Forcing players to maintain a mental model of the positions of the pieces by using blindfolds seems interesting, but I've been unable to find any official rules for playing blindfold chess.
What are the rules for playing?
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The rules from Amber are a good start, but in slightly more casual blindfold games, different rules apply.
I'm not aware of any official source for these rules other than common practice in my own blindfold games and observing many other blindfold games.
The main thing here is that two illegal moves loses the game. In the Amber tournament, players have a computer in front of them in order to input moves - the rules above apply more to the situation where two players are just playing without any board (i.e. during a car ride).
These were the rules for the 2006 Amber blindfold tournament with many super-GMs participating:
Rules of play
Rules for the blindfold games
- Play will be governed by the FIDE Laws of Chess, except where they are overridden by the following rules.
- Players are not allowed to record the moves.
- At the start of the game each player has twenty-five minutes on his clock. Before a player makes his move twenty seconds will be added to his remaining time.
- The computer clock marks the end of the time-control period.
- The monitor will show the players when the same position has appeared on the board three times or that the "50 moves rule" can be applied. In this case either player has the right to claim a draw.
- If a player makes an illegal move, the monitor will display the message: "Illegal move, make another move". In this case there is no need for additional action by the player.
- If a player needs the assistance of the arbiter, he may call the arbiter. The arbiter will in this case interrupt the game; interrupting of the game takes about 5 seconds. In this situation the players may not leave the playing area of the playing hall and may not watch the position on the monitors.
- Players, who leave the playing area without permission of the arbiter, will lose the game immediately.
Regulations in case of computer breakdown
- After a computer breakdown, it is forbidden to speak to anybody except the arbiter.
- The games will be continued on empty boards in the two playing halls and, if three games are in progress, also in a room of the hotel.
- The time will be controlled using the Fischer clock; the time will be transferred as accurately as possible from the computer system to the Fischer clock. 25 seconds extra will be added for each move (instead of 20 seconds).
- Two persons will control the game; the arbiter will write the moves down on a scoresheet, which is hidden from the players, and operate the clock. The assistant will play the moves on a pocket set, which is hidden from the players. The arbiter will check the intended move for legality, and if it is legal he will operate the clock and then write the move on the scoresheet. Note: it is possible that it takes a few seconds for the arbiter to check the move and press the clock, but in any case the time taken is not more than for the player to enter the move on the computer.
- The players shall show their moves on the empty board by pointing to the start and destination square of the move they intend to make; at the same time, they will speak the move aloud. If the move spoken differs from the move indicated on the board, then the arbiter shall say, "What do you mean?"
- If a player makes an illegal move, then the arbiter will say "Illegal move" and he will not push the clock. For example, if a player says "Rook takes d6" and the move is not a capture, then the arbiter will say "Illegal move", or if the player shows d1-d6 on the board and says "Queen d6", but the piece on d1 is actually a rook, then the arbiter will again say "Illegal move".
SOURCE: ChessBase News, 2006