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Chess with a Limited Supply of Squares

This file describes a set of chess variants played on normal-sized boards with a limited supply of squares: in other words, instead of the 8x8 board starting off with its normal complement of 64 squares, there are holes in the board.

The Basic Game

The following set of rules is not sufficiently complete to permit a game to be played, but all the games branch off from this set of rules.

Rules of the Basic Game

  1. The rules of FIDE Chess apply except where specifically superseded by the following rules.
  2. The normal setup and pieces are used, on the normal 8x8 board; however, only 32 squares (the squares under the initial setup of pieces) are always present on the board. The entire area between the two armies may be empty, with no squares there.

    Specific games may provide for the presence of more than 32 squares in the initial position.

  3. Jumping pieces (and with the FIDE set of pieces, only Knights are jumping pieces) can leap over empty squares.
  4. Long-range pieces require an unbroken string of squares to use their long-range powers. For example, if a Rook on a1 wants to go to a8, there must be a square at a2, and at a3, a4, a5, a6, a7, and a8.
  5. The rules of the specific games will make it possible to move an empty square from its current location to some other location that currently has no square there. An occupied square can not be moved, and two squares cannot occupy the same location or capture each other (although one can imagine some interesting variants that allow any of these things).

  6. The rules of the specific games may give each player some squares in reserve, that may be placed on the board at empty locations.

  7. Each turn each player may either move a piece from one square to another, move an empty square from one location to another, or play a square from his reserve onto the board. In no game may you move the square your opponent has just moved (that would be silly, you see).

  8. Check and checkmate can be blocked by moving a square.
  9. A stalemated player loses the game; of course, moving a square counts as a move in most games.
  10. The game must be played with at least two different armies. Oh, you can skip this rule and let both sides use the Fide Chess army, but the author of the game would be unhappy.

The Postal Rule

One expects that the game will take more moves to play than FIDE Chess, because of the necessity of moving squares so that the pieces can move. In games played by mail or email, a quicker pace may be desired, so the Postal Rule is supplied as part of the basic game.

The basic rules are modified to allow the players to take two (or even three) actions per turn: first move a piece and then either move or place a square, or even do both (if you can do both, it's the Postal Plus rule).

Note that the rule is not to move the square first because that would become too similar to FIDE Chess.

On the first move of the game, there is no penalty if you cannot move a piece (otherwise, White might be stalemated and lose the game in the opening position, which would be no fun). After that, you must move a piece or lose by stalemate; this is different from the basic game because moving a square does not count as avoidance of stalemate.

Discussion of the Basic Game

This game of course gets some inspiration from Cloudhopper Chess.

When the players start with squares in reserve, and they have a limited number of squares in reserve, and the number is small, it will be difficult to move, and it may be worthwhile to keep one square in reserve in order to help defend your King (or it may be worthwhile to play all the squares to maximize your mobility).

If each player starts with an unlimited number of squares in reserve, soon the board fills up and becomes FIDE Chess. In this case, only the opening phase of the game is affected by the limited number of squares.

If there is no reserve, then the game must start with some number of squares already in place between the armies. This seems less interesting.

Clearly the best and most distinct form of the game is the one with a small reserve, so that form will be covered first.

Hans38 Chess

As you can guess, the chance to win the Hans38 contest had some influence on the size of the reserves in the following rules; however, 3 squares per player seems to be a very good number.

The Rules for Hans38 Chess

  1. The Rules of the Basic Game as given above apply except where specifically superseded by the following rules.
  2. Each player starts with 3 squares in reserve, making a total of 38 squares in the game.
  3. Each player owns the squares in hand and the squares under her starting army, and a player may not move squares owned by the other player.
  4. Moving a piece onto an enemy square captures the square. In other words, a square belongs to whoever last placed the square or had a piece on the square.

    Note: Pawns capture squares by moving straight forward. A Pawn may not capture a square by moving diagonally onto an empty square. Of course, a Pawn, or in fact any piece, can capture a square and capture a piece, both in one move (gambits may be too expensive).

  5. A square moves like a King, Knight, Dabaaba, or Alfil; in other words, one or two locations in any direction, leaping over obstacles as needed.
  6. Squares placed from reserve may be placed on any empty location of the board.

Discussion of the Rules for Hans38 Chess

Given the limited number of squares in the game, and the fact that stalemate loses, and the concept that squares are owned, quick knockouts are always possible. The shortest win by stalemate is 3 turns: White places at a6, Black captures the square, White places at b6, and so on.

The reason for the rule about the way squares move is that I want them to be slow, but it is no good if they are locked within your lines. For example, after Ng1-f3, the square on g1 is empty but cannot make a King move; and when there are so few empty squares available, this feels like bad game design.

Each player's first move must be to place a square on the board, because there simply is no other legal move. After this, it may seem desirable to keep either one or two squares in reserve; one for emergencies, and one to keep for awhile because the squares already on the board are slow, and a square placed from reserve can go anywhere. Keeping two squares in reserve may make your moves too predictable, but on the other hand perhaps you gain a tempo by not taking the time to place more squares. This tension between two strategic choices is part of the design of the game.

Sample Game of Hans38 Chess

This is where we find out if the design was good.

1.  @@f3        @@f6
2.  Ng1-f3      Ng8-f6
3.  @@e3        @g8-e6
If I merely said "g8-e6" it would look like a Pawn move, so I chose the notation "@g8-e6"; then, placement looked to much like short-form algebraic notation, so I decided that "@@f3" was the way to write it.

White's strategy is to place all the squares from reserve, Black's strategy is to try to keep the reserve.

4.  e2-e3       e7-e6
5.  Bf1-e2      Qd8-e7
6.  O-O         @d8-c6
7.  @@d3        Nb8-c6
8.  d2-d3       @b8-d6
9.  Bc1-d2      d7-d6
10. Rf1-e1      Bc8-d7
11. Be2-f1      @c8-a6
12. @c1-c3      a7-a6
13. Nb1-c3      Ra8-a7
14. @e2-e4      @a8-b6
15. e3-e4       @b7-b6
16. Ra1-b1      Ra7-b7
17. @a1-c1      @a7-a5
18. @c1-e2      a6-a5
19. @h1-g3      @a6-c5
Black is clearing out the corners to concentrate towards the middle, White is trying to assemble some mobility from empty squares towards the center.

Some of the moves here were made with a different rule for moving the squares; it is all still legal, but some of the moves may look silly now.

Next, (email removed contact us for address) e5? would be met with 21. e4-e5! and so Black needs to place a new square.

20. @g3-f4      @@h6
21. Bd2-f4      h7-h6
22. @e3-e5      Rh8-h7
23. e4-e5       d6:e5
24. Bf4:e5
Is a Knight worth more than a Bishop in this game?

Should White have pushed and traded? Now each side has one more empty square to move to, so the position is less cramped. Probably (email removed contact us for address) d4 (to be followed by d3-d4) was better.

Black's strategy was strategically logical with my old rules but logistically impossible. The old rule for moving squares was "one space if you can, otherwise you can move two spaces". After I realized I had written down several illegal moves, I knew the rule would be too hard for players to follow, and nobody would like it.

White's strategy of simply leaving the R at a1 looks pretty good. Now I realize that pieces will eventually be exchanged and the character of the game will change drastically as more empty squares become available (this is good, of course); and so the Rook can simply wait there for awhile and preserve itself for the endgame when it can make more Rook moves.

All in all, this seems to be enough of a sample to indicate that it's a good game. Takes a lot of moves, but they're easy moves because it's not a highly tactical game.

A game with more strategy than tactics seems like just the right sort of thing to play, for example, at a birthday party. Fun and relaxed.

Hans38 with Neutral Squares

What if we get rid of the rule about ownership of squares, and just let anybody move any empty square (except, of course, the one just moved by the other player), would the game be better or worse?

1.  @@f3        @@f6
2.  Ng1-f3      Ng8-f6
3.  @@e3        @e3-d5
This is an example of what I didn't like about that rule. Black has "stolen" this square; White can't move it right now, and Black will continue by moving it to e6 and putting a Pawn on it, thus giving himself more mobility than White has; but then White must "recapture" by stealing a square with @e7-f5 then @f5-e3.

This seems like a silly game that isn't chess....

The Game of Infinite Reserves

If you start with an unlimited number of squares in reserve, then of course the board is fully populated after 16 placements each and the game reverts to FIDE Chess; and there's no reason to move empty squares around.

Unless, of course, you add some rule that removes squares from the board.

The obvious rule is that every time a piece leaves a square, the square is removed from the board. It's boring if you start removing pieces too soon, so let's suppose instead that we use the Postal Plus Rule, infinite reserves and you *must* place a square every turn, and start removing squares only after the third turn; that is, starting on the fourth turn, whenever a piece moves the square it leaves is returned to reserves. (When Castling, only the King's square is voided; when capturing en passant, only the capturing Pawn's square is vacated.)

Since you must move a piece every turn, and you must place a square every turn, it follows that the number of squares on the board will be constant. By a happy coincidence, this number turns out to be 38.

Every turn you place a square and move a square, so "stealing squares" doesn't seem very important. We'll use neutral squares, either player can move any empty square except the two that his opponent just touched.

Empty squares move 2 spaces, same as in Hans38.

This game has a snappier pace and a bit more tactics. Even so, it's not as intense as FIDE Chess because "each move next move's madness does prepare": your first action will be to move a piece, and so you must move to a square that is already there; thus, the square you place and the square you move most often determine what you play next move.

Moving Occupied Squares

Empty squares move 2 spaces, same as in Hans38.

An occupied square moves just one space. You can only move squares occupied by friendly pieces.

The square the King is on cannot move.

Add this rule to The Game of Infinite Reserves, and you get a real slugfest; quintuple check should be possible.

This is an excellent game for international snailmail play; the ability to move two pieces at once can save a lot of postage.


Other Games

I can think of several other variations on this theme that would make good games, but since I'm already up to 300 lines I'll stop.
Written by Ralph Betza.
This is an entry in the Contest to make a chess variant on a board with 38 squares.
WWW page created: October 27, 1997.