since the mind appears to be a product of the brain, I find it very reasonable to assume that whatever mechanisms shaped our bodies also shaped our thinking.
Did you miss the whole bit about the Hard problem of Consciousness? Neurology has singularly failed to support the notion that the mind is a product of the brain. That is the whole point.
What we have are Neural Correlates on fMRI, but causation and mechanism have never been demonstrated. So we can confidently say they are likely related in some way to each other, but the mind does not 'seem' a product of the brain unless starting out with an assumption that it must be - from some form of materialism a priori.
A good example was some recent studies from Australia in which they did EEGs on volunteers undergoing muscle relaxation - but no Anaesthesia. While fully awake, the EEG (in the form of BiS monitoring) appeared as how we thought a person looks when sedated. Similarly, EEG monitoring and fMRI in subjective states of heightened mental activity like Meditation, show decreased brain activity - which is counter-intuitive.
Free will and making choices aren't the same thing. A computer makes choices, but in that case it's obvious to us that the choice isn't the product of a free will. Even if the calculations are too complex for us understand, we still know that in the end, it's just a calculation, even though it can appear to be either deliberate or random.
If the brain is basically a computer, then surely it's not impossible for it to calculate things like probability?
We have an intuition that our reasoning and making of choices happen in our consciousness, but I believe that is false. We don't make choices with our consciousness, it's probably more correct to say that we become aware of our choices.
Of course that raises the question of what consciousness is for. I wouldn't pretend to know :/
You must be careful here. You are confusing metaphor for reality.
Computers don't think. They don't make choices. Computers are glorified calculators that take input, process it, and then present output based on their programming. In essence, they run functions and math of binary numbers, and any meaning thereof is ascribed by us humans once presented on an output screen. Its 'choice' is merely the result of its programmed functions.
When Computers came to be made, we used the metaphor of our brains and thinking processes to describe what they were doing - which in actual fact was wholely other. Now, people reverse the metaphor and try and describe the brain as a computer, since computers are now so ubiquitous.
We know computers are deterministic. We know they don't think or reason or choose. We have no evidence humans don't do this, but every evidence from personal qualia to intersubjective experience that they do. When these terms were ascribed to computers, they were knowingly used as a metaphor to describe processes assumed to be very different - which people have now forgotten, and fallaciously try and reverse it.
So no, a computer can't calculate probability. A computer can calculate inputs given to it, which a human can then ascribe the meaning of probability to, once presented as output, yes.
The metaphor of the 'brain is a computer' has no veridicality to it at all. Neurons function by electro-chemical gradients via depolarisation of Sodium and Potassium over cell membranes - which neither makes a circuit, nor acts as a voltage gate or switch as found in computers. Further, we don't actually know how most information is 'processed' in the brain, though we can pinpoint vague areas. Certainly it is far more complex than any computer, as axons and dendrites connect multiple neurons over large areas. Again though, subconscious activity and conscious awareness have not been shown to have much more than correlation subjectively by report of the subjects investigated. It does not lend itself to mathematical modelling even. Nor does it seem the brain merely processes information, but adds and changes it; like Inattentional blindness; or that if you wear glasses making the world upside down, your brain will spontaneously swop the picture rightside up after a while. Or in things like phantom limbs or hallucinations the brain creates what there is no input to account for, or in more quotidian things like creativity perhaps as well. What computers and the brain have in common is that both process information (though not solely that in the brain), using electromagnetic properties - that is about it. No further relation can be drawn without being fully fallacious.
A computer is a fancy calculator; and anything a computer 'does' is basically something a human with a fancy calculator did.
But if they didn't also have a sense of us vs. them, they'd probably be slaughtered by more violent groups.
More violent groups first need to arise. They don't just exist. That is what the Prisoner's dilemma and Game Theory try to model. How to mix differing behaviours observed. The inconsistency lies in that they don't use the same model, but change it depending what they are trying to excuse - oh, altruism and adoption then group selection, but then turn around and ignore it otherwise to assert Selfish Genes. In essence, it models poorly as the mechanism needs to be constantly altered, even to the point of mutual exclusion, to maintain the premise of evolutionary origin thereof.
Don't get me wrong, I don't presume to say all this theorising is definitely wrong - but it is haphazard, inconsistent, and evolutionary modelling of psychology and human behaviour certainly does not fit "well", as you would have it. For instance, why do we "all have conflicting desires" as you said? You can't just assume that, but need to justify its evolutionary existence - as no ant has conflicting desires as to the colony or so. This works better in animals in which we can safely put aside subjective evidence and purely observe behaviour, than in humans in which they can explain their motivations and thought patterns that accounted for the behaviour (though you can always ignore that evidence, as many Determinists are wont to do - very scientific minded bunch, excluding things that don't fit their a priori ideas).
As we would expect them to if evolution is true
You seemed to argue the opposite in posts 122 and 126, where you assumed familiarity leads to identification with them. This is mistaken, as infants identify firstly, assume the best, but only develop stranger anxiety later - along with cultural prejudices. Familiarity seems to breed contempt of some, and closer identification with others. As the impulse of the Revolutionary or the rebellious teen shows, not even this is consistently applied. Granted, you can ascribe it to Evolution - but that is the problem, that it is ascribed to Evolution and then worked out how this can be the case, instead of the reverse. So no matter what evidence is presented, by hook or by crook, Evolution will be held responsible. Classic question-begging at its finest.
When reaching something like Depression that obviously has no advantage, it still needs to be assumed to have arisen from something advantageous as byproduct, spandrel or maladaption. So happily it will be, as obviously our axiom can't be wrong...
As I said, the entire paragraph I quoted. I didn't understand any of it. Again, I know I can sort of dechiper it flipping back and forth between dictionaries and Wikipedia articles explaining the details of the words, but I was kind of hoping you'd put it in simpler terms. Personally, I try to say things like "hey, you're going after the guy instead of addressing his arguments" rather than "you're committing the ad hominem fallacy."
I rewrote the whole once already in what I assumed you would more easily grasp. These posts are long enough already, that I don't feel it necessary that I have to write a whole dissertation to explain terms to you. If you care enough, you can look up what you don't understand and ask for clarification, but expecting me to spoonfeed concepts is a bit beyond the pale. It would be more to anyone's advantage when approaching something unfamiliar, to go read it up yourself and ruminate thereon, than to complain about the way it is represented and thus just ignore it further. It is easier to use established terms than to reduce it to basic language only - that is why scientific, philosophic or medical terminology exist, as they have implied semantic meanings. They are shortcuts to those familiar with them, and spurs to education to those who are not. If I say "the heart physiologically circulates the blood" , that means something subtly very different from "the heart pumps the blood around the body". The former implies anastomoses of blood vessels, the non-ejected fraction in the ventricle, preload and afterload, etc., so has far more meaning, than the latter which is much simpler - to say the same, would require paragraphs of explanation in 'simple language' in the other.