January 22, 2021

An Awesomely Evil Test Question And The Game Theory Answer

This test question went viral on Twitter and then got coverage in the Baltimore Sun and other mainstream media. But most of the coverage was wrong. This video explains the game theory answer.

Blog post with a summary and more detailed discussion:

Tweet of exam question:

Baltimore Sun:

Reddit discussion:

Professor Dylan Selterman (who posed this question)
Washington Post article (published 7 days after this video):

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“The Joy of Game Theory” shows how you can use math to out-think your competition. (rated 3.9/5 stars on 32 reviews)

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“Math Puzzles Volume 1” features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews.

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“40 Paradoxes in Logic, Probability, and Game Theory” contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews)

“The Best Mental Math Tricks” teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews)

“Multiply Numbers By Drawing Lines” This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews)

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  • Hi Presh, what if there was a twist? If more than 10% choose 6, only those choosing 6, will get zero. Those who chose 2, get 2. So kind of high risk/reward for choosing 6. What should be strategy in that case? Is it just a chance (gamble)?

  • No… If you think you can do well in the exam, pick 2. If you are not one of the best students i the class, then pick 6

  • Technically, even when <10% of the others choose 6, you can raise the % to more than 10% by choosing 6 yourself and thus get 0 points.

  • You made up the part about "if =10%", that wasn't part of the puzzle.
    Just goes to show why point spreads are set at x and a half points. -(8D

  • Just fudge the matrix by:

    a) Threatening to (insert violent action) people to pick 2, starting with the weakest links. Repeat until <10% are picking 6.

    b) Start a petition to end this unfair, twisted game, and get the teacher sacked.. get 1000 signatures, and take it to the Dean. You've successfully boosted your CV through advanced organisational skills and got the superior grades.

    c) Declare to everyone you're going to pick 6, promising to split the excess 4 points with everyone who picks 2. Instruct them to decide who the other people will be who pick 6, so you can maximize your points. For a finishing touch, convince everyone of the morality of the sacrifice, "for the greater good".

  • Solution: Conduct an open lottery for who get 6, allocated to the maximum possible people.
    Eg. in a class of 100, 10 people will be chosen by lottery. If any of the "2s" try to move to 6, everyone will get 0.
    From my experience, the future people who's going to read your grade paper aren't going to care how many of your other classmates get A+ or 3.9 GPA, they will only see "oh, you got A+ or B in your econ class" (if that matters at all).
    So the solution presented will benefit almost every students (moving from C+ to B or A to A+) and individual students can't gain point by acting individually.

  • You are looking only at the "logical" pick. What about the "moral" pick? If there is one. cf the train switch dilemma.

  • True, if your concern is only for the greatest good for a singular being. However, if your goal is the greatest good without knowing what others are choosing, it is better to choose 2, as it improves the chance of anyone getting any points.

  • Picking 6 is logical ok
    Then everyone prb pick 6 then no point
    But if >90% ppl is pick 2 then boom points
    So if u pick 6 there is <10% chance that u can get 6 points
    Pick 2
    If there is <10% ppl pick 6 with then boom points
    So u have <90% chance getting 2 points
    Prb wrong somewhere but i will still choose 2 anywae
    One more thing, if u put this test to like 1000 ppl but they do it in a sequence then that =10% is literally happen everytime and u are one of 900 ppl who decide whether everyone get point or not
    Prb wrong

  • And that's how capitalism was born, better for a few to get everything and risk everyone getting nothing, instead of cooperation where every one gets a share.

  • It's only logical if we assume that you're self interested. If your goal is to maximize the total score of the class, it's illogical. So yes, if you pick 6 you're selfish.

  • When I played a similar game, the end result was that we have got zero as predict but it turned out that there were several other classes and some of them got non-zero scores.

  • The question dictates a condition:
    "If … of the class picks…"
    If I was the class, I'd let somebody else pick..
    This way, the condition will never be met, even in case of a 100% pick rate of 6 points.

  • The problem is the grading is a scaling one so the two extra points wouldn't matter anyway since everyone else is also getting two points and making the scaling go up, unless you luck out six points and pull ahead.

  • Wait, you're telling me that US college scores are relative instead of absolute. What kind of messed up educational system do you have?

  • When you got everything right and one of your classmates needs 2 points to get the perfect grade, you pick 6.
    With 10 people in the class, you guaranteed them 2 points.

  • There is a fundamental flaw in the explanations given here:

    YOU are a part of the class, thereby INCLUDING you in a 10% participation. If we represent the total students in the class with a letter ("x"), then the algebraic equation for figuring out 10% of that number ("y") whilst excluding yourself would be as follows:

    (x/10) – 1 = y

    However, there is not a single number to represent "x" that can make this statement true, because we're dealing with the idea of positive integers since we logically cannot have a negative total of students.

    Now, in the case of a class having only 10 students, the video's explanation still holds merit because you are a direct 10% factor vs any other case which would leave you as a fraction of that 10% total. So if the class has 20, 30, 40, etc. students, you can no longer reliably determine your fate as you now have to share the collective 10% with AT LEAST one other student.

    The legitimate probabilities of these scenarios playing out in your favor can likely be found using tables, but it's 6:30 AM and I haven't slept yet.

  • It's like the prisoner's dilemma.
    The best choice mathwise is the option that benefits you most, but if everyone thinks this way you'll get nothing.
    But if you all take the least beneficial choice, you'll end up with a better outcome.
    Sometimes the best thing you can do for yourself is is to not think of yourself only

  • But if you assume everyone is equally logical and selfish as you are, then everyone would be pick two because there is no better alternative.

  • I think you're better of to pick 2, because the scenario in which more than 10% pick 6 is more likely to happen if you think about it that every other student just picks randomaly or picks 6 because it's more than 2.
    Also it depends weather you like taking risks or not, and weather most of your class like taking risks.
    This "theory" in the video is not likely to happen most of the time since it depends on personality.

  • Motive analysis time ; why would any teacher offer such a scenario?? answering that question is the more pertinent issue, let the speculation begin!!!

  • There's math and logic vs empathy. In principle is not to hurt anyone picking 6. I know world is cruel and we have to be selfish to survive, but 4 points of 50 or 100 is worth of ruin solidarity?

  • Well, the better thing would be if you pick 2 you get 2 points, and if you pick 6, you only get 6 points if less than 10% of the class picked 6.

  • Isn't this a common knowledge problem? If everyone is reasoning in the same way, assuming there is no curve it is logical to pick 2. If everyone else is picking 2, it's safe to pick 6 for yourself. But everyone will be thinking that way and picking 6 and so on. There is no solution. If there is a curve then picking 6 is logical, but nobody gets any points regardless because everyone will pick 6.

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