NOTE: This document is provided for informational purposes only. If this document is found to be in disagreement with the official rules as provided by an official reference,
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There are two sides, White and Black. White always goes first, which theoretically gives Black a slight advantage. The two sides take turns. No side may skip a turn, but either side may concede the game.
The game is played on an 8 × 8 checkerboard. The checkerboard is placed so that White has a light-colored corner square at his or her right hand, and the same is also true for Black.
Each side gets sixteen pieces: one each of a king and a queen, two each of bishops, knights and rooks, and eight each of pawns. The initial placement of these will be illustrated in the next section.
The objective of the game is to trap your opponent's king so that there's no escape: if he stays put, he's captured; if he moves, he's captured; and no other piece can rescue him. Of course your opponent is trying to trap your king likewise.
There can only be one piece on a space at a time. Centering the pieces is a preference, not a requirement: the important thing is that the placement of the pieces be unambiguous, by making sure the base of a piece is strictly within a light- or dark-colored square, and not straddling a square of the opposite color.
White always goes first. Black makes the second move, and they alternate on and on until either one player wins, one player resigns, a stalemate is reach or there is some other draw. No player is allowed to skip a turn.
It is an actual rule that once you touch a piece you're committed to moving that piece that turn, and must make a valid move with that piece even if it is strategically disadvantageous. This rule is generally enforced even in an informal context, though it may be relaxed for coaching.
When not capturing an opponent's piece, a player may only move one piece (except in the special case of castling, in which case he or she moves two pieces of his or her own side).
When capturing an opponent's piece, a player may only move two pieces: the captured piece, which is then moved off the board, and their own piece, which then takes the place of the captured piece (except in the case of en passant, which will be explained later on in this document).
Under no circumstance can a player legally change the position of more than two pieces in a single turn. I'm not aware of any chess variants in which this is not the case.
In an informal context, a player may request to take back a move, and the opponent may grant that request. In a tournament, no valid move can be taken back.