Infinite Unfair Shuffles and Associativity

We consider a general shuffling operation for finite and infinite words which is not necessarily fair. This means that it may be the case that in a shuffle of two words, from some point onwards, one of these words prevails ad infinitum even though the other word still has letters to contribute. Prefixes and limits of shuffles are investigated, leading to a characterization of general shuffles in terms of shuffles of finite words, a result which does not hold for fair shuffles. Associativity of shuffling is an immediate corollary.