn's moves (see below). Leapers (knight, ninja and archer) promotes to compound of all three leapers. Pawns and girls are unaffected, but they will be able to promote (in board's corner) to pieces, wich comes after promotion of other pieces (still able to promote to normal pieces). Bishops and emperor are not affected at all.
Crooked unicorn alternates left and right turns.

/\
/  \
----
/\  /\
/  \/  \
--------
/\  /\  /\
/* \/  \/* \
------------
/\  /\* /\  /\
/  \/  \/  \/  \
----------------
/\  /\  /\  /\  /\
/* \/  \/CU\/  \/* \
--------------------
/\  /\* /\  /\* /\  /\
/  \/  \/  \/  \/  \/  \
------------------------
/\  /\  /\  /\  /\  /\  /\
/  \/  \/* \/  \/* \/  \/  \
----------------------------
/\  /\* /\  /\  /\  /\* /\  /\
/  \/  \/  \/  \/  \/  \/  \/  \
--------------------------------

Another one triangle variant: one of setups from first variant, but bishop is replaced with unicorn, pawn with girl, queen with duchess, king with duke (steps one orthogonally or triagonally, royal) and, optionally, knight with archer.```

Notes

```It's possible to play according to rules of different historical ches variants on same board. Chaturanga-shatranj-makruk queen moves 1 step like bishop, chaturanga-shatranj bishop leaps 2 diagonally, chaturanga-makruk bishop (or silver general) moves like this  (from side setup):

/\
/  \
----
/\  /\
/  \/  \
--------
/\* /\* /\
/  \/* \/  \
------------
/\* /\SG/\* /\
/  \/  \/  \/  \
----------------
/\  /\* /\* /\  /\
/  \/  \/  \/  \/  \
--------------------
/\  /\  /\  /\  /\  /\
/  \/* \/* \/  \/  \/  \
------------------------
/\  /\* /\* /\  /\  /\  /\
/  \/* \/SG\/* \/  \/  \/  \
----------------------------
/\  /\  /\  /\  /\  /\  /\  /\
/  \/  \/* \/* \/  \/  \/  \/  \
--------------------------------

Shatar queen is like rook, wich also can step diagonally.
Other rules are as in chosen game (sometimes promotion rules must be thinked out before playing).