Hi everybody!

Recently I have thought of how can I solve such problem: There is a root of a tree. At each step player can create on any leaf of a tree either left child (with probability p) or right child (with probability 1 - p). What is the expected value of a height of a tree after n player steps?

UPD: Leaf is chosen with the same probability (equiprobably).

Leaf -- is a vertex with the number of children less than 2.