The Problem of the Bones

I've just stumbled upon an extremely interesting problem, to which I've only been able to derive a partial solution after some intuitive thinking. The problem itself is called "The Problem of the Bones". Here's the problem statement :

Imagine that a creature from outer space walks you before a pit. In the pit are 10,000 leg bones. The creature tells you, "I have cracked each bone at random into two pieces by throwing them against a rock. What's the average ratio of the length of the long piece to the length of the short piece?

This problem is pretty difficult to solve. I've only been able to obtain a solution for the case where there are infinity leg bones in the pit.

I'm now attempting a simulation to obtain the answer. If you are able to solve this problem, please leave the solution in the comments.