Manipulating a coin toss is easy enough. Just palm it and close your hand when you catch it, then run your thumb over the surface pointing away from your palm. With a little practice (and non-calloused thumbs) you know which side that is in a split second. If it’s the correct side, fine, if not you just put a tiny bit of pressure on the very edge of the coin with your thumb when you’re flipping it over to the back of your other hand and it’ll rotate to the other face.
You can also get a really quick glance as you bring your hand to the back of the other. If it’s one smooth motion, no one ever notices. Squeezing the coin also rotates it as well.
Obligatory:
Ulysses, Nausicaa, where Bloom is musing on a beach, after having masturbated to a stranger teenager he watched who was exhibiting herself for his pleasure:
He flung his wooden pen away. The stick fell in silted sand, stuck. Now if you were trying to do that for a week on end you couldn’t. Chance. We’ll never meet again.
“The stick fell in silted sand, stuck.” Nice, huh? I often think of that sentence when I think of chance, and always when a coin – or, as hasn’t been mentioned – a pill falls and stops on its edge.
I realize this is a zombie, but no one ever answered the initial question. Since the OP assumes a stuck landing (in sand or mud), you’re basically just spinning a wheel and seeing how often it lands with the CG over the edge of the coin. So find the angle of the right triangle from the CG to the edge and quadruple it.
arctan(1/13.245)*4/360 = 4.79%