Even if the player that can no longer get enough points to get higher then 4th place might still be able to make a play or even two that effect the remaining players. for example Red is in first and getting cocky. leaves his queen hanging in line for the 4th place player to take it.
Granted that scenario is highly unlikely but removing the option for a player to make moves that could or would definitely affect future play for the remaining players is sort of like saying you can play but only as long as you don't mess with my winning the game by a landslide
I think the earliest I have been put out was on/before my 3rd move. That was my first or second time playing the 4 player version.
Oh, the reason for my response to your post is #4
the resign button would change for 2nd and third place once there is no chance for the other players to get the points necessary for them to over take the higher position.
I dunno... lol I have a hard time with "quitting" to keep from losing or perhaps "Quitting to Win" is the better way to phrase that
I know your scenario explains that there is no way for improvement of the losing players position.
Once a player resigns though all of their pieces gray out and become just obstacles. If those pieces still had point value how much would that change the desire to resign?
We are already familiar with the Resign button changing name to Claim Win, when a player becomes immediately qualified for the first place. Why not extend this textual convenience to all outcomes of the resign option? Of course doing so is only reasonable when the outcome is single and unambiguous. What I propose is this:
1) Resignation guarantees the first place: The Resign button changes to Claim Win
2) Resignation guarantees the second place: The Resign button changes to Claim Second place
3) Resignation guarantees the third place: The Resign button changes to Claim Third place
4) Resignation guarantees the fourth place: The Resign button changes to Claim Fourth place
4a) Alternatively the Resign button changes to Admit Defeat
4b) Alternatively the Resign button changes to Admit that you are an utterly incompetent Loser
Under the current point system, that includes no cases of score reduction, the case (4) does not demand that only two players are remaining. Claiming fourth place can become a reality very early in the game. As soon as everyone else has got at least one point, and you are still at zero points, you are qualified for the last place by simply resigning!