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The answer depends entirely on what "rarely makes mistakes" means.
If the prediction is correct more than 50.05% of the time, then I would take the mystery box. Expected value = 0.5006 * 1,000,000 = 500,600
If the prediction is correct less than 50.05% of the time, then I would take both: expected value = 1000 + (1 - 0.5004) * 1,000,000 = 500,600
Since "rarely" usually means some value much less than 50%, I would definitely take the mystery box.
An angle I don't see people looking at is to reframe the problem with amounts that are much more understandable, there is one thousand times more money in the mystery box, so let's do the following:
The Open box has 1 cent in it, and the mystery box might have $10, what do you do?
Y'all are telling me you'd rather take a penny and have a tiny Chance at $10, rather than taking $10 with a tiny Chance of getting zero?
As the values are already settled, I take both boxes.
This. Iβll take a guaranteed $1,000 with a chance at a million every single time.
It means that the people in the experiment have $1,001,000 to give way, for free.
What if I rob them first?
What if I convince them to unionize and they redistribute all the money fairly among the workers and force management to not conduct shitty social experiments on people?
this guy thinks outside the box
Mmmm, this sounds like an idealist hypothetical problem that in reality canβt exist, so to engage with it is to engage with nonsense.
The predictor rarely makes mistakes becauseβ¦ just because. Itβs axiomatic. The predictor runs on the magic of unsupported assertion.
Some version of it could exist. Not with the big numbers and not with the high degree of certainty in the problem, but you could have, say, somebody who's on average 70% accurate at reading people and the boxes are $1 and $10.
It is somewhat idealist in that it's a contrived scenario, but it's really just idle curiosity on my part. Maybe it could reflect something about people's thought processes, or maybe it's just people interpreting the question differently.
Even if it were to exist in the short run, it wouldnβt be stable. The predictor must be predicting somehow, which eventually could be at least partially sussed out, and future decisions would change as a result. Unless the predictor runs on literal magic, it would eventually no longer fit its own definition.
You can flip the problem around and have it be mathematically the same. The predictor has some knowable accuracy, you can run the experiment many times to determine what it is. Let's also replace the predictor with an Oracle, guaranteed 100% always correct, and we'll manually impose some error by doing the opposite of its prediction with some probability. This is fully indistinguishable from our original predictor.
Now, instead of the predictor making a prediction, let's choose our box first, then decide what to put in the mystery box afterwards, with some probability of being "wrong" (not putting the money in for the 1 box taker, or putting the money in for the 2 box taker). This is identical to having an Oracle, we know exactly what boxes will be taken, but there is some error in the system.
Now we ask, should you take one box or two? Obviously it depends on what the probability is. There's no more "fooling" the predictor. So, you do the EV calculation and find that if the probability is more than 50% accurate (in other words, if the probability of error is less than 50%), you should always take 1 box
A rule of thumb I think is good for most sorts of investment is, what choice can you feel good about making whether or not it works out? I can handle not getting 1k, but I would feel like a real chump missing out on an easy 1m without giving my best effort. If I pick just the mystery box and win, I feel like that win is deserved. If I pick just the mystery box and I walk away with nothing, then at least I don't have to live with the shame of being a 2-boxer, which is more valuable than $1k. If I pick both boxes, I most likely get a little bit of money and a lifetime of bitter regrets, or in the less likely case get 1.001 million dollars and a sense of having barely avoided disaster and not really "deserving" it. Choosing only the mystery box is the clear choice because it is the choice I am more able to handle having made, on an emotional level.
Fuck those boxes and the game. Steal the computer. Any computer that can predict individual human behavior with 99% accuracy would be worth billions. If such a thing existed and could be controlled, it'd be a total waste to have it running grad school human lab experiments. That's actual god-tier power.
I'll take the guanteed $1000 and not the mystery box so the prediction is always wrong :)
I am, admittedly {confused by the premise|too hypothetical to warrant reasoning about}, but, I am interested in how there is ever a possible downside to taking both?
It's {$1000|one box}, {$x|one box}, {$1000+$x|two boxen}. $1000+$x > $1000 because the hungry alligator eats the bigger number
That's what has me confused. I thought I was misreading something cause I couldn't see a downside to not taking both boxes. If the box is empty, you still have the $1000 and if it's not then you get even more money.
The point is to reveal the different frames of analysis people use to make the decision.
This thought process, "The decision's already been made, either way it's always a free $1000," is one way of looking at it. But another way of looking at it is, "Those who choose one box tend to walk away with more money, so the evidence shows that taking one box is the better approach." These approaches sort of "talk past each other," because they're looking at completely different parts of the problem in order to draw their conclusions, and those different parts indicate very opposing conclusions.
It obviously depends on the computers mysterious ability to predict what I'm going to do.
once the prediction has been made, your choice no longer influences the outcome.
This statement doesn't make sense. The computer would predict that you would think that.
Take out my gun, pistol whip the researcher, and steal the $1,000,000.
Assuming I knew that my behaviour was being modelled and this model would influence the outcome, I'd remove myself from the decision making process and flip a coin.
I think the numbers are a little off for this to be tempting, if Iβm getting $1,000,000 then a K is a rounding error and I see no reason to make the mil any less likely for it. Like if I wanted that extra grand throwing 10% of the mil into a short GIC would be how Iβd get it personally, for a risk free $1,001,000
This feels like the poison scene from the princess bride, so I'll approach it with that level of intellectual derangement.
Which means the obvious first step is to recognize that the house is a cheater who wants you to stay poor so your choice doesn't matter. There is poison in both cups and I will lose either way. Money no longer influences my decision.
Next, I flip a coin ten times and note my reaction to the choices. That's my gut instinct and obviously what the model predicted unless it's either not smart enough to know my gut or smart enough to predict my double bluff, therefore useless.
Next, I decide which variables are most likely to influence the prediction (gender, age, education level, big 5 personality score) and realize this is the adult marshmallow test. I obviously think I'm smart and want the model to know that, so it obviously predicted that I would take one box because I'm a good little goodie two shoes who delays instant gratification for the potential bigger payoff. Therefore I choose two boxes because the model would never expect someone as smart as I to make such a dumb greedy move. Surely, I have outsmarted the supercomputer with my quadruple bluff and have won.
And then I remember I am dumb and the model knows that, because in my excitement, I forgot that the house is a cheater who always wins (and there was likely never any money in the mystery box because researchers never get that kind of funding). I am forced to believe that the model accurately perceived me to be a greedy idiot who took two boxes against my better judgement, shattering my ego.
But hey, I at least got $1k out of it.
two-boxers are why we cant have nice things. and they themselves cant either.
I already opened the mystery box before you finished explaining.
Just the mystery box. If the computer rarely guesses wrong, then Iβm $1,000,000 richer.
I'm playing with the house's money.
If I get nothing, I'm no worse off than I was before.
Besides, the mystery box is a mystery, and I love a mystery.
my favorite flavor of Dum-Dum
I'm the kind of person who would ask for their definition of "rarely". How many 9s are we talking? If it's at least three nines, I'm one-boxing it.
Link to the Veritasium video if anyone is wondering:
https://www.youtube.com/watch?v=Ol18JoeXlVI
I'm on the 'just grab the mystery box' side π
Do a coin toss to choose.
So, if I'm understanding right, the computer said there's a great chance at $1 million in the mystery box if I'm the type to pick it and only it, which I am.
But I pick it for this bad reason: friends and I like to make fun of my troll luck. I'd take it, and somehow get $0 despite several more people after me will get $1 million after me, including two boxers. We'd laugh at "can you believe this shit?" and know it just wasn't in the stars, just like that time I broke my ankle and all the automated walkways at the airport were broken. It's that kind of thing (and yes that happened). My infamous troll luck strikes again!
Or it's all superstition and I get a million bucks, since I'm pretty sure my infamous luck is just confirmation bias. Either way, fun had by all.
1 box
I don't need the 1000, so the mio-gamble would be my choice.
If I'd really need 1k right now, those would be the choice. Gambling is stupid.
βYou took the box! Let's see what's in the box! Nothing! Absolutely nothing! STUPID! You so STU-PIIIIIIIIIIID!β
I don't need $1M. I'll take just the $1000, if the other box has a million in it they can put it towards the next experiment.
Weird, I just saw a video about this. I'm a second box guy. Feel like talking both boxes is trying to "cheat" or "trick" the computer. Or maybe a greed thing. I'm not really sure. But I'd probably go for just the second box.
One box. I might be unlucky and lose out on $1000 in that other box, but I wouldn't be too bothered. On the other hand, if I were to grab both and get $1000, the thought of what if I took just one box and got a million dollars would gnaw at me for the rest of my life.
The decision changes dramatically if the box with less money were closer to a million though.
I only know about this because of zero escape lol.
One box, I'm not messing with anything powerful enough to predict the future.
One box
I'd just walk away entirely.
I'll take the safe grand and not bother with gambling.
When I watched the video I immediately knew I was a 2-boxer. "Its just 1000$ more, the mystery box doesnt magically change". Of course I know it is better to be the kind of person to only take the mystery box, because for me it will be empty. But saying "I would take only one" feels like cheating, like the mystery box would still be empty because the supercomputer knew I was only pretending.