greendawn
if some of these mutations happen to be advantageous (1)
I can't imagine this being anything other than a random process driven by chance. (2)
This is where you are going wrong. You understand well enough upto the sentence I haven marked (1), but your mistake is thinking that the selection process in (1) is correctly described as you do in (2).
Whilst the VARIATION may well be random the SELECTION is not random. It is the entire point of the theory of natural selection... the selection is non random
For example, say you assign six chacteristics like this;
1: Brown Hair
2: Black Hair
3: Blonde Hair
4: Red Hair
5: Curly Hair
6: Straight Hair
... and then roll a six-sided die to assign one to a test organism.
The selection of which characteristic (or mutation) the test organism has is random.
However, if the organisms with characteristic 4 produce more offspring in the environment they dwell in than characteristics 1-3 and 5 & 6, eventually all the organisms in that environment will have red hair. This is not random. It really is SO not random...!
I know you've seen this explained a dozen times before in such threads. I hope the explanations you get on this thread are clearer and prevent you making this mistake again.
With such a profound misunderstanding of evolution it is not surprising you've found it hard to see it as a credible theory.