Spotify Shuffle is neither a shuffle nor a randomizer.
Like carlcanyon explains in his post on the matter, a randomizer picks out of a set list, giving each item the same probability every time, and does not discriminate based on any facts/statistics. It is random. A shuffle on the other hand takes every song, shuffles them in a random order, and plays them one by one until every single one has been played, before starting over with a new order.
Spotify shuffle however doesn't care about our silly math definitions. It picks 50-100 songs, shuffles them together and plays them constantly whilst you are on shuffle, only to replace some every now and then. The proof of this lies in the statistics. Ask any user who uses shuffle daily with a big playlist(500+ songs). Most of them will tell you that they hear the same song at least twice per 100 songs. This is true for me as well. As i am writing this my "Songs" playlist contains 664 songs. Meaning that every song, in an ideal world, has a 1/664 of being no. 1->664 whenever i press shuffle. This however, is not the case. Since i started using one big playlist for everything instead of seperated little ones about 4 years ago, I have experienced repeating songs with set frequencies. It's as if spotify seperates all your songs into groups based on genre, artist, time period and date added. I might end up listening to 5 John Mayer songs in a very short period of time, which is quite interesting, as all my John Mayer songs are placed fairly high in my list as I only just added them to my "Songs" list recently. Songs by Skrillex and other dubstep/trap/house artists are also frequent for some reason, despite me not adding any of those for over 3 years. What i rarely hear though, are the songs in the middle. I had a period about 1.5 years ago where i listened exclusively to slipknot and slayer. There is a section about 15 songs long, or about 1/40 of my songs, that maybe gets visited once a week. This is strange, considering the fact that my spotify is probably running on average 10+ hours a day.
Just now as I was writing that last sentence, Black and White by MJ came one. That is the second time tonight. It also played once or twice last night. The odds of that happening are again, incredibly low if we assume this is a random system, based on all of this, my conclusion is; Spotify's Shuffle algorithm has nothing to do with the traditional definitions of randomizing or shuffling a set list of items.