Four 50-sided dice are rolled so that the numbers are all different, then assigned randomly to players A, B, C, and D. The players with the highest and lowest numbers pair up, as do the two with the middle numbers. The team with the higher total pays the team with the lower total the difference. You are one of the players. Someone offers you a way to fix the game so that you start with a given number from 1 to 50. Question 1: What is the best number to pick? Question 2: Assuming you choose X as the best number, and there is an auction to sell the hack that lets you start with X, how should you bid? (Is this just asking for the expected value of the hack, or is there more to consider about bidding strategies?)