Star Trek 3-D Chess Rules (rev Roth-2012-09-21)

Charles Roth, 8 October 2010       (Techblog top)
Last updated 23 September 2012

I. Introduction
In the summer of 2010, I bought the instructions for building your own Star Trek 3D chess board by Andrew Bartmess.  My 10-year-old daughter Emma and I proceeded to build it from scratch (which was a lot of fun all by itself) and then played several games.  While the booklet had great construction details, some aspects of the rules puzzled me.

Mr. Bartmess was apparently the first person to try and reverse engineer a playable version of chess from this 1960's prop piece, and while he did a great job, there were a few remaining ambiguities.

So I thought it would be an interesting challenge to extend Mr. Bartmess' work with a clear and concise set of rules that cover the remaining ambiguities.  This turned out to be more of a challenge than I thought!  But with the help of several friends (who cheerfully shot down my first several attempts), I believe that I have achieved a truly consistent set of rules, based on Mr. Bartmess "Federation Standard 5.0" rules booklet.

The resulting game is eminently playable, and in my opinion is very well "tuned".  It balances the the addition of another dimension, with appropriate limitations, which keeps the game from "exploding".  This is a tribute to Mr. Bartmess' original intuitions about how such a game could work.

II. The Rules ("Federation Revised Standard 5.0", as extended & clarified)

  1. Board layout.  The image at the top-right shows the full board in perspective.  There are 3 "main" boards (4x4 squares each), and 4 "attack" boards (2x2 each), aka "AB"s.  The main boards are fixed, but the attack boards can move(!).  More on that later.  (Note that the total number of squares is the same as a regular chess board.)

    The "flattened" diagram to the right shows a view of the board at the start of a game, looking down from above, with some main boards partially overlapping each other.  Each square is uniquely identified by

    1. its file (the letters a thru f)
    2. its rank (the numbers 0 thru 9)
    3. its elevation or z-level (the numbers 1 thru 7)

    The main boards are, starting from the bottom, at elevations 2, 4, and 6.  The attack boards in their starting position are at elevation 3 and 7.  I'll use these square notations to show specific examples of how pieces move.

  2. Starting position.  Shown below.  The white Bishops and Knights are at elevation 2 on the low main board, and the King, Queen, and Rooks are at elevation 3 on the attack boards.  Note that the King and Queen pawns are directly over the Knights.  (Well, just slightly off of directly over, due to the way the board is designed.)

    The black pieces have the equivalent starting position on the high main board and attack boards, but mirrored, so that each side's Queen is, as in normal chess, on its own color.


    (Click to enlarge)
  3. Moves on the main boards.  Moving across the main boards is like normal chess, but with an option to change levels.  Look "down" at, and "through" the stack of boards, and imagine that you are moving a piece in its normal style across the board(s).  The important difference is that you may choose to (try to) end the move on a different level (any different level) than you started. 

    For example, assume we have a completely empty board, with just one Rook at b5(4), meaning file b, rank 5, elevation 4.  For the purpose of figuring out its movement, we call this its "start" or "starting" square.  If we viewed the board "edge on" from the side, and just considered the "b" file, it would look something like this:

         o   o   o
       +---+---+---+---+                    (level 6)
    
                 o   R   o   o
               +---+---+---+---+            (level 4)
    
                         o   o   o   o
                       +---+---+---+---+    (level 2)
    
         8   7   6   5   4   3   2   1      (rank numbers)
    

    Moving along the b file, the Rook could move to any of the squares marked with an "o":

    Note that it cannot move "straight up" to b5(6).  You must move at least one square horizontally in order to move vertically.

    The square you want to move to is called the target square.  Here's how you figure out if you can move there:

    1. Think about the boards.  The "higher board" is the higher of the starting or target boards. 
    2. Ignore any other boards above the higher board.  (I.e. pretend, for this one move, that they don't exist.)

      Example 1: you want to move from a square on level 2 to another square on level 2.  Ignore levels 4 and 6 entirely.

      Example 2: you want to move from level 2 to level 4.  Ignore level 6 entirely.

    3. Now imagine the path from the starting square to the target square.  There is one and only one path the piece can take.  It must be the highest path possible, on the squares between the starting and target squares, on the remaining boards (after you throw away anything above the higher board).

      Another way to think of it is to drip paint from above onto the path on the remaining boards.  The squares the paint lands on is the path your piece must take.

    4. If there's another piece in the way along that path... then you cannot make the move.  Just like in normal 2-D chess.  (Unless you're moving a knight, in which case it doesn't matter.  Again, just like in normal 2-D chess.)

    This sounds complicated, but just put a couple of pieces on the board and try it out, and it will become clear.

  4. Moves on the attack boards.  The attack boards make things more... interesting.  They modify the previous rule... just a little bit.

    The rules described above work (almost!) exactly as before, now including the attack boards as well.  So if a piece starts on level 2 and wants to move to an attack board at level 5, then we "throw away" levels 6 and 7, and find the "highest path" along the remaining boards at levels 1 thru 5.

    The exception is that, in some cases, an attack board may add one (and only one) alternate path.  Here's how that works.

    1. First, calculate the regular "highest" path as described above.  Call this "Path A".
    2. Now, if the "higher board" is a main board, and there is an attack board immediately above it, then treat that attack board as the "higher board".  Throw away everything above that, and recalculate the new "highest path".  This is "Path B". 

      (Note: it does not matter whether the attack board is upright or inverted, only that it is one level above the main board in question.)

    Example 1.  (This example assumes that some attack boards have been moved from their original position.  Movement of attack boards is described later.)

                   +---+---+                     (level 7)
                       |
       +---+---+---+---+                         (level 6)
    
                            +---+---+            (level 5)
                      q       b |
                +---+---+---+---+                (level 4)
                                                 
    
                                      N  
                        +---+---+---+---+        (level 2)
    
          8   7   6   5   4   3   2   1      (square numbers)
    
    The black Queen at b5(4) wants to take the white Knight at b1(2). 

    For Path A, we "throw away" levels 5, 6, and 7, since they are above the starting and target boards.  This gives us a possible path along b4(4), b3(4), b2(2), to b1(2).  But the Queen is blocked by its own Bishop at b3(4), so the capture cannot happen along Path A.

    But in this (rare) case, we can have a Path B, because there's an attack board (level 5) immediately above the "higher board" at level 4.  So now we "throw away" levels 6 and 7, and recalculate the highest path among levels 2, 4, and 5.  This gives us a path along b4(4), b3(5), b(2)5, and then down to b1(2) to take the Knight.

    Example 2:

       +---+---+---+---+                         (level 6)
       
                              p
                +---+---+---+---+                (level 4)
                                          R
                                    +---+---+    (level 3)
                                        |
                        +---+---+---+---+        (level 2)
    
          8   7   6   5   4   3   2   1      (square numbers)
    
    There's only a "Path A" in this case, after we throw away level 6.  The white Rook (R) can take the black Pawn (p), which seems more-or-less intuitively obvious, via b1(3), b2(2), b3(4).  Though the Rook briefly "drops" down to level 2 for one square, this is still the "highest path".

    This all sounds complicated.  But in practice, it becomes quite intuitive.  Find the higher (of the starting or target) board(s), then throw away everything above it, or everything above an attack board immediately above it.  That gives you your one or two paths.  There can only be two paths maximum, no hopping on-and-off attack boards "in the middle", so to speak, unless absolutely required by the "follow the highest path" rule.

    If further clarification is helpful, there are some additional examples.

  5. Pawn Promotion.  This is an easy one.  White Pawns promote (normally) whenever they reach rank 8 or rank 9.  Similarly, black Pawns promote whenever they reach rank 1 or rank 0.

    Note that a Pawn promotes if it moves by itself to the appropriate rank... or if the attack board it is on moves to place the Pawn on that rank.  (See the next section.)

  6. Moving the Attack boards.  Yes, the attack boards can move.  The white player initially owns the attack boards at (mounted in the corner of) squares b1(2) and e1(2).  The black player owns the other two.

    On their turn, a player may, instead of moving a piece, move one of their attack boards.  The board must be empty, or contain only one of their own pawns.

    1. The board may invert.  This means flip to the opposite post on the same square, turning the board upside down (or right-side up, if it was upside down before).  If it was mounted above a main board, now it "hangs" below that same board.  (If there's a pawn on the board, it stays in the same relative horizontal position as it was before the inversion -- it's just moved up or down 2 levels.)  Or...
    2. The board may move 1 or 2 squares along the same file, floating up or down to the appropriate level.  Or...
    3. The board may move 1 or 2 squares along the same file, and invert.

    AB moves are written as QL or KL, and the target square (of the post that the AB is mounted on).

    The movement rule means that an AB is always "stuck" on its starting file, it can only move forwards or back.  Aside from inversions, there are only a few choices.  E.g. a QL at b8(6) can move to b6(4), then to b5(6), and then either to b4(2) or b3(4).  (And then from b3(4) to b1(2).)

    Attack boards ignore any pieces on the main boards when they move, somewhat like a Knight.  An attack board can move to a square (be attached to the post on a square) even if there is a piece on that square.  Of course, you cannot move an attack board to a post that already has an attack board... although a square could have an attack board in the upright position on a post, and another attack board, inverted, "hanging" from the same post, below.

    Moving an attack board that is "piloted" by a single pawn can be a faster way to advance a pawn to promotion, "over" any pieces in its way.  It can also open a path to a piece that was previously blocked by squares on a main board.

    Finally, a player must have at least one pawn remaining (anywhere on the entire stack of boards) in order to move an attack board.  This preserves the essence of normal 2-D end game play.  (For example, a lone King must move, rather than just shuttling the attack boards around.  Otherwise draws become much easier than in 2-D chess.)

  7. Capturing Attack boards.  If the black player captures the last (only) white piece on one of white's attack boards, that board now belongs to black, and may be moved by black in the normal way.  And vice-versa for white.

    A board with no pieces on it is safe and cannot be captured.  But its (most recent) owner can still move it.

  8. Castling.  The King and the Rook in question may not have previously moved.  The King must not be in check on either its original or destination square.

    King-side castling in particular is a good way to move a Rook into play.

    Note that the only squares that exist on rank 0 are a0, b0, e0, and f0 (when the attack boards are in their original position).  So a piece cannot move from (say) b0 to e0.  The same goes for rank 9.  The only exception is the "teleporting" king.

  9. Special pawn moves.  All special pawn moves play out normally:
    1. On a pawn's first move, it has the option to move forward 2 squares.  It can be tricky to remember, however, that a pawn that started at (say) b1(3) and moved to b2(2) cannot then move directly to b4(2), since it has already taken its first move.
    2. If a pawn is on an attack board, and the attack board moves, the pawn has effectively "moved", and no longer has the option to move two squares forward instead of one.
    3. "En passant" captures also work.  But the capturing pawn moves to the square where the captured pawn would have been (had it only moved one square), along the "highest path" that the pawn did travel.  Remember that en passant captures are only good immediately after a pawn moves 2 squares -- "use it or lose it".  (Note that the en passant capture rule also applies if a Rook pawn moves two squares sideways -- see next section.)

  10. Rook Pawn option.  A standard (but considered by this author as "optional") rule handles the case of the "stuck" Rook Pawn (e.g. at a1(3), or anywhere on the a or f files).  The darn thing can't normally go anywhere, unless the opponent is dumb enough to place a piece on the diagonal (e.g. b2(2)), or if the whole attack board moves.

    So this rule allows (only!) pawns on the a or f files to (also!) move inwards one or two (if 1st move) squares, or to attack diagonally inwards.  Once the pawn has landed anywhere on the b thru e files, it behaves normally.

    For example, assume the white Queen's level is at its starting point, mounted on the post at b1(2).  The rook pawn is still at its starting square at a1(3).  Assuming that b1(3) is empty, the pawn can move "sideways" to b1(3), b1(2), or c1(2).  If somehow there was a black piece at b0(3) or b2(2), the pawn could capture it, since the capturing moves are also rotated 90 degrees as well. 

    (Personally, I prefer not to use this rule, as I think the Rook pawns are best used to "pilot" the attack boards and threaten a fast promotion, which more than makes up for their "stuckness".  But it is part of the "official" rules.)

III. Thoughts on game play.

  1. The best way to play the game is to put it on the floor and look down.  This makes it much easier to see "through" the boards and see which squares are directly above and below which.  Remember that the squares line up by color, i.e. a red square is always directly above or below another red square.

    Spock and Kirk may have played looking sideways along the board, but they were, after all, just acting...

  2. Bishops seem less powerful than in normal chess, and Rooks and Queens are probably more powerful.  Center control seems to matter less than opening up long files to attack along.

  3. Pawns are often a nuisance, at least early in the game.  But watch out for those warp-speed "piloted by a pawn" attack boards!

  4. I like to attach little sticky-note tabs to the outside edges of the main boards, to label the ranks and files.  This makes it a lot easier to notate a game, or to replay a game that you wrote down previously.  The Java program can also help clarify legal moves.

  5. Have fun, and forgive your opponent's easy/obvious mistakes while you're both learning.  Live long and prosper!

IV. Specific changes and clarifications

For the most part, the rules above are simply clarifications (I hope!) of Andrew Bartmess' "Federation Standard 5.0" (aka FS5) rules.  However, I have introduced several specific rules that extend FS5 in places that were ambiguous, or may not have been fully thought through.

  1. Path A and Path B movement across attack boards.  FS5 is unclear about whether an attack board provides a single path (above a main board, instead of travelling on the main board), or multiple paths (on the main board and on the attack board).  The Path A and Path B approach is consistent with both the spirit of, and all examples in, FS5, while retaining complete internal consistency.  Plus it's fun, simple, and does not explode into too many alternate paths.
  2. Movement of attack boards: 1 or 2 squares.  FS5 says "move to nearest post", which has a problem.  A black AB at b5(6) could only move "forwards" to b4(2) -- and now it's forevermore stuck oscillating between those two squares!  Furthermore, this puts the squares on the AB in exactly the same (horizontal) position as they were at b5(6)!  So I think that the FS5 "nearest post" rule needs to be interpreted as "move 1 or 2 squares".
  3. AB movement requires one remaining pawn.  In a 2-D end game, it is often critical that the weaker side (think K vs K & R, or K & N vs K, R, & N) must move one of its few remaining pieces.  If the player could, instead, just shuttle an AB around, draws become much easier in those situations.

    On the flip side, the 2-D stalemate rule (where a draw is declared if one side cannot make any legal moves) would be meaningless if AB movement was allowed in all cases.

    There are several possible rules one could imagine that would limit AB movement so as to satisfy the draw and stalemate scenarios.  But given the strategic entanglement of ABs and pawns, this rule seems most natural.

  4. En Passant captures.  FS5 did not specify where the capturing pawn "lands", although the "highest path" rule suggests the answer.  This has been clarified.
  5. Pawn option when AB moves.  FS5 is ambiguous about whether a "piloted" AB move counts as a pawn move.  I think the most natural choice is that a pawn moving on an AB has effectively moved, and no longer has the 2-square option.  Any other interpretation would make it difficult to know, just by looking at the board, whether the pawn had used its option or not.
  6. Rook Pawn option.  As noted earlier, I prefer to play without the special Rook pawn move that allows pawns on the a and f files to move "sideways".  It's rather artificial and potentially quite confusing.  I believe that using the Rook pawn to "pilot" the attack board is extremely powerful and more than makes up for the "stuckness" of the Rook pawn.  It's almost a new kind of piece, as it were.

V. Java Program

I have written a small Java program that implements these rules.  It does not play the game on its own, but rather validates moves, provides the ability to save and restore games, display a (somewhat clumsy) 2D representation of the board, and so forth.

You can download it directly as st3d.jar, and run it with Java 6 or higher as "java -jar st3d.jar".  (Run it as "java -jar st3d.jar --help" to see additional command line options.)  Or you can download the source from my svn repository at svn://caucus.com/st3d/trunk.  The current version will play through the sample game accurately, but it is still considered "experimental" and not 100% complete.

VI. Acknowledgements

I would like to acknowledge several people for their assistance in putting together this set of clarifications:

VII. Sample Game

I constructed the game below by playing against myself, but attempting to play two very different strategies (personalities?) throughout.  I also "bent" the direction of the game to demonstrate several key ideas:

  1. The strategic power of the "piloted" ABs.  I believe that the "warp speed" promotion threat will be a key element of any decent game.
  2. How the Path A / Path B rule comes into play -- and how rare it really is.
  3. Center-control strategies (from traditional 2D chess) vs. pushing piloted ABs forwards.
  4. What "en passant" looks like in 3D.
  5. The challenges of the end-game in 3D.

This game starts out with the official rules, including the special rook pawn option to move sideways.  At move 35, I split the game in two: how the official rules would play out, and then a separate thread for playing the game without the rook pawn option.  Both illustrate interesting (and different) aspects of play.  Several "saved" game positions (to load into the Java program) are available; see the links in the game record.