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Reading some recent posts about the 50 move rule made me realize that I've never seen an explicit order of actions for chess. By way of comparison, the order of actions in Monopoly is given here:

(1) Throw the dice
(2) Move the indicated distance or to jail (if 3rd double in a turn)
    - collect $200 if land on or pass Go
(3) Resolve space
    - ownable properties
        = pay rent if owned and not mortgaged
        = buy it if unowned (optional)
        = auction property if still unowned (not optional)
    - non-ownable properties
        = resolve as indicated.
        = collect $200 if resolving puts you passing Go.
(4) Pass the dice or roll again, as appropriate.

A chess move combines three actions (shifting wood, writing move, hitting clock) and the game can end in various ways (mate, stalemate, dead position, agreement, 50 move rule, 3-fold repetition, 75 move rule, 5-fold repetition). For simplicity, let's put to one side for now resignation & irregularities e.g flagfall).

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The FIDE Laws of Chess provide some guidance.

Rule 6.2.1 says you must move the piece before hitting the clock:

During the game each player, having made his move on the chessboard, shall stop his own clock and start his opponent’s clock (that is to say, he shall press his clock). This “completes” the move.

According to rule 8.1.2, you must move the piece before writing down the move, usually:

It is forbidden to write the moves in advance, unless the player is claiming a draw according to Article 9.2, or 9.3 or adjourning a game

There is a little bit of flexibility as to when exactly you write down the moves, according to 8.1.3:

A player may reply to his opponent’s move before recording it, if he so wishes. He must record his previous move before making another.

So, you must move the piece before doing anything else. Ordinarily, you would then hit the clock, and finally you would write down the move. I am not sure if it would be a violation of 8.1 to write the move after moving the piece but before hitting the clock - technically, the move is not "completed" until the clock is hit - but it gives no benefit to do so. In practice I've only seen it when someone forgets to hit the clock altogether.

Offering a draw is done after making the move but before hitting the clock, and claiming a draw is done by writing down the move but not playing it, and seeking the arbiter.

The 5-fold repetition and 75-move rule may be claimed by the arbiter whenever applicable, so you can't really give them any set place in the order.

This gives us the following order:

(1) If claiming a draw: 
     - Write move (if this move is required for draw)
     - Stop clocks (not required, but wise)
     - Declare draw claim to arbiter
     - If claim is upheld, game is over

(2) Make your move on the board
    - If this move results in checkmate, stalemate, or dead position, game is over

(3) If offering a draw, offer draw to opponent
    - If opponent accepts draw, game is over
    - If opponent declines, or delays decision, proceed to (4)

(4) Press clock
    - (Probably this could be done after (5), but this order is preferred)

(5) Write move
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    Great summary. I'd add on (3) that often the opponent doesn't accept the draw immediately, so the player offering the draw is under no obligation to wait for a decision before proceeding with (4) and (5).
    – Samantha
    Commented Apr 6, 2018 at 5:52
  • Yes a great start. One nit is that "insufficient material" is no longer a thing. It is one sub-type of dead position; other sub-types being unavoidable future stalemate and blocked position. Also, can claim at beginning of turn that drawn position already exists on the board.
    – Laska
    Commented Apr 6, 2018 at 6:02
  • Another nitpick: In article 8.1.2, I would consider "in advance" to mean making, not completing, a move. Therefore, in my opinion, (4) and (5) may be interchanged, although that is by no means common.
    – chaosflaws
    Commented Apr 6, 2018 at 7:08
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    @MátéJuhász No, you are wrong. There are lots of situations where it is reasonable to pause the clock including when you claim a draw. The ultimate arbiter of whether or not your action was reasonable is, of course, the arbiter who will punish you if you did so unreasonably. Reasons to pause the clocks include: draw claim (not offer), illegal move, disturbance by the opponent, illegal activity by the opponent (eg looking at his phone, adjusting pieces when it is your turn, not writing moves, asking others for advice). In short, anything which involves you calling for the arbiter.
    – Brian Towers ♦
    Commented Apr 6, 2018 at 10:53
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    @itub The rules specifically state that you may reply to your opponent's move before notating it. It's difficult to put in steps that may be done at any time - the monopoly example didn't try to do that either; it omits things like building houses that the player may do at any point on his turn.
    – D M
    Commented Apr 6, 2018 at 16:33

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