[Miiko]

> Is it possible for a position to occur in a legal game of chess where all pieces and pawns are on the board, all of them are on their original squares, and white does not have the move?

No, and that's quite easy to prove: With all pawns on their original position, the only valid moves are by knights and rooks, and for each such move the moving piece changes the color of space it occupies (for rooks that's because they have only 1 empty place to move).

That is, in order to return to the initial position, each side must make an even number of moves (knights exchanged or not), so next move will be always white's.

[tzs]

You are 100% correct that if a position is ever reached where everything has returned to the initial position, white must have the move.

But note that I asked if white has the move any time a position occurs where everything is in its initial position, and so we must also consider the initial position before any move has made.

When the pieces are in their initial positions before the first move has made, does white have the move? You would think so, but actually that is not the case. Nor does black have the move.

The FIDE Laws of Chess define having the move thusly:

> The game of chess is played between two opponents who move their pieces alternately on a square board called a ‘chessboard’. The player with the white pieces commences the game. A player is said to ‘have the move’, when his opponent’s move has been ‘made’.

Nobody has the move until while makes the first move, then black has the move.

This stupid way FIDE defines having the move can show up in another situation. Consider this game:

  1. Nf3 Nf6
  2. Ng1 Ng8
  3. Nf3 Nf6
  4. Ng1 Ng8

The initial position has now occurred 3 times (at the start, after move 2, and after move 4). Can white claim a draw by threefold repetition? Could black have claimed a draw before making 4. ...Ng8 by writing it on their scoresheet and informing the arbiter?

With the way FIDE defines having the move, the answer should be no. This is not yet threefold repetition. Part of FIDE's definition of a repeated position is that the same player has the move in both, and so the positions after move 2 and move 4 are not repetitions of the position at the start because white has the move in the later two but no one had the move in the former.

[Miiko]

The last time I studied chess in any serious way was like 40 years ago. All I can answer is which side has their turn to move in "returned" position, but the fine details of whether they have to make that move or can claim a draw is well beyond my expertise, sorry.