I believe the delegates from some states are bound thru the second ballot. A few may be bound through three ballots.
But it would make sense in a way to keep them tied to their candidate for the first couple of rounds. Let's say that after the first round of votes, Candidate A is 100 votes ahead of Candidate B, but still 150 votes shy of securing the nomination because Candidate C controls those deciding delegates. It would make sense that they would give the candidates time to broker some sort of deal (like giving Candidate C the Vice Presidency in exchange for his delegates) instead of turning it into a massive free-for-all.
It could turn out to be a very interesting summer.