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Children at my school have become very interested in playing chess during morning break and in before/after care. However, they only have a limited amount of time to play and must clean up...so, they cannot leave pieces on the board. In this situation, what is the best way to declare a winner?

Is it fair to use point count for the pieces captured?

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Point count is a fair way to start evaluating a chess position; even the strongest computer engines do so. I see two potential problems:

  1. One player might have less material but an initiative, e.g. a strong kingside attack. On this level, it is not usual to sacrifice material for an initiative, so this might not be a big problem for you.

  2. What constitutes a decisive advantage? One pawn is -usually- not enough to win an endgame, but it might be, when combined with other advantages.

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In my workplace when someone needs to go to a meeting and can't finish a game, we adjourn it.

If camera phones are allowed in your school, take a photo of the position with an agreed indication of who is to move (e.g. you can put a white pawn on h1 if it is white to move).

Of course, if your school doesn't allow camera phones, then it may be that the position is recorded on paper in FEN notation. But this is something else to digest for students with a lot to learn and is not as easy to implement as taking a picture.

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