What Are the Ideal Proportions for a Cylinder to Act as a Three-Sided Die?

[Helios]

There is a cylinder of certain proportions, that when dropped, lands either on its side or one of its two ends with equal probability. A coin is too short of a cylinder. A solid pipe is too long of a cylinder. Somewhere in between is a cylinder that acts like a three-sided die. I've imagined this problem but don't know how to solve it.

 

[Vanadium 50]

Draw a picture. (Always good advice)

You have a cylinder that touches the ground at one point on the rim, tipped at some angle. Draw the forces acting on the cylinder and ask for what angles does the cylinder tip over to the side and for what angles does it tip back to land on an end. You now have a relation between the length of the cylinder and the random angle it lands at.