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BELIEF (aka faith) is not complicated.
It's simply ambiguous.

What a person believes may be complicated.  But belief itself is not complicated after you recognize the term as ambiguous.  It labels two completely different concepts which are erroneously conflated in most minds because they appear to occur simultaneously.

1. JUDGMENT OF PROBABILITY
belief-1 		2. TRUST
belief-2

As abstractions these concepts can be separated and contrasted.

belief-1 JUDGMENT OF PROBABILITY is an involuntary act.
It happens in the mind without conscious effort or choice as soon as evidence and logic make a conclusion appear probable(more than 50% likely).  We judge evidence and automatically believe(1) whatever appears probable at that time.  Of course, deliberate cogitation may change our minds from what we first believed(1).  And new evidence may change our minds.  But at any point in time, we judge probability based on the evidence we have seen, and logic we have figured out at that time.  We cannot willfully choose to believe(1) otherwise.  Anyone who claims to believe(1) something which he considers improbable is either confused or lying, possibly to himself.
belief-2 TRUST is a voluntary act of will.
Though we usually choose to trust what appears probable or reliable, we are not obligated to, and may have sufficient motivation not to.  Though trust begins as a mental decision, it cannot be shown to exist until it is manifest in action.

In practice these concepts usually overlap.

Sometimes completely:
I believe(1) that my car's brakes will work.
I believe(2) it enough to drive on the freeway,
and act as though I am certain of it.
 belief-2

Sometimes partially:



1.  I believe(1) my home is safe.
 2.  I believe(2) it enough to leave it unattended,
belief intermediate

3.  but not enough to leave it unlocked.

On rare occasions, not at all:
    Some long shots are worth betting on.

I believe(1) my home is safe...
belief-1
I don't believe(1) I will win the lottery...
but I may buy home insurance.
belief-2
but I may believe(2) it enough to buy a ticket.

In each case, belief(2) is a separate event from belief(1), and happens temporally after belief(1) has begun.

Religious issues are no more complicated.

I may believe(1) a God exists, but not believe(2) it enough to obey him.
I may believe(1) a God doesn't exist, but believe(2) it enough to do what I think a God would want me to do.
Believing(1) something in order to gain reward or avoid punishment is something that can't even be done by a person of integrity.

For you Scripture buffs:

The idea of conflating probability judgment with trust may not have originated with Jesus, but it has been entrenched in our language because of the New Testament.  Note the ambiguity implied in the story of the woman who touched Jesus' garment in order to be healed.  (Mat 9:22, Mk 5:34, Lk 8:48)  Was it faith(1) or faith(2) that supposedly healed her?

All that Paul vs. James stuff is resolved:
Paul: You are saved by faith(BELIEF(2)) alone.
James: Faith(BELIEF(1)) without works is dead.

    Mark 9:24 Lord, I believe(2).  Help thou my unbelief(1).

Moral of the story?

You don't have to believe(1) bullshit in order to believe(2) in a just and righteous God.

However, two factors may possibly complicate the issue - the combination of emotion and irrationality.  If a person is irrational enough, he may try to believe(1) what he wants to believe(1) despite perceived evidence to the contrary.  And for all I know, he might succeed.  Actual self-deception may be possible.