Strategic negotiations in digital tabletop displays have not been well understood. There is little reported in the literature on how users strategize when group priorities and individual priorities conflict and need to be balanced for a successful collaboration. We conducted an observational study on three digital tabletop systems and a real-world setup to investigate similarities and differences in real-world and digital tabletop strategic collaborations. Our results show that in the real world, strategic negotiation involves three phases: identifying the right timing, using epistemic actions to consider a task plan and evaluating the value of the negotiation. We repeated the real-world experiments with different digital tabletops and found several differences in the way users initiate and perform strategic negotiations.