The odds of that depend very heavily on the environment in which the coin was flipped, the speed at which it was flipped, the height at which it was flipped at and so on. eg if you slip the coin very slow low to the ground the chance it will land on the edge is much greater than if you flipped it quickly and from a greater height.
As for randomality, nothing is ever random. As soon as you try to do something at random (such are the numbers example above), you are infact subconciously placing them in such a way that seems the least orderly. eg you will subconciously or conciously not put 1 2 and 3 in sequence, therefor you are infact not picking at random. While the mathematical chances of placing the numbers 0 through 9 in order are infact the same as placing them in any other 'seemingly random' order (such as 4 7 5 0 9 6 2 8 1 3). The theoretical chances that your outcome will be 4 7 5 0 9 6 2 8 1 3 are infact much greater than 0 1 2 3 4 5 6 7 8 9. Because your mind will specifically try to avoid such obvious orders.
This is the same for almost all 'random' number generators (such as $rand in mirc). Due to the simple fact that they are designed on some level to avoid obvious orders. Since the chances of each combination is not equal, this perhaps ironically means that an ordered outcome from a random number generator is infact more random than an unordered outcome.
Anyway, i probably rambled a little, but for the other math/physics enthusiests this is explained to some degree by both Chaos Theory and Quantum Chaos Theory.
