in any case, my post was serious, regardless of the % number, if you are inspecting their algorithm and writing your own, I can't understand why you wouldn't use theirs in yours. Finding an isomorphism might be fun, but it's not necessary.
That is not what it's predicting. You have changed the definition of predict so that an incorrect prediction can be misinterpreted as a correct prediction.
To put it more plainly: if you were wagering on the outcome, would you rather win 50% of the time (EV=0) or 100% of the time (EV=max)?
100% misprediction is only relevant if a 3rd party adversary is observing the game. In the absence of such an adversary, being reliably wrong it worthless.
50% misprediction cannot be improved upon with trivial methods.
You have two choices.
I predict correctly or I predict incorrectly. If I'm randomly guessing, I will be right 50% of the time (effectively, this is a coin flip). If I always guess incorrectly, then I'm correctly guessing the incorrect choice. If I always guess correctly, then I'm correctly guessing the correct choice.
I'm trying to explain why 50% is your target for "fooling the algorithm" and not 0%, which is not fooling the algorithm at all. There's no reason to be obtuse here, I'm legitimately trying to help you understand some statistics... this isn't an argument, it doesn't matter "what you believe" ... this is math.
No, you aren't, because you aren't saying that it is the incorrect choice. You are saying it is the correct one.
Thus “random,” aka, 50% is the target: this algorithm cannot predict what you do; you have free will.
If we conflate "free-will" with "ability to generate truly random sequences" then the goal should be to generate a completely incompressible, unpredictable sequence, which 50% would probably be closer to.
What they are saying is that when you have an algorithm you can reverse it to do the opposite. If you could reverse your basketball skills exactly that would be true for your statement.
50% means (if you're predicting their prediction) means you're achieving random.
"Free will" is a bit strong, it's more about whether people can produce randomness, which they generally can't.
50% prediction rate would indicate that half of the time you are predictable, meaning you don't have much free will.
0% prediction rate would indicate that you have 100% free will.
Randomness is not a good measure of 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.
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. ;)
A 0% prediction rate means that you are 100% predictable by simply taking the opposite of the algorithm’s input or output. Thus, you have no free will (according to this tool).
Your presupposition seems to be that randomness = free will.
I propose that being forced to choose a random letter is the opposite of free will.
Your interpretation of the goal is also valid, but not in a cryptography context, for example.