[Siegmund]

There is no unique answer, unless you specify exactly how you drop the coin.

If you drop it in random orientation *from a sufficiently low height*, choosing the length so that the center of mass is above each side of the coin for 60 degrees is good enough. (But that's not very effective randomizer, if you simply let go of it and then let it fall straight down without bouncing around any at all: your hand position before you release the cylinder determines the whole outcome)

Assuming no angular velocity when the coin is released doesn't help you, if the coin is dropped from a significant height, because it gains considerable angular velocity as soon as it strikes the ground, any time the center of mass isn't exactly over the point of first contact. Anything more than a few coin-diameters above the table and it will strike hard enough to spin past at least one face before coming to rest.