Hypothetical riddle thing
 

I came across this recently, and I thought it was a really interesting question, so I've decided to share it with you all!

"A priestess at Delphi has a record of .99 accuracy in her predictions of human behavior. On an altar before you are two boxes: an opaque one whose contents you cannot determine and a transparent one obviously containing a silver coin, which you judge to have the market value of $1000. She gives you two choices: (1) take only the opaque box or (2) take both boxes. As she correctly tells you, she has or has not previously placed inside the opaque box a large gold coin worth 1000 times the silver one, depending upon whether she expects you, as a rational agent, to take only the opaque box or both boxes. Should you take only the opaque box or both boxes, knowing that 99 out of 100 agents who took both found the opaque box empty? Or should you forego the silver coin and take only the opaque box, knowing that some- although only 1 out of 100- came up with nothing? Why?"

Well? What do you choose? I would pick just the opaque box. Seems like I'd be likely to get a million bucks out of the system if I do.

There must be something I missed here, cause it seems obvious that everyone would want to choose the opaque box. The reward for being the one out of 100 agents to get both the gold and silver coin is simply $1,001,000, the extra $1000 not being worth much at this point.

Wait... why are we agents? The catch must involve this somehow.

I agree that thee must be a flaw to the problem or the wording of the problem. First, with regards to expected value, the expected value of the gamble is far bent towards taking the opaque box and taking the chance, being $10,990. You know, 1%*1,000,000 + 99%*1,000. This value vs. a 100% at getting $1000 makes taking the risk worth it.

Second, it was worded that you either choose both boxes or just the opaque. Why not either / or? The wording in the last two sentences are unclear.

Hmm, should option (2) be taking the transparent box?

Coz then just to be 100% safe can't I take two boxes? Its a win-win situation... *confused*

Okay. So....I can take just the opaque box with a possibility of nothing in it, or both boxes with a possibility of one being empty and the other definitely with money in it?

Duh--I'd take both. I'd have an automatic $1000, and if the other box is empty, I'd sell both on eBay and make money that way.

And, since this sounded familiar, I did some searching, and discovered that it's a variant of "Newcomb's Dilemma." There really is no correct answer--it's philosophical in nature.

She will place a gold coin in the opaque box if she expects you to take just that box. If she expects you to take both boxes, she won't put in a gold coin. Remember that she is 99% right in her predictions.

Yeah, to some people it would seem painfully obvious to just take the opaque box. But to others it would seem ridiculous to not take both, their reasoning being that, since she has already decided whether or not to put the coin in the opaque box, why not just take both to be sure?

I think you need to break it down by cases, and look at expected values for both based on whether she screws up. Either you take the opaque, in which case you have .99 * 1000000 + .01 * 0 as the expected value. Or you take both in which case the expected value is .01*1001000 (total amount in the case she screwed up) + .99 *1000 = 11099.

99% of all people who took only the opaque box received $1,000,000.

99% of all people who took both boxes received $1,000.

The choice is obvious: go with only the black box and allow both history and the odds to favor you.