Calculating the probability of a coin falling on its side A classical example that's given for probability exercises is coin flipping. Generally it is accepted that there are two possible outcomes which are heads or tails. However, it is possible in the real world for a coin to also fall on its side which makes a third event ( $P(\text{side}) = 1 - P(\text{heads}) - P(\text{tails})$ ?). How would a mathematician go about calculating the probability of that? Could it be done by simply using respective surface areas or would a proper model be more complex?
I covered this question at my Fair Dice column.  If you flip your coin onto sticky pitch, it has a much better chance of landing on edge than if you flip it onto a smooth granite surface.  The potential to bounce makes a huge difference.

Roughly, you're looking at a 3-state object.  Each time it lands, it will lose some energy, and the chance that it will change to a different state varies with the energy.  The amount of energy necessary to topple from one state to another will let you build a transition matrix, and then multiply a series of these together to get expected behavior on a given surface.

More is at the site dicephysics. Cylinders of various size were mechanically rolled thousands of times on a variety of surfaces. Results closely followed the Energy State model of my thesis on dice.

Toppling must be considered.  Many objects have unstable sides, and will topple away from them. There is a Unistable polyhedron which will always eventually roll to the same face each time it it tossed.
of course it depends upon the thickness of the coin , if the thickness is much then the chances of finishing its motion on the side could be infinite coz it has infinite points on its side.