Been thinking about this for a long time now. When the Architect starts explaining when the Matrix was first built, he references 2 designs...the first being perfect utopia that failed miserably then a second more hellish version which also failed quite miserably.

But then he talks about the emergence of the Anomaly (The One) which is when he started counting the versions. But surely the first 2 count as Matrixes as he specifically calls them that.

Architect: The Matrix is older than you know. I prefer counting from the emergence of one integral anomaly to the emergence of the next, in which case this is the 6th version.
Neo: There are only two possible explanations, either no one told me, or no one knows.
Architect: Precisely. As you are undoubtedly gathering, the anomaly is systemic – creating fluctuations in even the most simplistic equations.
Neo: Choice. The problem is choice.
Architect: The first Matrix I designed was quite naturally perfect, it was a work of art – flawless, sublime. A triumph equalled only by its monumental failure. The inevitability of its doom is apparent to me now as a consequence of the imperfection inherent in every human being. Thus, I redesigned it based on your history to more accurately reflect the varying grotesqueries of your nature. However, I was again frustrated by failure. I have since come to understand that the answer eluded me because it required a lesser mind, or perhaps a mind less bound by the parameters of perfection. Thus the answer was stumbled upon by another – an intuitive program, initially created to investigate certain aspects of the human psyche. If I am the father of the matrix, she would undoubtedly be its mother.
Neo: The Oracle.
Architect: Please. As I was saying, she stumbled upon a solution whereby nearly 99% of all test subjects accepted the program, as long as they were given a choice, even if they were only aware of the choice at a near unconscious level. While this answer functioned, it was obviously fundamentally flawed, thus creating the otherwise contradictory systemic anomaly, that if left unchecked might threaten the system itself. Ergo those that refused the program, while a minority, if unchecked, would constitute an escalating probablility of disaster.