If you take the free lottery ticket, you have a 100% chance of winning, based on past performance. If you take the free lottery ticket and the $1,000, you have a 0% chance of winning, based on past performance. So why wouldn’t you leave the $1,000 and just take your $1,000,000?
So I walk into a room and there are these two boxes. Whose room is it? Do I have any idea who owns the boxes? Have I been given any reason to believe that it would be appropriate for me to take ownership of these boxes and their contents?
Absent answers to these questions, I’d probably take the $1000 to safeguard it on behalf of its presumed owner, and contact the owner of the facility to let them know some property had been left in the room that I’d be happy to return to its owner. (If I can walk into that room, others can presumably do the same.) I’d leave the opaque box alone, figuring that it was less likely to be stolen than the loose $1000 would be.
Because the box already has whatever it has in it. That’s not affected by your actions in the room.
Unless you believe the computer is cheating, and secretly adding or removing money while you are there.
Anyway, if the computer is that good, it knows I’m too curious to just leave the box alone, and also, that i don’t trust it. 
What I want most is for the opaque box to be filled.
That is not my decision at the point I make the choice.
All I can choose is (value x) or (value x+$1000). Since the computer knows I can follow logic it’s already almost certainly left the box empty.
I realise that by being able to figure this out I’ve preemptively shot myself in the foot, but at the point I make the decision there’s nothing I can do about it.
The options as I understand the OP’s post are:
- Take the box with the known $1000, leaving the closed box.
- Take the unknown box, leaving the $1000.
- Take both boxes.
Leaving both isn’t mentioned as an option.
What do we know?
- One box definitely has $1000.
- The other either has $0 or $1,000,000, but we won’t know until we open it.
So any way you look at it, the second box is equivalent to a coin flip from our perspective. We have no way of knowing what the computer predicted or why, and all we know is that when we open it, there will either be money or not. And from the information we’ve got, those have equal chances of being true.
So with that in mind, your options are still the same, but you can think of them slightly differently.
- Take the known $1000, and choose NOT to flip the coin.
- Flip the coin and leave the $1000
- Take the $1000 AND flip the coin.
So why wouldn’t anyone sensible take the third choice? There’s no downside to it, versus the other two which potentially leave money on the table.
There is $999,000 of downside to it. If I have a million, what do I care about leaving $1000 on the table? As I posted above - change the dollar amounts and rethink it.
No, it isn’t. But your actions in the room are impacted by your past, and the predictor can know your past, and it is good enough at taking people’s past and predicting future behavior that it got it right 1,000 out of 1,000 times.
Your actions in the room might not impact the money in the box, but the same causal chain that led to you making the decision you will make also led to the predictor predicting the decision you will make.
I don’t, I just don’t believe that I’m so much more special and unpredictable than the 1,000 people who went in the room before me.
Then it will have left you $0 in the second box
A coin flip has equal odds of landing heads or tails.
The computer does not appear to have equal odds of being right or wrong; it has gotten it right 1,000 times before, and the odds of doing that by chance alone are astronomically low.
Therefore, it’s not a coin flip.
(Bolding mine) This is the problem I have with your response. I totally get the logic for both choices, and I’m firmly set on my choice of one box. But I wouldn’t go as far as to say that taking both boxes is not sensible.
And that’s okay, because i don’t take other people’s money that’s lying in boxes in rooms. If i take one, i take both. But i don’t trust it, and don’t take even the $1000.
It kind of is, because (as I said earlier in the thread) at the point of making the decision you know that the mystery box either has less than $1000 or it has more than $999. The upshot is - would you put $1000 on black on a roulette table? I most certainly would.
Since a few people have said this already, if we need to posit that outside the first room is a man who tells you he has given $1,100,000 to a robot to give to you if you win a game, and that he will also match your winnings with a donation to an orphanage. So even if you don’t want to take his money, you’re still motivated to maximize winnings, and there are no questions of ownership.
It still isn’t a random outcome with a 50:50 chance.
There’s no randomness, the predictor is making a prediction, not guessing. And the odds aren’t 50:50, the computer has been correct 1,000 times so far.
That’s true for the computer, not the person making the choice.
The outcome isn’t random to the person making the choice, either. The mechanism by which the outcome is determined and the results of that outcome are unknown, but unknown is not the same as random.
Yes, but an unknown for a person making a choice with 2 possible outcomes (even if they are predetermined) is still 50:50. Randomness doesn’t enter into it.
So…wait…what am I doing with the cannoli again?
This does not follow. At all.
I have probably less than a one in a thousand chance of winning when I scratch off the ticket by taking and opening the box. Probably less. Probably much less. If I leave it I have zero chance of winning more than a thousand dollars.
Do I bother to metaphorically take the lottery ticket and scratch it off? Why wouldn’t I?
Again, assuming I play. Because I don’t trust what the computer says and I am not stealing someone else’s money just because they left in an open room in an open box with a computer …
I suspect you screwed the set up. You may have meant to say you can take either box but not both. Then there is a cost to taking the opaque box.
But as set up there is no cost.
Just because an outcome is unknown does not mean the odds are 50:50.
When I choose to take one box, the unopened box, there are two possibilities:
-
the computer predicted that I would take one box, and so put $1,000,000 in it.
-
the computer predicted that I would take both boxes, and so put $0 in it.
You’re saying that I should treat these as 50:50 equally possible possibilities. But if the computer was right in the last 1,000 trials, I’d be pretty silly to operate under the assumption that there’s a 50% chance that it is wrong.