What it is actually for: the offer is always below the average of what is left, and the screen shows you that average the whole time. Taking it anyway is not a mistake — it is a real preference about risk, and the point is getting a room to say out loud which one it has. The debrief compares what was taken against what was in the case and against every offer that was refused.
Best with the room voting on every decision. One person deciding is a game; a room deciding is an argument worth having.
It does not get opened until everything else has been. There is no clever way to choose it.
Still sealed.
You chose yours before you knew anything. There is no information in that choice — and none in this one either.