... or something like that. I worked in corporate travel planning for 9+ years, and our travel agent explained it as the best room the hotel has available at check-in.

Here are some references to support this:

Available in three rate choices: Run-of-House, Deluxe Garden View and Beach Front. (Run-of-House = Best available accommodation at the time of check in.)
http://www.impulsefiji.com/airnadi.html

Run of House - The Run of House room has one king or two double beds and can accommodate a maximum of four guests. Run-of-the-house room is the best available room upon check-in. The rooms can accommodate a maximum of three adults or two adults and two children. http://www.vacations.net/barbados/sam_lords_castle_resort_al...

Hope it helps.