## Help For Quadrature

### Introduction

Welcome to the network Quadrature server. The rules of Quadrature are below. The commands are the same for all pbmserv games.

### QUADRATURE by Mark Steere (c) 1996

Author's note: Feel free to distribute this document.

```
QUADRATURE - INTRO
==================

Quadrature is a two player strategy game.  Each player
has a set of 16 checkers.  Players start with 9 checkers
on the board with 7 held in reserve.  The board is an 11
by 11 square grid.  Players also have "markers" explained
later in the Rules section.

. . . . , , , . . . .	  OOO   White
. . . . . . . . . . .	  OOOO  |0| <-- White marker
. O O O O O O O O O .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. # # # # # # # # # .
. . . . . . . . . . .	  ###   Black
. . . . , , , . . . .	  ####  |0| <-- Black marker

Players take turns making basic moves.
A basic move is to move a checker *one space* forward,
diagonally forward, or sideways.  Players cannot
move backwards or diagonally backwards.

In the following diagram, white has moved a checker
diagonally forward.

. . . . , , , . . . .	  OOO   White
. . . . . . . . . . .	  OOOO  |0|
. O O O O O O O . O .
. . . . . . . . . O .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. # # # # # # # # # .
. . . . . . . . . . .	  ###   Black
. . . . , , , . . . .	  ####  |0|

"Squaring" is an aggressive maneuver in Quadrature.
To "square" an enemy checker, you move to form a rectangle
on the board with three of your checkers and one enemy
checker.  So you have three "squaring" checkers and
one "squared" checker.

For example:

. . . . . .     . . . . . .
. O . . # .     . O . . # .
. . . . . .     . . . . . .
. # . . . .     . # . . # .
. . . # . .     . . . . . .
. . . . . .     . . . . . .
Black's turn.   Black's squares
a white checker.

The enemy "squared" checker is then removed
from the board and replaced with one of your own
reserve checkers.  Removed checkers are returned to their
original owners.  Players do not take ownership of
each others checkers.

To complete the previous example:

. . . . . .     . . . . . .     . . . . . .
. O . . # .     . O . . # .     . # . . # .
. . . . . .     . . . . . .     . . . . . .
. # . . . .     . # . . # .     . # . . # .
. . . # . .     . . . . . .     . . . . . .
. . . . . .     . . . . . .     . . . . . .
Black's turn.   Black's move.   "Squared" white checker
is converted to black.

Sometimes you can square more than one enemy checker
at once, as shown in the following example:

. . . . . .     . . . . . .     . . . . . .
. O . . . O     . O . # . O     . # . # . #
. . . # . .     . . . . . .     . . . . . .
. . . . . .     . . . . . .     . . . . . .
. # . # . #     . # . # . #     . # . # . #
. . . . . .     . . . . . .     . . . . . .
Black's turn.   Black squares   The two squared white checkers
2 checkers.     are converted to black.

A chain-reaction can happen in Quadrature.  When
you replace an enemy checker with one of your
own reserve checkers, your newly added checker can
square additional enemy checkers.   And so on.

Such a chain-reaction occurs in the following
example:

# . # . . .     # . # . . .     # . # . . .     # . # . . .
. . . . . .     . . . . . .     . . . . . .     . . . . . .
O . O . . .     O . O . . #     O . # . . #     # . # . . #
. . . . # .     . . . . . .     . . . . . .     . . . . . .
. . # . . #     . . # . . #     . . # . . #     . . # . . #
. . . . . .     . . . . . .     . . . . . .     . . . . . .
Black's turn.   Black squares   White checker   2nd white checker
one checker.    converted.      converted to black.

This basic intro gives the main features of Quadrature.
Quadrature gameplay is tense, aggressive, and addictive.  It
has been described as a "sudden death" game.  Once the aggression
starts, annihilation can quickly follow.

QUADRATURE - RULES AND OBJECT
=============================
BASIC MOVES AND THE MARKER
--------------------------
As explained in the introduction, players move towards each
other with forward and diagonally forward single-space moves.
Players can also make sideways moves, but sideways moves are
limited by the use of the "marker".

Each player has a marker which is a flat square chip.  Each
player's marker is the same color as his checkers.  The marker
has a single dot on one face and two dots on the opposite face.
If you make a non-aggressive, sideways move, you must place
your marker on the board with the single dot face up.  You can
put it anywhere on the board.  The location doesn't matter; it's
just showing that you made one non-aggressive sideways move.

|0|, |1|, and |2| in the examples represent the markers off-board,
on-board with one dot showing, and on-board with two dots showing:

. . . . . .       . . . . . .
. . . . . .       . . . . . .
. O . O . .       . O . O . .
. . . . . .       . . . . . .
. # . # . .       . # . . # .
. . . . . . |0|   . . . . . . |1| <-- Black marker now shows "1".
Black's turn.     Sideways move.

If your marker is already on the board with the single dot face up,
and you make a non-aggressive sideways move, you must flip your
marker over so that the two-dot face is showing.  This shows that
you have made two consecutive, non-aggressive sideways moves.
A non-aggressive sideways move is a sideways move which does not
kill any enemy checkers.

For example:

. . . . . . |0|   . . . . . . |0|   . . . . . . |1|   . . . . . . |1|
. . . . . .       . . . . . .       . . . . . .       . . . . . .
. O . O . .       . O . O . .       . O . . O .       . O . . O .
. . . . . .       . . . . . .       . . . . . .       . . . . . .
. # . # . .       . # . . # .       . # . . # .       . # . . . #
. . . . . . |0|   . . . . . . |1|   . . . . . . |1|   . . . . . . |2|
Black's turn.     Black sideways    White sideways    2nd black
move.             move.             sideways move.

If your marker is on the board with the two-dot face showing,
you are not allowed to make a non-aggressive sideways move.
You must make a forward, diagonally forward, or aggressive
sideways move. An aggressive sideways move kills enemy checkers.

Once you have made a forward, diagonally forward, or aggressive
sideways move, you must remove your marker from the board.  It
doesn't matter if it is showing a single dot or two dots; a forward
move always clears your marker from the board.

For example:

. . . . . . |1|   . . . . . . |1|
. . . . . .       . . . . . .
. O . . O .       . O . . O .
. . . . . .       . . . . . #
. # . . # .       . # . . . .
. . . . . . |1|   . . . . . . |0| <-- Black marker now shows "0".
Black's turn.     Forward move
clears marker.

There is no limit to the total number of non-aggressive sideways
moves you can make.  You just can't make more than two non-aggressive
sideways moves consecutively.

This rule was instated because players have a tendency to approach
each other and then stall the game by making an endless series of
non-aggressive sideways moves.  The marker forces players to engage
each other in combat, no matter how reluctant they may be.

SQUARING
--------
Squaring was covered in the introduction, but here I give a few more
details.  A "square" is a rectangle formed by three of your checkers
and one enemy checker.  It must have horizontal and vertical sides. The

square can be anywhere on the board as shown in the following diagrams.
It doesn't matter if additional checkers are on the lines of the square

or in the square or whatever.  Just as long as the square exists.

. . . . . .     . . . . . .     . . . . . .     . . . . . .
. . . . . .     . . # . # .     # . . . O .     . . . . . .
O . . . . #     . . . . . .     . . . . . .     . . # # . .
# . . . . #     . . . . . .     . . . . . .     . . # O . .
. . . . . .     . . O . # .     . . . . . .     . . . . . .
. . . . . .     . . . . . .     # . . . # .     . . . . . .

NO SUICIDE MOVES
----------------
You must not move an on-board checker to any point that completes
an enemy square.  Suicide moves are not allowed, no matter what.

Example of illegal move:

. O . O . .     . O . O . .
. . . . . .     . . . . . .
. O . . . .     . O . # . .
. . # . . .     . . . . . .
. # . # . .     . # . # . .
. . . . . .     . . . . . .
Black's turn.   Black's illegal move
completes an enemy square.

While you cannot *move* to complete an enemy square, you can *add*
new checkers to the board in places that are squared by enemy
checkers.  In the following example, black makes a legal move
to square a white checker:

O . O . O .     O . O . O .     O . O . O .
. . . . . .     . . . . . .     . . . . . .
O . O . . .     O . O . . #     O . # . . #
. . . . # .     . . . . . .     . . . . . .
. . # . . #     . . # . . #     . . # . . #
. . . . . .     . . . . . .     . . . . . .
Black's turn.   Black squares   White checker is converted to black,
white checker.  even though now squared by white.

When black replaced the white checker with one of his own reserve
checkers, the new black checker completed the white square in the upper
left corner of the board.  However the new black checker remains in
place and is not automatically reconverted back to white.

TO CONVERT AN ENEMY CHECKER YOU MUST FORM THE SQUARE
----------------------------------------------------
DURING YOUR CURRENT TURN.
-------------------------
To square and convert an enemy checker, one of your three squaring
checkers must have been moved or added during your current turn.

To continue the previous example, it is now white's turn.  Even though
the black checker in the center of the board is already squared by
white, white cannot immediately convert it back to white, because white

didn't form that square during his current turn.

O . O . O .     O . O . . O     O . O . . O     O . O . . O
. . . . . .     . . . . . .     . . . . . .     . . . . . .
O . # . . #     O . # . . #     O . # . . O     O . O . . O
. . . . . .     . . . . . .     . . . . . .     . . . . . .
. . # . . #     . . # . . #     . . # . . #     . . # . . #
. . . . . .     . . . . . .     . . . . . .     . . . . . .
White's turn    Sideways move   Black checker   2nd black checker
squares black.  converted.      converted to white.

White's aggressive sideways move squares one black checker on the
middle right of the board.  By converting the squared black checker to
white, white squares an additional black checker in the center of the
board.  White then converts this additional black checker to white.
Chain reaction moves, such as this one, can lead to large numbers of
enemy checkers being killed in a single turn.

Once again, squaring is an aggressive action, not a passive situation.
You can only convert an enemy checker to your color when at least
one of your three squaring checkers was moved or added during your
current turn.

Whenever you remove an enemy checker, you always add one of your own
in its place.  So the total number of checkers on the board should
always be 18.

OBJECT
------
There are two ways to win in Quadrature.  If you kill enough enemy
checkers to leave your opponent with two or less checkers on the
board, you win.  Also, if you can get three of your checkers onto the
enemy "home plate", you win.

A player's home plate consists of the three points in the middle of
his side of the board.

. . . . # # # . . . .         . . . . , , , . . . .
. . . . . . . . . . .         . . . . . . . . . . .
. . # . . . . . # # .         . . # . . . . # # . .
. . . . . . . . . . .         . . . . . . . . . . .
. . O O O . O O . . .         . O . # # # # . # . .
. . . . . . . . . . .         . . O . . . . . . . .
. . . . . . . . . # .         . . . . # . # # # . .
. . . . O . . O O . .         . . # # # . . # . . .
. . . . . . . . . . .         . . . . . . . . . . .
. . . . . . O O . . .         . . . . . . . . . . .
. . . . , O , . . . .         . . . . , , , . . . .
Black wins by getting         Black wins by reducing
3 checkers into white's       the number of white,
home plate.                   on-board checkers to 2.

ETIQUETTE
---------
When you square an enemy checker, instead of just taking
it off the board and replacing it with your own, you should
place your checker *on top of* the enemy checker.  When
your opponent realizes what happened, he removes his own
checker from underneath yours.  This will help to resolve
potential disputes before they happen.  Sometimes you will
kill several enemy checkers in one turn, and it can take your
opponent a minute or two to realize what happened to him.

EQUIPMENT
---------
The Quadrature board is an unusual design not used in other
games.  But it should be relatively easy to construct.
Even though the game calls for 16 black and 16 white checkers,
a standard set of 30 backgammon chips will suffice.

I have a rather beautiful Quadrature board made of Corean squares
with resin filled in between the cracks.  The checkers are swirled
polyester Backgammon chips with felt on the bottom.

ORIGINS
-------
For a few weeks I tried to invent a new game playing mechanism.
Something that would extend the set of basic maneuvers like the
Chess take and the Checkers jump.  I found this in squaring.  I
particularly liked the chain-reaction effect of squaring.
Then I wanted opposing forces to sift through one another as
happens in Checkers (Draughts) and Backgammon.

I invented Quadrature in February 1992 and Tanbo in October 1993.
Since then I've tried to invent more games but I haven't really
come up with any workable concepts.

Dennis Landon helped in play testing and shaping Quadrature.  The
original version was smaller, with a different initial configuration
and no markers.  Quadrature won the American MENSA award.```