Results of Zeno's Challenge #36

After some delay (with apologies!), the results of Challenge #36 are finally in. Wow!!! Brace yourselves for the outcome....and our man Charles can rest easy, given the responses. But first, here's the original challenge:

Ever-so-Bold Charles Challenges Again!

After numerous Zeno's patrons' urgings, it seems that our man Charles has kept his eye on Zeno's players, and has done some calculating--at least to his own satisfaction. After the earlier challenges #13 and #20, Charles has now agreed to again put his money where his mouth is! He has assured respondents that he will ACTUALLY PAY winners, if there are any, for any winnings in the latest on-demand Coffeehouse challenge...So let's get busy and see if we can outsmart Charles in this decision-scenario, but he seems confident! Here's the challenge:

You are to choose either Box A, B, or C, and only one.

Choose Box A and you will win \$1 if 1/3 of those playing choose A also; otherwise, you win nothing;

Choose Box B and you win \$10 if 3/4 of those playing choose B also; otherwise, nothing;

Choose Box C and you win \$5 if 1/2 of those playing choose C also; otherwise, nothing.

So there it is, yet once more--think about the best choice, and submit your entry. Charles seems confident!!!

Results: There were 88 submissions to the challenge, which means, given the ground rules, that any winning entry must satisfy one of the following necessary conditions:

for A (\$1 winner), at least 29 votes; for B (\$10 winner), at least 66 votes; for C (\$5 winner), at least 44 votes).

Zeno's submissions were as follows:

A=17; B=54; C=17

Hence, nobody wins anything!!!!!

I've included below examples of votes cast by three individuals, with their thoughts on the matter, in order to share some reasoning on the minds of fellow patrons...these reflections are representative of the others, I might add. I am curious as to what you all think went wrong, as you reflect on the nature of this exercise. Curious indeed.....

Del Engineering, from Pennsylvania, writes:

comments: I choose A.  It is the easiest threshold to meet.  The best I can hope for is non-thinking cohorts for a 50/50 chance.
If there is only 1 Player I win.
If there are 2 Players I win
If there are 3 Players I win
If there are 4 or more Players I am at the mercy of human nature.
If my partners were random like dice. Where a die role of
1 or 2 = A,
3 or 4 = B, and
5 or 6 = C
I would have an edge because my one vote for A would tip the scales just over 1/3 and into our favor.

Assuming that my cohorts can reason as I do, they would see that A is the most probable choice and that would give us all a greater chance of winning.  Sadly, groups of people that can not communicate are worse than random players (dice). My cohorts, being human, will probably tip the scales to something short of the 1/3 threshold we need to win.  Because unlike a non-thinking die. Humans share the same brain evolution as the monkey who gets his hand stuck in the coconut not willing to let go of the contents. Greed will overcome reason and none of us will succeed.  Given the power to communicate we could make a coordinated attempt at B and succeed, but without communication, A is the only choice with a chance of winning.

Avrit, from New Jersey, writes:

comments: I choose box B. This is becuase i have no money to lose.  I have a chance of making the most money. I am also contributing to the 3/4 that are needed to win this.  If i were to pick another box i would take away from the 3/4.  If i don't win then i don't lose money either. Why not go for the biggest amount?

Anonymous, from New York, writes

comments: Box C. Why? Because it is the more risky than A and less risky than B -- the middle option is best. always strive for balance.

John Symons, from Canada, picked B, but his comments rang true in the end, unfortunately:

comments: I choose Box B.  If everyone picks the same box, everybody wins.  Since entrants can't communicate with one another, we need to look at something within the question which helps us agree on a box.  I think Box B presents itself as the obvious choice, as it offers the highest reward.  Of course, it's likely that many people will ignore the  cooperative element of this game, and I expect the vote to split and for no one to win any money.  Still, it should be interesting to see what the results are.