This is a great topic.
I admit I haven't read your article in full yet.
But here are some issues that always bothers me, when I think about the issue of randomness and roulette.
Btw, I agree with you that physics is 'theoretical' in comparison with medicine and agriculture
. But it is 'empirical' in comparison with mathematics. See more on this here
Now to the main issue of randomness.
I see some relation between gambler's fallacy and randomness testing. I see some sort of logical and philosophical contradiction. Here are my thoughts.
If we believe that the result of each spin is totally independent, then every possible spin sequence is equally probable.
This means that this sequence: 5,5,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,......
is equally probable with this sequence: 36,30,1,1,4,9,17,17,4,30,30,36,18,22,6,7.....
Then on what grounds is it possible to evaluate a spin sequence and give a verdict on its randomness?
To ask it in another way. Is randomness something unknown or known? If it is totally unknown how can you evaluate it?
Does randomness has limits or not? If it doesn't then how can you evaluate it?
PS: I see a similar contradiction on the house edge argument
. They say every spin is independent and unpredictable and nothing is due, yet they fully expect the 2,7% zero effect to stop you from winning, because it is due... But this is a totally different discussion and there is no point in arguing about this here.