Here was the last Challenge #70, along with several thoughtful responses. Thanks so much!
Ron Barnette

## Charles' Variation of Newcomb's Paradox

Charles and Maggie have been celebrating at the Coffeehououse the critical thinking responses to Challenge #69 by Professor Peace's logic students and the others who submitted their thoughtful deductions. "How nice it is to receive so many thoughtful responses...congratulations to all!," added Maggie. "Charles, do you have a new Challenge to pose for Zeno's patrons?"
"Yes I do, dear Maggie, and let me pose our new challenge as my variation of a long-standing paradox known as 'Newcomb's Paradox.'  I want to exercise creative decision-making thinking, and some inductive logic, as our Zeno's patrons are challenged to think and reason abstractly. I learned of this from our good patron Troy last week. Mine, however, goes like this for our next Zeno's Coffeehouse Clallenge, so read it carefully."

Assume the following as a true fact, hypothetically, as your decision depends upon this assumption.
A foreseer claims to have the ability to predict your thoughts and actions days in advance. But unlike most who claim to foresee future actions, this being has been correct 100% of the time with over 100,000,000 precictions and with no single error! You have agreed to take part in an unusual test of the foreseer's powers. Several TV news programs have provided the facilities and put up a large sum of money. All you have to do is abide by the conditions of the experiment. On a table in front of you are two boxes: A and B.

Box A contains a thousand-dollar bill. Box B either contains a million dollars or is empty. You cannot see inside either. Of your own free will (if there is such a thing), you must choose either to take Box B only or to take both boxes. Those are the only options.

The true assumption you must make is this: Twenty-four hours ago, the foreseer predicted what you would choose and decided then whether to put the million dollars in box B. If the foreseer predicted correctly that you would take only box B, he put the million dollars in it. If the foreseer saw your taking both boxes, he left box B empty.

Personally, your only motive is leaving the experiment with as much money as possible. You are not so wealthy that money means nothing. The thousand dollars in box A is a lot of money to you. The million dollars is a fortune. Your Zeno's Challenge is to analyze the situation and decide on the most profitable of the two options, given the assumptions. What should you do? Take both boxes or just Box B?

Please keep up the effort. Thanks!...Ron Barnette

From Brett Welland in Australia: I would choose Box B only...a thousand dollar bill doesn’t exist thus Box A is purely misdirection however, the probability of success, whether Box B has 1 million dollars in it or is empty is even. Nothing to lose and everything to gain, by that choice alone.

From Belinda Welland in  Australia:
Hi,
One would think that with an error rating so favourable, it makes sense to gamble on box B only.  If the foreseer is wrong, then you will lose \$1000 that you didn't have anyway, so you are no worse off. But if she is right (and you have more than adequate reason to believe she will be) then you are \$1,000,000 better off.

The other option, to take both boxes results in you being guaranteed \$1000, but in order to do so you are sacrificing the \$999,000 that you could have received had you chosen different.

The answer comes down to your willingness to gamble.  Small risk = small gains, large risk = large gains, but either way you will not be worse off than you are now, therefore I suggest just taking box B=

From Troy Williamson:
Okay, Ron ... you had me scratching my head with this one. There is "logic" on both sides. Here's my "official response":
==========
If I flip a coin 50 times and "heads" comes up each time, what is the probability of getting "heads" on the next flip of the coin? The probability is 50% (= 1/2 = 0.5) ... because a fair coin always has a probability of 50% of showing "heads" on any single flip -- regardless of what has occurred on previous flips. (The coin doesn't remember that it has shown "heads" 50 times in a row, after all.)
However, if I were to flip a coin 100,000,000 times and got "heads" on each and every one of those flips, I would have good reason to suspect that the coin is not fair. (And I'd have a sore thumb ... but that's a different issue.) While getting 100,000,000 "heads" is possible, it is so improbable as to be "practically impossible."
In the current situation, we have a foreseer who whill predict my choice. On the surface, we want to say that it is impossible to predict the future, so the probability of him "guessing" my choice of box(es) is 50%. Just like the coin, the probability of the current prediction is not affected by the outcome of previous predictions. (To believe so would be to fall prey to the "gambler's fallacy.")
However ... 100,000,000 correct predictions with no errors is so extremely improbable that it is hard to believe that there isn't SOMETHING else involved here. Maybe the foreseer DOES have the ability to see into the future. The feat resembles a magic trick, and the foreseer must have SOMETHING "up his sleeve" to be able to do what he is doing. There is no logical explanation for it.
And so I face the "paradox" of making my choice. I can choose both boxes, guaranteeing myself at least \$1,000 ... or I can choose Box B only, trusting in the foreseer's ability to predict. And probability won't help here ... because all four possibilities seem equally likely -- there is nothing to indicate that one outcome is more or less likely than the others. (And, much to my chagrin, the foreseer is laughing, knowing that I would go through this long drawn-out thought process to try to determine the better choice -- while he already knows how much money I'll be taking home after the show!)
While I am nothing if not logical, I believe I would choose Box B only. I cannot offer a reason to believe the foreseer's ability -- I do not believe that such a foreseer could exist. But if it was documented that over 100,000,000 correct predictions had been made with no single error along the way, I would have to believe that something unexplainable must be involved -- that there is SOME trick that the foreseer is playing, enabling correct predictions to be made. My "logic" is telling me that the probability of such a feat happening by chance is so miniscule that the "evidence" suggests that there is some factor involved that isn't being (or isn't able to be) considered. Based on this, I'd take Box B only.
After all, I'm not paying to play this game -- if I leave with nothing, I'm no worse off than when I began. And, as a game show, there may be parting gifts for the losers anyway.

==========
I trust you had a wonderful holiday and that the new year is off to a good start for you. Drop a line when you can!
Regards,
Troy

From Steven Splinter:
I would sit there a while, pondering. Whether The Predictor knows my
> ultimate decision is meaningless to me - he's not the one
> deliberating. Just a parent may know what a child will choose, but the
> child will still ponder the options, as their perspective is different
> and has more immediate impact.
>
> But I'm not the only one in the hot seat, am I? This Predictor, what
> will happen to him? Is he happy being a predictor? Has he started to
> feel any pressure from always being expected to come up with the right
> answer? The Predictor becomes predictable, and people start expecting
> it of him and treating him accordingly. He may not want it. Maybe for
> him, this is a way out! He can purposefully predict wrongly, and be
> absolved any responsibility others will heap on him, justly or not. If
> I were a predictor as good as he, I may want out. So I'd want to know
> this man's history; a psychological report and interview would be nice
> too.
>
> The puzzle doesn't grant me that, though. I am given only the
> situation. I can say that just as the fact the sun has risen every
> morning for millions of years doesn't mean it will rise again
> tomorrow, the fact this man has predicted correctly so often doesn't
> mean he won't be wrong now. I should take both boxes and hedge my
> bets; I'm guaranteed \$1,000. But that thinking doesn't really serve me
> here. If a purportedly normal tossed coin consistently landed on
> heads, we'd be well within our rights to say something was unusual
> about that situation - it may be a trick coin, or modified some how,
> or the tosser knows just how to flip it to always land on heads. The
> point is, unusual and verified outcomes do matter, and should bear on
> our decisions.
>
> In the end, I'd take only Box B. If The Predictor is wrong, well, I'm
> sure I can get a few interview and media deals worth a couple
> thousand.
>
> -Steven

From Sue Chetwynd in the UK:

If it is really true ex hypothesi, that the foreseer can foresee your thoughts with 100% accuracy, then to maximise your income you must take only box B, since the foreseer will have correctly predicted you would and will have put the \$1m in it. However, if the foreseer were guaranteed to predict correctly, there would be no point in doing the experiment. The existence of the experiment presupposes some doubt as to the foreseer’s abilities. Under these conditions, and particularly being a risk averse person, I would take both boxes and the chance that the foreseer gets it wrong. This also presumes that the foreseer is the only person who decides what goes in box B.

Sue Chetwynd