That bit after watch?v= is an 11 digit string. The first ten digits can be a-z,A-Z,0-9 and _-. The last digit is special, and can only be one of 16 values. Turns out there are 2^64 possible YouTube addresses, an enormous number: 18.4 quintillion. There are lots of YouTube videos, but not that many. Lets guess for a moment that there are 1 billion YouTube videos – if you picked URLs at random, youd only get a valid address roughly once every 18.4 billion tries.

We refer to this method as “drunk dialing”, as its basically as sophisticated as taking swigs from a bottle of bourbon and mashing digits on a telephone, hoping to find a human being to speak to. Jason found a couple of cheats that makes the method roughly 32,000 times as efficient, meaning our “phone call” connects lots more often. Kevin Zheng wrote a whole bunch of scripts to do the dialing, and over the course of several months, we collected more than 10,000 truly random YouTube videos.

Source: How Big is YouTube?