Multiple Occupancy Miscellany

Recently, I have been investigating various possible forms of rules that would allow multiple pieces on the same square.

This article concludes the series by presenting a few odds and ends, scraps left over from the mill.

Rules about Leaving

Most of the Crowd Chess games have assumed that any piece which is on a square where there are multiple pieces may freely move off the crowded square.

Don't Go

"Don't Go" would be the name for a game where a crowd must always be multicolored, so that the last piece of one color would be unable to leave the crowded square unless the opponent also had only one piece there.

In this game, capturing into a crowd would remove one enemy piece from the crowd; because a crowd must always be multicolored, the last enemy piece in a crowd cannot be captured!

An unexpected effect of this rule can be shown in an example: if the square e4 contains two White Pawns and a Black Queen, the Queen cannot move -- is immobilized by the two Pawns -- although adding another Black piece to the crowd would free the Queen, in a change of hostages. However, adding another Black piece would also make the Q vulnerable to capture!

I don't think the "Don't Go" rule makes a good game, at least not by itself. Perhaps in combination with something else?

Stacking and Queueing

Pritchard mentions a game called Stacking Chess; although the full rules are not given, it is known that multiple pieces of one color could be on the same square, that all would be captured at once, and that a special additional rule allowed Castling onto occupied squares. What is not mentioned is the rule about leaving crowded squares.

Unless we assume that the name of the game was poorly chosen, this game must have implemented the well-known "last in, first out" protocol of stacking. For example, if White played Ng1-f3 and then played f2-f3, the Pawn could move but the Knight could not; or, if f2-f3 were played first and then Ng1-f3, the Knight could move but the Pawn could not. The obvious logical complement to stacking would be Fifo Chess.

Limited Occupancy

Limited occupancy would be another type of rule. If the fire department has determined that occupancy of a single square by more than 4 pieces is dangerous and unlawful, the limit is by number; limited occupancy by piece type would permit no more than one Pawn (or King or Rook, etc.) to be on the same square; limited occupancy by weight would permit (for example) no more value on a square than represented by one Rook, or five Pawns, and so on.

The Reverse of a Crowd

Instead of having multiple pieces on one square, how about one piece on many squares? It's here

Crowd Capture

What happens when you make a capturing move that ends on a square where there is more than one enemy piece? Many rules are possible.

The simple cases are that you capture

one enemy piece, chosen by the attacker (in this case multicolored crowds are common),
all enemy pieces, as in Troll Chess
All pieces, friend or foe,
No pieces at all.

However, there are many other possibilities. I'll mention only one.

In many wargames, multiple units on a square are called a "stack", and when the stack is attacked one unit takes care of the defense. In a chess variant, one might have a rule that capturing into a crowd removes one enemy piece from the board, that piece to be chosen by the defender.

Crowd Formation

First, the simple case of voluntary crowd formation: If crowds are dangerous, the rules should allow crowds to be formed freely, simply by moving onto a square that already contains either a crowd or a friendly piece. If crowds are advantageous, the rules should make crowd formation more restrictive (as in Safety in Numbers).

One of the other possibilities is involuntary crowd formation, for example in Falling Off, the momentum of a careening piece can put it on the same square as another friendly piece. There are endless possibilities for involuntary crowds, as they could be formed by momentum, by teleportation, by parachute (for example imagine a variant of Chessgi in which you are forced to place reserves on friendly-occupied squares, and crowd capture grabs all enemy pieces; the character of the game is different -- less intense and explosive perhaps -- and it's a new game).

Another way to limit crowd formation is to permit like pieces to start a crowd, after which any friendly piece can join.

Crowd Dispersal

Once there were laws against loitering (such laws violated the right of peaceful assembly, and are laws no more). A cop would tell a crowd to break up and keep moving along the sidewalk; and so in any crowd more than one turn old, every piece but one would move to an adjacent square. Pawns could reach the first rank, or the 8th without promotion, and new crowds could be formed this way to break up next turn (because pieces that are dispersing can freely move onto occupied squares -- and cannot capture or promote, by the way). First you make a legal move (get out of check!) and then disperse crowds that were formed by your last move (you choose what goes where), including crowds that were formed by your last move's dispersal phase. Crowds are formed freely, captures take one enemy piece off the board. All dispersals take place at the same time, in effect, so the order doesn't matter, and no piece moves more than once in a single dispersal phase -- but a piece can move into an existing crowd and then be dispersed. Since crowds can be recreated by other dispersals, the same square might have a crowd every single move.

Loitering Chess is not play tested. There's some chance that it's an incredibly good game. Both players make as many crowds as possible because it gives extra mobility; and things get complicated. Maybe too complicated?

Summary

When I started to think about having multiple pieces on the same square, it was in the context of a type of Subway Chess (not the same as the game that already used that name!). When I learned that there already existed some chess variants with multiple pieces on a square, I was at first disappointed; but then I realized that their use of the concept of the crowd was limited and unimaginative, and I got irritated.

But then I realized that it was a great opportunity! Crowd Chess was rather unexplored, so I could dash in and plant my flag on all the notable landmarks; and I did. Perhaps I've overlooked a few major mountain ranges or inland seas[1], but I've certainly made a try at discovering all the easily-discovered ideas in Crowd Chess.

[1] You may consider this as a challenge. There's gold in them thar hills!

Written by Ralph Betza.

WWW page created: April 23, 2001.