[fsckboy]

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.

[withinboredom]

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.

[brvsft]

> 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.

[withinboredom]

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.

[lupire]

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.

[withinboredom]

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.

[nocman]

> If I always guess incorrectly, then I'm correctly guessing the incorrect choice.

No, you aren't, because you aren't saying that it is the incorrect choice. You are saying it is the correct one.

[benjaminbachman]

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.

[LanceH]

In the case of this test, 0% means you're defeating the prediction algorithm.

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.

[bena]

100% misprediction of two choices is an error in the algorithm. You could flip the prediction at the end and be 100% right.

50% misprediction cannot be improved upon with trivial methods.

[mapcars]

> 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.

[jhbadger]

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.

[brvsft]

Okay, I get you. And you're right, if I pitted a 'random' program against this site, the outcome would tend toward 50%.

[jtbayly]

Yes, but...

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.

[Kranar]

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.

[withinboredom]

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).

[_notreallyme_]

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.

[1] https://en.wikipedia.org/wiki/Zero_knowledge_proof