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According to the current FIDE rules of chess:

The game is drawn upon a correct claim by the player having the move, when the same position, for at least the third time (not necessarily by a repetition of moves):

a. is about to appear, if he first writes his move on his scoresheet and declares to the arbiter his intention to make this move, or

b. has just appeared, and the player claiming the draw has the move.

Watching the current World Cup an interesting episode appeared when Wang Hao claimed a draw against Alexev Dreev. Wang stopped the clock and contacted the arbiter, claiming the draw. The arbiter saw that Wang had not written down his move before claiming the draw. Therefore Dreev got 3 mintues extra time and the clocks were restarted. With only seconds left on his clock Wang wrote down the move he planned to make and stopped the clock again.

Crazy as it might sound, if it now turned out that the position had not been reached for the third time the arbiter would have had to give the game to Dreev (as you apparently can only claim something incorrectly once). Luckily for Wang the position did appear for the third time and the game was drawn.

(more details and pictures about the incident here)

According to live commentator Susan Polgar the rules for claiming the draw have changed several times and are different from federation to federation. I certainly understand Wang as in any other situation writing down the move before you make it is not legal according to the same rules. My brother claimed a draw in England some years ago and then the arbiter told him that he should not have written down his move before he claimed the draw (his GM opponent then deviated and avoided the draw).

Finally my question(s): When did the rules change? What does the USCF/BCF rules say? Why don't the federations follow FIDE on this? Do you know of any other rules?

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FIDE's "Laws of Chess" is a good place to start, as these are generally accepted as the governing rules of the sport: http://www.fide.com/FIDE/handbook/LawsOfChess.pdf

Article five has the general rules for a draw and article nine has more detail on them. Article 9.2 is relevant to your question. It seems clear that the arbiter was correct in Wang's case, as he had not written down his move. Everything that transpired in this case, down to the three minutes of extra time, appear in accordance with FIDE's rules.

Of course, things differ in blitz and speed chess - and this is where I think different federations might really come up with their own takes and interpretations of procedural rules, since these iterations of the game have often been developed in a less formal context.

It's also quite possible that the arbiter in your brother's case simply didn't know the rules.

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My brother claimed a draw in England some years ago and then the arbiter told him that he should not have written down his move before he claimed the draw (his GM opponent then deviated and avoided the draw).

The English arbiter was wrong.

Unfortunately when a low level player makes a claim playing a GM the arbiter can often either automatically take the side of the GM or unconsciously be biased towards the much stronger player. Arbiters are human and can make mistakes and even be prejudiced. Just ask Nigel Short, who has been on the wrong end of some shocking decisions despite being a GM.

What does the USCF/BCF rules say?

First note that the BCF (British Chess federation) changed to the ECF (English Chess Federation) a few years ago.

Federations affiliated to FIDE generally follow FIDE rules and this is the case for the ECF. The ECF rules for draws are the same as the FIDE rules for draws.

There are only two exceptions. First, federations may have more strict rules than FIDE. Second federations may have different, less strict, rules for non-FIDE rated tournaments for weaker players, typically young children.

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The FIDE rules that Kenzo cited applied in 2013:

  1. The player intending to claim a draw as a result of 3 occurrences of the same position with the same characteristics* writes down his move on the scoresheet, stops the clocks, and announces his claim to the Arbiter/TD.
  2. If the claim is valid, the game is drawn.
  3. If the claim is invalid, 3 minutes are added to the opponent's clock, and the game is resumed.

Note that Article 8, The Recording of the Moves, specifically states: "It is forbidden to write the moves in advance, unless the player is claiming a draw according to Article 9.2..."

It's also worth noting that if the claim is disallowed, the player must make the move he intended in accordance with Article 4, i.e. if he made the move on the board. Therefore, it is in the player's interest not to touch the pieces while he is making the claim, in case it is disallowed. This preserves his right to make a different move, if he wishes.

*The position is only occurring again if all of the following conditions are met:

  • The same player is on move (no triangulation games, folks)
  • All rights of both players are the same, including castling rights
  • All of the same moves must be available to each player. Specifically, if a pawn could have been captured en passant as the next move in the first occurrence of the position, that occurrence of the position is not eligible to be counted, because the en passant capture is no longer possible in the following occurrences
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  • "Therefore, it is in the player's interest not to touch the pieces while he is making the claim, in case it is disallowed. This preserves his right to make a different move, if he wishes." - This part is wrong on two levels. First, if you touch a piece, you lose the right to claim a draw, even if the claim would otherwise be correct. Second, you may not change your mind after writing down the move; if your claim is denied you must make that move, even if you didn't touch a piece. See rules 9.4 and 9.5.3.
    – D M
    Dec 13, 2020 at 18:34
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For comparison, here's the rule under USCF. It's broadly similar to FIDE's in that you write but not make the move and stop the clock, but the penalty for a rejected claim is 2 minutes instead of 3.

14C2. How to claim.

If a move is required to complete the third occurrence of the position, the player claiming the draw under 14C should write this move on the scoresheet but not play the move on the board, stop both clocks (5I), and state the claim. If no move is required to complete the repetition, the player should stop both clocks without moving and state the claim.

In both cases, if the opponent agrees, the game is drawn. If the opponent does not agree, the claimant may make the claim to a director. If a director denies the claim, the claimant is still obligated to play any announced or recorded move. The director awards the opponent two extra minutes.

Just, Tim. US Chess Federation’s: Official Rules of Chess . United States Chess Federation. Kindle Edition.

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If I remember correctly from when I was first learning chess, draws can result from:

  1. Agreement
  2. 50 move
  3. 3 fold
  4. Not enough material to mate
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