I work in an ER, so my answer is a bit different than the others. We take great pains to make sure nurses are NOT assigned in the same rooms two days in a row. In fact, they get very upset if they are. We try to give everybody a chance to rotate through everything that they're qualified to do (I say "qualified to do" because not all of our staff are certified for the trauma bay or have the required year of experience to be out in triage.) Our assignments are made in 24 hour increments by the department coordinators.
Typically, we assign the nurses either 3 or 4 rooms (all in a row so they don't have to run around all over the department.) If there are patients with higher acuity (i.e. an ICU patient that hasn't been stabilized enough to travel upstairs yet or something and the nurse needs to provide 1 on 1 care and can't take any other patients) we take that into account and change the room assignments up as needed. We are "supposed" to have 12 nurses on duty all the time but we generally only hit this mark on day and evening shifts. Nights typically makes do with fewer, resulting in up to 5 patients per nurse, but as we increase our staffing we are able to more closely mirror on nights what happens on the other shifts.