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View Full Version : An elegant triple rep definition



Jesper Norgaard
09-05-2010, 07:06 AM
The current rule about triple repetition in 9.2 is the following:

"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.

Positions as in (a) and (b) are considered the same, if the same player has the move, pieces of the same kind and colour occupy the same squares, and the possible moves of all the pieces of both players are the same. Positions are not the same if a pawn that could have been captured en passant can no longer be captured in this manner. When a king or a rook is forced to move, it will lose lose its castling rights, if any, only after it is moved."

I have a proposition for simplifying the latter part of the rule. To me this sounds like a cookbook recipe for the arbiter of how to check if positions are the same. Kind of the rule of opposition for a player to figure out if a pawn endgame is won. However, consider this much simpler definition:

"Positions as in (a) and (b) are considered the same, if any possible series of legal moves are the same."

Hoopla! We avoided definition of pieces and color of pieces, en passant, castling, castling rights, who has the move etc. in one simple step!

So does it hold water? It does unless you can find two positions where all the possible series of legal moves are equal, but the positions are not the same according to the old 9.2. In fact, in the April column of ChessCafe "An arbiter's notebook" Geurt Gijssen shows two positions where he claims this is the case. However, I think his argumentation is bogus, by overinterpreting the part about castling rights. Consider the following position 1:

4kr2/8/8/8/8/8/8/2B1K2R w - - 0 1
White has not moved king and rook during the game, so he has castling rights. It is clear that black has lost his castling rights. In this position 1.0-0 is an illegal move, but this series of legal moves is possible: 1.Bd2,Rg8 2.Bc1,Rh8 3.0-0,Rg8+ 4.Kf2,Rh8 4.Ke1,Rg8 5.Rh1,Rf8 reaching position 2:

4kr2/8/8/8/8/8/8/2B1K2R w - - 0 1
It is clear that position 1 is not the same as position 2 because the series of legal moves from position 2 is not including that white can be castling again.

This is position 3 from Geurt Gijssen's column:

6k1/8/8/8/2b5/8/8/4K2R w - - 0 1
"In this position, the first time it appears in this game, White still has the possibility of castling, even though it is not possible at the moment because of the bishop on c4. White plays 1.Kd2 and loses the right to castle. The game continues 1...Ba6 2.Ke1,Bc4 This is the second time that we have this position, but here castling is not possible. Yet, all possible moves are the same in both positions. In my opinion, all conditions of Article 9.2 are fulfilled. The conclusion must be the positions are the same. Jacob de Boer (The Netherlands)"

I completely agree, and this is also the result of my much simpler rule 9.2 as defined above. Geurt answers in part:
"... When a king or rook is forced to move, it will lose its castling rights, if any, only after it is moved.
The situation was extensively discussed during the FIDE Congress in Dresden 2008. The final result of this discussion was the addition of the last sentence, which came into force on July 1, 2009."
However, that addition is moot, since this definition " ... and the possible moves of all the pieces of both players are the same." does not mention castling rights, so clarifying when these are lost does not matter. It is in fact a completely bogus and superfluous statement that I believe was constructed by Geurt himself.

If the statement had been "... and the possible moves of all the pieces of both players are the same, and en passant rights and castling rights are the same." then the latter definition of Geurt would have made sense, and I agree that under such a definition position 3 and position 4 which appears after 1.Kd2,Ba6 2.Ke1,Bc4 would be different.

However, from a practical point of view, why would you consider two positions where the same series of legal moves are possible, as different? Both players had the same choices and chose to repeat the position. The insisting on castling rights as an important detail here seems academical. I'm sure it would not hold in court.

Consider the following game from the start position:
1.f4,e5 2.fxe5,d5 We have reached position 5.

rnbqkbnr/ppp2ppp/8/3pP3/8/8/PPPPP1PP/RNBQKBNR w - - 0 3
It is clear that one possible mini-series of legal moves would be 3.exd6 en passant, and in fact this is a well-known position for opening theory (ECO A02). The sequence of moves was different (2...d5 instead of 2...d6) but the position is the same.
After 3.Nf3,Nc6 4.Ng1,Nb8 we reach position 6. This is different from position 5 because the move 5.exd6 e.p. is no longer possible.
After 5.Kf2,Nc6 6.Ke1,Nb8 we reach position 7. This is different from position 6 because the sequence of moves 7.Nf3,Nc6 8.g3,Be7 9.Bg2,Nh6 10.0-0 is not possible.
After 7.Kf2,Ke7 8.Ke1,Ke8 we reach position 8. This is different from position 7 because the sequence of moves 9.Nf3,Be7 10.g3,Nh6 11.Bg2,0-0 is not possible.
Only after 9.Kf2,Ke7 10.Ke1,Ke8 (position 9) 11.Kf2,Ke7 12.Ke1 we have reached a position where in fact a player can claim a draw, black can declare a draw since he will play 12...Ke8 to reach position 10, since positions 8-10 are in fact the same.

Consider the following game:
1.e4,Nc6 2.Ke2,Nb8 3.Kf3,Nc6 4.Kg4,Nb8 5.e5,d5+ This is position 11.

rnbqkbnr/ppp1pppp/8/3pP3/6K1/8/PPPP1PPP/RNBQ1BNR w - - 0 6
It is clear that white considering the double push forward by the d5-pawn theoretically has the move 6.exd6 e.p. but this is not a legal move because it would leave the white king in check.
After 6.Kf3,Nd7 7.Kg4,Nb8+ we reach position 12. This is in fact equal to position 11 since en passant is not a possible move.
After 8.Kf3,Kd7 9.Kg4,Ke8+ we reach position 13. This is in fact a different position than 11 or 12 because the following moves are not possible 10.Kf3,g6 11.Ke2,Bg7 12.Ke1,Nh6 13.Nf3,0-0 as well as 10.Kf3,Nc6 11.Ke2,Be6 12.Ke1,Qd7 13.Nf3,0-0-0 is not possible.

Only after 10.Kf3,Nd7 11.Kg4,Nb8+ (position 14) 12.Kf3,Nd7 13.Kg4 black can at last write 13...Nb8+ (position 15) on his scoresheet and declare a draw to the arbiter since positions 13-15 are identical.

Finally, can we construct a position where a dead piece that can't move is equal to having a different one? In fact, this is not possible unless the position is dead.

Consider the following position 16:

4k3/8/8/p1p1p2p/P1PpP2P/2pBp3/2P1P3/4K3 w - - 0 1
It is clear that the Bd3 can never leave from d3, so should this have the same possible series of legal moves like this position 17?:

4k3/8/8/p1p1p2p/P1PpP2P/2pPp3/2P1P3/4K3 w - - 0 1
Yes, the exact same series of legal moves are in fact possible from both positions even though they are both clearly dead positions. But since they are dead already, an arbiter would rule them dead long before a triple repetition claim would ever occur.

Consider the following position 18 from a Blitz game where the white promotion was not completed by changing the pawn for a piece:

r5P1/7K/5k2/8/8/8/8/8 w - - 0 1
It is clear that the pawn on g8 is "dead wood", or in these silicone-driven days perhaps "dead plastic". It can't move and it can't be promoted anymore. But white has the option to use the square h8 because it is not threatened to play 1.Kh8!
In contrast in position 19:

r7/7K/5k2/8/8/8/8/8 w - - 0 1
white has only one legal move, 1.Kh6. It is clear that position 18 and 19 are in fact, different.

Consider the following game: 1.e4,e5 (position 20) 2.Qf3,Qe7 3.Qe2,Qd8 4.Qd1 (position 21) it is clear that the same series of legal moves is not present from position 20 and 21, since white can't play Qf3 from position 21 because it is black's turn.

The full 9.2 rule after my suggestion would be:

"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.

Positions as in (a) and (b) are considered the same, if any possible series of legal moves are the same."

I hope this suggestion can find acceptance. I have tried to turn every stone to find possible problems. The gordic knot should be cut with a sword!

Jesper Norgaard
20-06-2010, 04:39 PM
I sent the suggestion to Geurt Gijssen and he answered in the June 2010 column of "An Arbiter's notebook"

http://www.chesscafe.com/text/geurt146.pdf

Capablanca-Fan
21-06-2010, 08:09 AM
It's not a triple repetition but a double repetition or triple appearance.

Jesper Norgaard
21-06-2010, 10:11 AM
It's not a triple repetition but a double repetition or triple appearance.
I see your point. :doh:

Would a 3-times repetition be better, or would it inherit the same problem?
A triple appearance is a bit vague, I'm sure Obama appeared 3 times in the White House, but he did not necessarily do the same "act" each time.