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many red ballsQuanta Magazine
•74% Informative
A mathematician at the University of Toronto posted a series of probability puzzles about urns and coin tosses on Twitter .
Quanta spoke with Litt about what makes a great puzzle, and why simple probability questions can be so deceptively difficult.
Litt ’s project demonstrates the limits of our mathematical intuition, and the counterintuitive nature of probabilistic reasoning.
In a coin-flipping puzzle, you try to find out who is more likely to win than Alice and Bob .
The puzzle was designed to defeat a heuristic that someone had proposed for one of the previous variants.
But the puzzle suggests that your intuition has to be very sensitive to the setup of the problem.
If you look at all the possible differences between Alice and Bob ’s scores, these average out to zero .
But you can also compute the “ second moment,” where you average the squares of the differences, and the third moment.
The community that has been working on your puzzles seems like a pretty wholesome ecosystem.
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