There is a strange bias that affects every human even if they believe the opposite.
For some reason, the reality we inhabit appears absolutely consistent and perfectly integrated. Everything happens for a precise reason, affecting everything else through an unbroken chain of logical connections without a single flaw or glitch. There has never been the tiniest violation of the laws that govern our minds' reality.

That is odd, because there are VASTLY more possible ways for minds to have completely absurd experiences. A randomly selected mind from the list of all possible minds should be having constantly changing meaningless hallucinations. Even their memories should be unstable.

It appears we are not randomly selected minds, but some type of special case. Specifically: our perceptions are entirely limited by the universe we appear to inhabit. Which implies this universe is not an illusion of our minds; instead our minds are fully part of the universe. 

This fact has been used to argue that we are not "Boltzmann Brains".
In the distant future of our universe, an infinite number of Boltzmann Brains will briefly "pop" into existence in empty space before immediately disintegrating again (this seems to be inevitable). Almost all of these Brains will have completely absurd experiences. But we are definitely not part of that infinite group.

Mathematically, this implies that a larger number of fully realized physical universes must also come into existence in the distant future, similar to Boltzmann Brains. Several ways have been suggested this could happen ("A Big Bang In A Little Room", Zeeya Merali, 2017), but there could be easier ways. We are actually probably part of a "Boltzmann Universe". 
In fact it may be EASIER for nature to create an entire universe that contains minds, than to create just a mind by itself.

Another way to look at it is to consider any string of random numbers without end. Eventually, you will come across a string of numbers that describes a "Boltzmann Mind", which will (almost certainly) have a very brief and absurd existence. 
However, LONG before then, you will come across many mathematical equations that will fully describe entire universes if you solve them. In fact the type of equation that generated our universe may actually be one of the most "productive" such equations possible.

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However, LONG before then, you will come across many mathematical equations that will fully describe entire universes if you solve them.

There are very simple equations that just generate pi or something. But the same argument can then be run on pi. 

If equations that branch both don't get penalized, we would expect ourselves in  a universe that just considered all possibilities. If not, we wouldn't expect quantum mechanics. (well the quantum multiverse contains exp observers, so ok, the total likelihood is reasonable.) 

I think you've overstated the degree of observed consistency and determinism, and you don't need such a high amount to make an argument against Boltzmann brains anyway.

I like your ideas but I don’t think you can’t rule out the possibility of us being in the illusion of a mind. If we are one consciousness separated into fragments it follows that the world would be consistent. I like Tom Campbells big theory of everything.

Also, a separate point is that there are minority of people who experience very illogical happenings who do seem to see beyond the veil of reality. You won’t meet them as much in normal society. I had to stop my meditation practice when things (eg mounting synchronicities) got too strange and I began to find it hard to relate to people.