After business school one of my professors connected me with a startup he was an advisor to. They hired me as a consultant to help them develop their business model and pricing, and to help identify strategic partners. We soon selected a very interesting partner, a non-profit with access to a lot of data that would be very valuable to the new service we were developing, and a meeting was arranged at their office to see whether a deal could be reached.
Although negotiation wasn't technically part of my brief I took the CEO aside and asked if he wanted help preparing for the discussion. In particular I suggested we spend the afternoon role-playing the negotiation, which he agreed to try. I played the part of the partner and raised the sorts of questions and concerns I thought were likely. It soon became clear that our CEO wasn't ready for the meeting. He understood our interests extremely well but not the other party's interests, particularly the non-financial ones. To his credit, the CEO also realized that he was probably the wrong person to do the negotiation. (Happily for me, he concluded I was the right person and I took his place in a fascinating and ultimately successful negotiation.)
For a role-play that didn't happen but should have, look at this brief video from Harvard's Project on Negotiation. Guhan Subramanian recounts how he was asked to mediate a board dispute over an organization's strategic direction. A meeting was set up and board members were asked to take their name placards and to sit wherever they chose around a large table. As people filed in, Guhan realized the problem -- everyone was sitting according to their "sides" which set the stage for an adversarial discussion rather than mutual problem solving. Worse, he had been brought in by one side and by chance the seat that the company's counsel had chosen for him was on "his" side, making it much harder for him to be seen as a credible mediator by those advocating the other strategic direction.
Negotiations are full of things that can go wrong. Experienced negotiators can avoid many pitfalls simply from knowledge but role-playing a negotiation, like a dress rehearsal for a play, can help identify other potential snags and increase the chances that the negotiation follows the path you've designed.