There are 2 boxes on a table, #1 has $1,000, #2 has $1,000,000. You can choose either #1 or both.
Prior to you entering the room, a highly accurate supercomputer analyzed your psychological makeup, and if it predicted you’d choose both boxes, removed the $1,000,000 from box #2.
What’s your choice, box #1, or both? Post your answer.
I’m definitely a “both boxer”.
intercst
I am also a 2-boxer.
JimA
I think you have it backwards. You can choose the mystery box ($1,000,000), or both boxes.
If the computer predicts you’d choose the mystery box, you’d have $1,000,000 if you choose it alone. If you choose both, and the computer thought you’d choose only the mystery box, you’d have $1,001,000. If you choose both and the computer predicts you’d choose both, you end up with only $1,000.
If you know the computer is super accurate, choosing the mystery box alone makes sense. You’re betting that the extremely accurate computer would have predicted it, awarding you $1,000,000. The only way you end up with $1,001,000 is in the rare event the super accurate computer is wrong.
I’m a mystery boxer.
You’re right, but my choice is the same. The “expected utility” of taking 2 boxes is $1,000, plus the probability of the supercomputer being wrong on my choice".
I’m making the same calculation when I chose to invest in a Long-term Buy & Hold index fund, rather that use any of the thousands of other strategies that produce lesser returns for some where between 95% to 98% of the investing public. If I can guarantee that I’ll end up somewhere in the top 5% of investors in terms of investment returns, why work harder to produce inferior results? Holding an index fund is a financial “free lunch”.
intercst
This is not an accurate description of the puzzle because it omits that you can see the content of the $1000 box.
As described by @intercst these are the odds:
The real puzzle?
The Captain