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Triple repetition

So here goes my question to the chess gurus:

Imagine we have a starting position. Then white goes Nf3 Nd4 Nb5 and Na3 and then gets the B1 knight to g1, via Nc3 Ne4 Ng5 Nf3 Ng1. Then white plays Nb1. Black was moving his queen knight all the time. Now it's whites move, so white goes Nf3 black replies Nc6 white goes Ng1. Can black claim the draw? (it's the same position regarding possible moves but the pieces on the squares are not the same)

And then what would happen in this same idea with rook endings when both roocks swap their squares.
No draw. The pieces have to be the same and also the player to move must be the same. Does that sound right?
This is so simple I don't know why its even being discussed. OK imagine you are watching over a chess game and after every move of each player you mark the position of all the pieces on the chess board. Once you see the same set up 3 times during the game you call a draw.

The logic of this rule is that once the same position is repeated once there is no logical reason to repeat the same position again if you do then the chess rules would see that as a draw because neither player wants to deviate from that position and get on with the game.

Because this rule can happen so quick it does feel like the rule is too unforgiving but in chess you need to be quick and know the board and the rule is unforgiving because the game of chess is unforgiving.
Yes, but now imagine you have a nice stylish piece set with a red dot over the Q knight and R and a blue dot over the Q knight and R.

My point is that it is strange to claim it's the same position since the G1Knight arrived to his square only last move.

I mean if we difference White pieces vs Black pieces and do not just randomly claim that a King is a King. Why not we difference right and left as well? (A rook is a rook but the physical chess piece on the A1 square is a totally different physical piece from the rook on H1) Originally chess was thought to be played with material chess pieces not FENs, right?
Imagine, before my next move I say “I adjust”. Then I swap my rooks or bishops, or knights, or two of my pawns! Do you feel the position will be different? :)
The old masters started moving with black. Go and try it now! (it's all the same, yet you won't see it anywhere) If they are different they are different if they are the same then they are the same. And as white is white and black is black, right is right and left is left.
In the old times it was indeed common to start with black pieces. It made no difference for the chess notation used and (i guess) they were too lazy to switch the pieces. For example in the Immortal Game Anderssen started with e7-e5. Sauce German Wikipedia.

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