The Fifty-Move Rule : the fifty move rule is among the least understood rules in Chess . This rule essentially states that if no progress is made after fifty moves by both players then the game is declared a draw . Progress is defined by the capture of any piece, or the movement of a pawn . If fifty moves by each player are made without either of these events occurring then either player may claim a draw .
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A stalemate in chess can be reached if a player is unable to move or checkmate cannot be made due to both sides not having enough pieces.
Unable to move: if, for example, Player A only as a king left and Player B has many pieces left, if Player B were to move a piece on their turn in such a way that meant Player A could not move his king because all movements would cause Player A to be in check, a stalemate would be called.
Not enough pieces to call checkmate: if both Player A and Player B both have a king and a knight each, neither can call checkmate, as a result, a stalemate would be declared.
I've also heard of two other ways stalemate can be declared but I've never experienced them. One is if a move is repeated three times in a row. If this occurs, one player is allowed to call stalemate and no one wins.
The second way is if no pieces have be captured after fifty turns. Stalemate is automatically declared.
Also if both players agree to end the game, the match is a draw, although I don't think it's the same as stalemate.
Since a stalemate is a draw game, in tournament chess or scoring chess, each side would score half a point.