I agree with you on the difficulty in finding true randomness; notoriously, the software function used to generate a random number doesn't. Wolfram made a note of that under the problem 10 link. The only math I've seen that would be a fair toss of the coin is Chaitin's Omega.
The research I've done thus far has focused on information theory and molecular biology and therefore my emphasis has been on algorithms. But the subject of algorithms brings in Chaitin, so I wanted to be more comfortable with the game rules and terms - to continue reading with comprehension. Thank you so very much for all your help and your patience!