How many times can the same position repeat?

Why is it so hard to get the actual point of the question?

Let me pose it in another way: Assume the same arrangement of pieces has appeared during the game two times. Can you claim draw by 3-fold repetition? No.

But if the same arrangement of pieces appears during the game three times, can you then claim draw by 3-fold repetition? Yes.

Except not always. Even though the arrangement of pieces may be the same, the position is not always considered having repeated. Among other things, castling rights are considered when evaluating whether the position is the same as a previous one (iow. even though the pieces may be on the same squares as before, if in that previous instance you had a castling right that you don't have now, it will be considered a different position).

So my question is: What is the theoretical maximum number of appearances of the same arrangement of pieces that could happen before you could claim draw by 3-fold repetition (taking into account all those extra requirement posed by the 3-fold repetition rule)?

Why is this so hard to understand? Responding with "claiming draw by 3-fold repetition is optional" is completely and absolutely missing the point of the question.

Heck, playing the game is optional. That still doesn't isn't a valid answer to the question. I'm not asking whether claiming the draw is optional or not. That has absolutely nothing to do with the question.

You are wrong, it's not 3 times, but it is 22!  Maybe a better way to word the question is, "What is the highest possible number of occurrences of a position without 3-fold repetition applying?", in which case that would be 21.  A position can occur 21 times with no 3-fold repetition, but by the 22nd time, there is no way that 3-fold repetition has not occurred.

It must be the same position, with the same player to move, both players having the same legal options.

Let's say, hypothetically, that it is White to move.  White has a pawn on d5, and that pawn is NOT pinned to the King, and Black's last move was c7-c5.  Both sides have not moved their kings.  Both sides have not moved their Rooks (either one of them).  Both sides have no pieces between the King and either Rook, and both sides can legally castle in either direction, meaning neither side is in check, and White is not controlling c8, d8, f8, or g8, and Black is not controlling c1, d1, f1, or g1.  Therefore, you have a position like the following:

Thank you. This is exactly what I asked.

LOL!  He ain't thanking you, fool!

Your post 13 is wrong and your post 21 is useless!

That's the answer.

Regarding Thrillerfan's example, the Kings and Rooks can't move because they will lose the castling privilege. That's quite an artificial set up. And even so, he's wrong. 

Each B has 20 legal squares it can land on. That's a heck of a lot more than 22 moves for a three-fold repetition. 

Either that, or I really don't understand the question. And that is entirely possible.

I like the question and I like the answer by Thrillerfan.

Secondly I think 3-fold repetition is not correct. It should be called 2-fold repetition or 3-fold occurrence or 3-fold same arrangement or so.

Chess rules consider a position to have repeated if each side has the same options on the move. If a position arises once when it's black to move and once when it's White to move, it's not the same position. If a position allows castling  in one but doesn't allow castling later, they aren't the same position. 

3 times repeating the same position is a draw, BUT if it's the opposite players turn to move in the same position, it's not really the same position, so it doesn't count. And as SymslovFan stated above, if castling rights, en passant..etc change, then it's not the same position. ZugZwang and triangulation positions also do NOT count as the same position for obvious reasons.

Re-read the post!  I never said 22 moves constitutes the draw.  I said the position occurs 22 times!

The exact same position can occur as many as 21 times maximum with no 3-fold repetition if you start out with a position where en passant was possible and all 4 directions of castling are possible (i.e. White Kingside, White Queenside, Black Kingside, and Black Queenside).

It is physically impossible to repeat the same position 22 times and not have 3-fold repetition occur somewhere!

The example I gave had no 3-fold occur, yet the same position occurred 21 times, but I mentioned that if that same position EVER occurs again, it will be 3-fold no matter what, regardless of who is to move.

AND, also triangulation, that adds another move.

We aren't talking MOVES!  We are talking NUMBER OF OCCURRENCES OF THE SAME POSITION!

But whose turn it is to move affects whether the position is the same or not.

@ Thrillerfan, if a position allows en passant the first time but not the second, they are two different positions!

The rules of chess are clear on this. Same wth bcastling rights.

That's already been considered in thrillers example.

Chess.com draws the game automatically with the third repetition.  It's not just the pieces; it's the empty squares too.

And that is why the same position, as in layout of the pieces, can occur up to as many as 21 times with no 3 fold repetition.  Once it has occurred the 22nd time, 3 fold repetition must have occurred somewhere, whether it be on the 22nd occurrence or earlier.  3 fold must have occurred at some point in the sequence if the same position occurred 22 times.  At minimum 3 of those 22 will have occurred with the same player to move and both players having the same legal options.  Up to as many as 21 times, it is PPSSIBLE that no 3 fold repetition has occurred, like the example I gave earlier.  21 occurrences and no 3 fold in that example!

Wrong.  Chess.com doesn't automatically draw the game with a 3 fold.  It must be claimed.

My opponent must have done it then

SmyslovFan, you are telling me what I already know and what I illustrated to answer the OP's question.

He was asking what the maximum number of times it could possibly take of repeating the same position before 3-fold occurs.

I showed that you can repeat the position 21 times with no 3-fold.  That was the whole point of that post.  The first had en-passant as a legal option, the next 4 had all 4 castling options available (twince each with White and with Black to move), the next 4 had no Black Kingside castling, the next 4 had no White kingside castling, the next 4 had no Black Queenside Castling, the next 4 had nobody able to castle, and after that point, which we are now at 21 occurrences, it is physically impossible to create a 22nd occurrence without 3-folding somewhere!  It might be the no castling ability scenario with White to move or it may be the no castling ability scenario with Black to move.  Doesn't matter, the 22nd occurrence of the position will GUARANTEE that 3-fold has happened somewhere!