At least in America, if a hotel bumps you, they have to legally provide you a room in another hotel of equal or greater value.

Worked out for me once during a trip to NYC where my hotel was full, but they sent me to a nicer hotel right over Times Square.

In a small town in Denmark, a hotel i was booked into was full, so they tried to send me to the other hotel in town, but that was full, so i slept on a sofa in a meeting room. The meeting room's floor was scattered with pieces of Lego, which made night-time trips to the bathroom somewhat terrifying. Not the most auspicious start to a business trip.

How was it full if you had booked? Do they sell more rooms than they have available?

They may, but sometimes rooms also become damaged due to rock stars throwing wild parties, or more mundane things like when we noticed a concerning amount of water dripping through the ceiling in our bathroom in Denver. Once they came to check it we got a free upgrade to a larger room.

I don't think keeping unbooked rooms "just in case" is economical so if this sort of thing happens you may well need to be moved out to a nearby hotel at their expense.

I don't know how the choose, but they bump you to another hotel.