Draw by repetition

Note: In the domain of composition the distinction between genotype and phenotype is not the only decider  As both the past of the diagram and the future play options are to some degree unknown, conventions were added to fill in the blanks. In combination with repetitions, interesting puzzles can be made.

Incredibly done sir!

Draw by repetition is one of my fallback tactics if I'm losing horribly and the opponent doesnt realizes it

Is that also part of your game preparation? Like, when you meet a strong but sloppy opponent, do you prepare for that by making a 1000 different repetitions?

I just do the bishop opening and move my queen h 6

In chess, a draw can occur in several ways, one of which is the "threefold repetition" rule. This rule states that a player can claim a draw if the same position occurs three times during the game, with the same player to move each time. The three positions do not have to be consecutive, but they must be the same position with the same player to move.

I'm almost certain that castling rights are relevant, regardless of available moves. E.g. 1. Na3 Na6 2. Rb1 Nb8 3. Ra1 Na6 4. Nb1 Nb8 . . . is no longer the starting position.

Just to reiterate.  Semantics trying to say that temporarily stopped castling is the same as permanently stopped castling runs up against both FIDE and US rules saying they are different.

A position with temporarily blocked castling ability versus one with all the same pieces on all the same squares (and the same person on the move) but with permanently lost castling rights are different positions, not the same.

from FIDE rule 9.2 while 3.8b1 and 3.8b2 differentiate between castling being temporarily illegal and permanently illegal.

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 its
castling rights, if any, only after it is moved.

From US Chess rule 14C (8A3 and 8A4 differentiate between castling being temporarily illegal and permanently illegal.  Those two different types of illegality make for different positions even if everything else is the same.  There is a difference between having the right to castle (existing on the first move) and having the current ability to castle (not existing on the first move - barring some Chess960 positions).

The game is drawn upon a correct claim by the player on the move when the same position is about to appear for at
least the third time or has just appeared for at least the third time, the same player being on move each time. In both
cases, the position is considered the same if pieces of the same kind and color occupy the same squares and if the
possible moves of all the pieces are the same, including the right to castle

As an arbiter in FIDE (higher than NA) and a tournament director in the US (hire than LTD) I would have no qualms ruling that a position with a temporary block against castling is different from a position with a permanent block against castling.

The distinction between temporary and permanently disabled castling is inaccurate. Even when no castling is possible in any future - which may be interpreted as permanently disabled castling - one can still have castling right per the same position articles. The right to castle is only determined by the game history and passed on like a noble title. Did your king and rook never move then they are considered to have retained the castling right they received at the game start, even when it is utterly impossible to ever cash in on that right! The common example is when check forces your king to move. Permanently disabled but yet castling right exists when verifying for a triple repetition later! What USCF says about it I don't know and don't care. 

Btw, Fischer already queried FIDE on this rule 50 year ago after he avoided an extra repetition which would have saved him some clock time until the next time control. He got essentially the same reply (after the game). The text of these laws has been rephrased since but their proper understanding has remained the same.

Perhaps redundant but it's worth examining the statement: "When a king or a rook is forced to move, it will lose its castling rights, if any, only after it is moved." This is indeed true but it's not a chess law. It is the the self-evident consequence of the law that prescribes that castling rights only depend on past events. The issue of king or rook being forced to move is of zero significance simply because the future of the game has zero impact on determining castling right. And that is the same reason why the distinction between permanent loss of castling right and temporary loss of castling right is utterly meaningless. It only leads to confused interpretations of the rules and ought to be removed from any text on the laws of chess.

I think some people are erroneously interpreting the bolded phrase by thinking it only refers to the possible moves in the current position.  It actually refers to the possible moves that can be made at some current or future time during the game.  Temporarily being unable to castle king-side still means that castling king-side is potentially available.  If the king-side rook moves and then moves back the position is different because castling king-side is no longer available for that player in that game.

9.2.2
Positions are considered the same if and only 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. Thus positions are not the same if:
9.2.2.1
at the start of the sequence a pawn could have been captured en passant
9.2.2.2
a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.

That said, after 1 d4 e5 2 e4 exd4 3 Qxd4 Qe7 4 Nf3 Nf6 5 e5 d5 there is a position where exd6 e.p. would be possible if the Black Queen was not on e7 but since it would be illegally allowing check e.p. is not available.  Since the Black Queen is currently on e7 that means it would be a valid three-fold after 6 Nc3 Nc6 7 Nb1 Nb8 (2nd time) 8 Ng1 Ng8 9 Nf3 Nf6 (3rd time).

I've been an arbiter for hundreds of thousands of games over four decades and this type of three-fold has never come up.

@jetoba: You missed the point. The castling right is a different interpretation of the possible moves of all the pieces of both players because it is not about possible moves in or after the present game state. It addresses the possible moves of the castling pieces as divinely assigned at the start of every game and only lost after the dumb action of moving the king or rook involved. Nothing in the analysis of game futures ever affects that verdict. Note that this is different for the e.p. move or for all the other pieces where the interpretation depends on moves which are actually executable. To define it formally: the attribute of possible move for castling pieces is assigned as a noble title at the start of the game and only retracted when its conditions of motionlessness are violated. You and many of your peers have not understood this all your lives possibly as a result of USCF background! Please note that the explicit case with regard to "only losing castling right after a forced king/rook move has been executed" is fully consistent with my argument. But to anyone understanding the actual rule the highlighting of this case is redundant. The answer was always trivial.

Note that I have a pedigree of my own in this field. As a composer of retrograde problems I have produced a number of castling/repetition based problems. Game arbiters meet these situations perhaps a few times in their lives though the Fischer case is not unusual. Composers always look for trouble and this is one of the great places where we find it. And it forces us not just to know the rules but interrogate FIDE on them and demand clarification on details. And sometimes we change the rules a bit but not on this point.

Note that there are deeper layers of this issue founded in the understanding of article 3 with its "legal moves" of a piece. Are the legal moves a private property of a piece (or 2 pieces) or a property of the product of a piece with a context? What context precisely? Is a possible move the same as a legal move? Even when the answers appear obvious there are instances where things aren't quite that simple. 

Aristokle, if you are saying that a position with all the pieces on the same square, person A on move, but castling possible is different from a position with all the pieces on the same square person A on move but castling not possible are two different positions then we agree and I was making the emphasis to show that even though there are others who do not agree.

If you are saying the two different positions are the same then we do not agree and I would not rule them the same if called to the board.

Yes, it's all about language. We agree on the same positions I suppose if that means that a camera shows the same pictures. The issue are "the possible moves". Not all "possible moves" per the "same position" evaluation need to be possible in the present position or in any future of that position. Concretely, "castling right" may exist as a possible move - and continue to exist while the castling pieces remain motionless - even when we can prove that the castling move can never be legally executed!

I find threefold repetition rule so annoying! I forget about it and draw games in winning positions.

Why are you repeating moves in winning positions? Shouldn't you try to win instead?

To simpify things further. Positions with and without "castling right" are never the same, not even when both offer no opportunities to ever execute the castling move. "Castling right" is always classified as a "possible move" even when the move is impossible in the remaining part of the game. Which obviously implies there is no significance attached to the concepts of "temporarily stopped castling" and "permanently stopped castling". These are stopped actions" while "castling right" is not an action but a token carried forward in the game by kings and rooks.

Btw, en passant right is not the same. Positions with or without en passant right are the same when the en passant move cannot be legally executed in both - which happens when the e.p. move would cause a selfcheck! That's why Andrew Buchanan introduced the concepts  phenotypal and genotypal as attributes of "en passant right" and "castling right" respectively.

The main reason people repeat the position is that any deviation may be losing for one, or both, players. Changes to castling rights may change the outcome, so the positions cannot possibly be considered equal. There are some aspects of the threefold repetition rule that irk me though, but this castling rights business is pretty straightforward.