Marble Parity Puzzle

A bucket contains an odd number of white marbles and some number of black marbles. Outside the bucket you have an unlimited supply of black marbles. You repeat the following procedure: 1. Randomly pick 2 marbles from the bucket. 2. If at least one of them is black, discard one black marble (put it outside) and return the other marble to the bucket. 3. If both are white, remove them both and place one black marble into the bucket. Each step reduces the total count in the bucket by exactly one. Eventually only a single marble remains. What color is the last marble?