There is nothing in the patterns anyone describes to indicate that the algorithm is not random. What we are looking at here are independent events. That is, that the algorithm has no knowledge of the previous choices it has made, and so those cannot influence its new choice. It cannot exclude a facility it has chosen previously. It cannot choose to pick a coins facility if it previously picked an FC facility because it has no memory of what it has picked previously.
Y'all need to study probability a bit more.
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