What does run of house (ROH) mean?
Run of House or ROH means different room types are offered by the hotel at the same price and when you check in the hotel decides which room you will be provided. Basically it means you get whatever room is available or decided by the people running the hotel desk.
So it can actually work out in your favor if you check in at the right time. You could end up getting a deluxe room or suite than if you requested a specific type of lower quality room. Then again you could end up being checked into a lesser value room. It depends on the hotel, the time you check in, and the person working the hotel desk.