As noted:
998/1000 is significantly better than 60% so yes I’d still take one box.
That’s an assumption.
If the choice is kill a healthy cat or feed and pat that cat, yes I can reliably be sorted into one of those choices. I don’t think I can, on this one. Certainly not by any remotely plausible technology. Bear in mind that my personal experiences continue after the boxes were filled.
And to the extent that anybody’s saying you “should” take only one box, yes that only works, even if we assume such a technology, if they think the choice at that moment somehow changes the previous action of filling the boxes. Otherwise they’re saying “you should somehow be a different person than you are.”
Dude, I even provided you the math for a 99% accurate computer. Two boxes, however likely such choices would be, increases or maintains the take home amount for every participant.
Your math ignores that as a two boxer the odds of the second box having money in it are astronomically low while as a one boxer the odds of the second box having money in it are nearly guaranteed.
I grant you that if you could someone take two boxes while being a one boxer you would get the most money, but if that’s possible, it’s incredibly unlikely.
(Here when I use the terms one boxer and two boxer, a one boxer is a person predicted to take one box and a two boxer is a person predicted to take two boxes).
My friend, it’s the best play! Doesn’t matter how likely or unlikely, it’s the best strategy! And that’s the question posed by the hypothetical: What should you choose? NOT, what do you think people will likely choose? Why this seems important to you, I can’t imagine.
If the computer does not have precognition, EVERY player increases their $$ or at worst doesn’t change it, by taking two boxes. Period. However likely you think a subset is to choose two boxes, it is still the best play. For EVERYONE.
And I provided the math that shows that even at 51% you are better off being a one boxer.
Your math is simply not relevant to the hypothetical.
I’ll walk through the numbers for you at 51% accuracy. Four possible outcomes.
One boxer A. It predicted wrong. This 49% gets no prize.
One boxer B. It predicted correctly. This 51% gets $1M.
One box EV $590K.
Two boxer A. It predicted wrong. This 49% gets $1,001,000.
Two boxer B. It predicted correctly. This 51% gets $1000.
Two boxer B EV $541,490
The hypothetical assumes there is. And in the hypothetical we have observed that it is very very good at making the correct predictions. I am an empiricist. I don’t need to understand why the phenomenon occurs. It is observed to accurate enough that it has not yet predicted incorrectly for both sorts of choices.
Sheesh, this is tough. For every one boxer in your scenario, they’d have walked out with more dough had they taken two boxes. Every single one.
Further in terms of utility - if the box had predicted me to be a two boxer and I chose just the opaque one, then I lost $1000. That’s my worst case. Once it made that prediction I can’t win more.
Seeing your last post. Do you understand how expected value works? Not trying to insult. Just not sure where you are not understanding the math?
Do you see any possible groups and outcomes other than the four I listed?
If it gets you $1000 in every trial, compared to a strategy that has gotten $1,000,000 in every trial, I have no idea how you could possibly think that.
You’ve completely misunderstood my point if you think it was about what I think people will likely choose.
It clearly isn’t, since that strategy has an expected value a fraction the expected value of the “take one box” strategy.
I understand EV. Your math is the EV should everyone select as predicted. That is not the proper math, since no one must do so, and indeed no one boxer should.
I’m not sure why this is controversial. Assuming no precognition, every subject maximizes their $$$ by taking two boxes. This is indisputable.
Only if they could fool the computer, which is far no one has done. If they cannot, they’d walk out with far less money if they took two boxes.
If 1,000 people before you were successfully predicted by the computer, you should assume that you can be too, not that you are some super special chosen one who is too unique and special to be predicted.
I explained it, several times. If the computer has precognition (and I believe in this hypothetical, it does), you should choose one box. If it does not have precognition, every subject maximizes their dough by taking two boxes. It is indisputable.
I don’t understand how you can make that claim when it clearly lowers their expected return significantly if the computer is even 60% accurate in its prediction which is significantly short of precognition. It is indisputable.
We’re getting nowhere. I will accept that someone is wrong on the internet.
Huh?
No. It has nothing to do with should. It is simply what the average outcome is for that choice if the computer was correct 51% of the time.
What someone should do with information is … an exercise for the reader.
What you are doing is going from the other direction. EV does not work like that.
And agreed with your getting no where assessment.
It doesn’t matter how accurate the computer is. With the rules set up (unchangeable boxes, no reverse causality) every person who takes 2 boxes gets more than if they’d taken 1.
The computer has divided people into “people who understand causality” and “people who don’t understand causality” and given the 2nd group a free million. The first group were never going to get a million as the boxes were fixed before they even walked in.
Except these are completely erroneous numbers because we know there is no causal relationship. Suppose we are told some extra information. That 90% of the successful players who left with a million, have less than 10 fingers. Should you cut off your finger before opening the box? The expected value says yes. The EV of opening the box with 9 fingers vastly exceeds the EV of opening the box with 10 fingers.
Causality is immaterial (unless a player knows as fact that the method the computer uses somehow does fit them). It simply is better than chance at predicting. None of know how. Lots of attributes have statistical associations and patterns that travel together. This computer has recognized sets of attributes that highly frequently travel together with what choice a player actually makes, even when the player thought they would do something else ahead of time.
There is a statement that I can agree with.