you write down your own moves (unsure about blitz..). You make your move, hit the clock button and write down your move in that order. It's pretty easy to get used to, and you can do it pretty quickly once you are used to it.
question about chess annotation
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in lightning chess, no way do moves get recorded. in international blitz then a non-player may record them, but it is unusual i think.
In top level blitz the moves definitely get recorded somehow, since we have the scores for all the games in major blitz tournaments. Someone else must record them, although there are these stories about people like Fischer being able to reel off all the moves of all his games in a tournament from memory (!).
There is usually a time delay in regular games, so it gives you a little extra time each turn to write down your move
In the US, players are required to keep track of their own moves, unless they have fewer than five minutes left on the clock. The US Chess Federation's rules for blitz explicitly state that scorekeeping by the players is not required.
In some tournaments (and I think this is more common in Europe), top-level games may be played on the DGT electronic board (see http://www.chessville.com/reviews/Software/DGT_Electronic_Board.htm , for example), which plays just like a regular board, but has a USB connection and automatically registers the moves.
By the way, your original question mentioned "annotation." What players are required to do is keep an accurate record of the moves played; annotation implies notes about the position, tactical possibilities, etc. Such note-taking on a scoresheet is (again, in the US) strictly prohibited.
i have not as of yet played any otb tournaments and i have a question that may be trivial to some, but for me it is still a mystery((:
how do things with annotation work on tournaments, especialy on blitz and lightning chess tournaments? i dont think that the players themselves write the moves during the game (or do they?) - that sounds illogical for me because it is time consuming... who writes it then? do they have a judge that writes it during the game?
can someone plz explain? thx in advance...