maybe I don't understand, 50% is the goal? when I played I thought % was how often it predicted what I pressed, and even though 0% is 100% wrong which is 100% right in a parallel universe, it would still represent me winning.
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.
50% means it is "no better than random" while 0% means it is accurately predicting what you won't press and 100% means it is accurately predicting what you will press.
> it is accurately predicting what you won't press
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.
If you have two choices ... and I always predict the wrong one ... another way to say that is: "I always predict the one you won't choose." If I can't actually predict which one you choose, then statistically, I should be right 50% of the time.
So? If I can reliably lose every basketball game, that doesn't make be perfect at basketball.
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.
You are comparing to things that don't even make sense in the current context.
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.
Another way to put it is that there obviously exists an algorithm that can predict what you will choose. It just isn’t this one, but the opposite. The entire point of this exercise is to prove that you have free will. If there obviously exists an algorithm that can predict what you will do, you don’t have free will, do you?
Thus “random,” aka, 50% is the target: this algorithm cannot predict what you do; you have free will.
50% or 0% are both interesting goals, but the headline implies that the website is some test of free will. If you get 0%, then it shows there is an algorithm that predicts your performance, and the Kolmogorov complexity is finite. That algorithm is the inverse of the one the website is using.
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.
> If I can reliably lose every basketball game, that doesn't make be perfect at basketball
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.
People who are good at chess sometimes like to play reverse chess where the goal is to get checkmated. If you are playing against another good player it can be quite difficult -- as difficult as winning under the normal conditions.
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. ;)
There really isn’t a “yes but” here, this is stats 101. Welcome to the class.
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).
The 50% goal is against an adaptative adversary. For some reason, Zero Knowledge Proof[1] came to my mind, so I interpreted the goal as reaching a 50% accuracy on the oracle side.
Your interpretation of the goal is also valid, but not in a cryptography context, for example.
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.