Maybe the issue is that we're being too discrete, thinking in terms of absolute predictability or absolute unpredictability.
Ultimately a 50% prediction rate means that you are as unpredictable as is possible, the state of maximum entropy. Any deviation from 50%, towards 100% or 0%, is a state of lower entropy.
You can forget the free will and just consider a fair coin toss. If someone had the ability to always guess a coin toss incorrectly, every single time, then you'd know that this person possesses something absolutely incredible and unique, rather magical. Similarly if they guess a coin toss correctly every single time they would also possess something magical.
It's the person who can only correctly guess a coin toss 50% of the time that is uninteresting, ordinary and possesses absolutely no special or magical insight. But deviating from 50% would require having some knowledge about the coin. A 0% prediction rate would require having total knowledge of the coin, so would a 100% prediction rate. It's 50% that requires having no knowledge whatsoever.
If we forget free will, then I will grant your position regarding statistics.
But suppose you could collect every bit of evidence in the universe and use it in a massive calculation to guess what my next decision would be.
This would be a test of whether I had free will, or whether I was simply doing what the universe made me do. If I wanted to demonstrate free will, I wouldn’t be aiming for random. I’d be aiming to make your guess wrong as often as I could.
If I could make your guess wrong 100% of the time, this would not mean that you could simply flip the bit on your guess next time. You can modify the calculation after every guess and it wouldn’t matter. I’d still do what your calculation thought I wouldn’t based on previous history. If I could do that, that would be a magical thing. Yes. I would have demonstrated completely free will according to this test.
This is why we call rand(), not freewill().
Free will is not random at all. It means you wear the shirt you want to wear, not a completely random shirt.
Oh, and before somebody objects, yes this is a terrible test of free will. Because whether I want to score high or low on the test or in the middle is up to me if I have free will. ;)
Ultimately a 50% prediction rate means that you are as unpredictable as is possible, the state of maximum entropy. Any deviation from 50%, towards 100% or 0%, is a state of lower entropy.
You can forget the free will and just consider a fair coin toss. If someone had the ability to always guess a coin toss incorrectly, every single time, then you'd know that this person possesses something absolutely incredible and unique, rather magical. Similarly if they guess a coin toss correctly every single time they would also possess something magical.
It's the person who can only correctly guess a coin toss 50% of the time that is uninteresting, ordinary and possesses absolutely no special or magical insight. But deviating from 50% would require having some knowledge about the coin. A 0% prediction rate would require having total knowledge of the coin, so would a 100% prediction rate. It's 50% that requires having no knowledge whatsoever.