The current game is definitely not decided, so it wouldnât make sense to suggest a ranking, someone would definitely disagree. Just as you shouldnât resign if you still might have some realistic chance of winning, you shouldnât accept a ranking if you think you have a realistic chance of getting a better placement by playing on.
We should also define what constitutes a âbetter placementâ in the presence of ties. Letâs say for simplicity that we go to scoring with scores 20, 20, 17, 12, 12. Some would call this a tie for first place, one player on third place, and a tie for fourth place. Iâm guessing it probably makes more sense in this context to call it a tie for second place, one player on third place, and a tie for last place (since winning alone should be preferable to winning in a draw). I think an equivalent way of saying this is that each player wants to maximize the number of players below them in the ranking.
But letâs say youâre choosing between a position where you share second place with another player (and there is no first place), and a position where they get first, you get second. Surely the first option should be preferable for you?