but the last few rooms available were usually held as a reserve for situations like this

Just a friendly counterpoint, but when I worked the front desk of a major hotel chain the rooms were overbooked each and every single night, purposely.

The front office manager even had a very special formula to calculate to try to get right at the 100% occupancy rate.

On a tangial side note, it really sucked working the front desk when you overbooked and someone who comes in with a guaranteed by credit card reservation has no room and you have to turn them away; fun times.