Help For QuadratureIntroductionWelcome 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) 1996Author'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.
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