Half the Average

A guessing game: each participant picks a real number between 0 and 100, and the winner is whoever is closest to half of the average of all picks. Use level-k reasoning: level-0 players pick uniformly at random (average pick 50), and a level-$k$ player ($k\ge1$) best-responds assuming everyone else is level $k-1$. What number does a level-3 player pick?