Four 50-sided dice are rolled so that the numbers are all different, then assigned randomly to players A,B,C,D. The players with the highest/lowest numbers pair up, as do the two middle ones. Then the team with the higher total pays the team with the lower total the difference. You are one of the players. Someone approaches you with a hack to fix the game so that you start with a given number 1-50. Question 1: What is the best number to pick? Question 2: Say you answer X to Question 2: The person hosts an auction to sell the hack that lets you start with X. How do you bid?
Question 1 has already been answered here: Expected winning of a player with highest lowest and second highest lowest grouping but I'm trying to figure out how the quartic function in Empy2's solution was derived. Also, this question was asked in an interview and I was wondering whether there would be an alternate way of solving this using a different (maybe faster) method. As for the second part, I have no idea how to start the question.
