In the hospitality world, the phrase "run of house" means that the hotel has priced all of its rooms at the same rate, according to About.com. As a result, reservations are available at a first-come, first-served basis. A guest stays in whatever room the hotel has available. Generally, a guest is offered the best room available at that time.
Run of house is related to a few other hospitality terms. The rack rate is the price charged for a hotel room before any discounts are applied. The set rate for a room is sometimes higher than it really is in order to later calculate discounts. Someone walking into a hotel and asking for a room for the night can expect to pay a higher price than if he had booked the room in advance.
The walk-up rate is the price charged to someone without reservations at that particular hotel. Usually, a higher rate is charged to the person without prior reservations, but under these circumstances, the price is negotiable.
"Accommodation on arrival" is a related term used in reference to a special holiday travel package that includes a hotel reservation. The individual does not know the name or location of the hotel until arriving at the destination.