This math challenge is a calculus challenge.
This challenge pertains to a game involving an infinite number of players, and 1 prize. The prize has a mass that is a random amount between 1 and 3 kilograms, just as likely to be less than 1.5 kg as more than 2.5. Each player in turn guesses a real number quantity of kilograms. The following is done for each player in turn: if the guess is less than the current mass of the prize: that mass is removed from the prize. Otherwise, that player receives nothing. You are player number 5. Assume you hear each of the previous players guess optimally. The challenge is to determine what is your best guess, and how much you will win on average.