Unexpected Phenomena

Collecting surprising phenomena that can be experienced mathematicallyNon-intuitiveAnti-intuitiveAnti-intuitive phenomenaSurprising relevance

• /prog-exercises/feeling-surprised-programming.

  • Efron’s Dice Efron’s dice
  • The “A beats B” relationship is not transitive. :

A = (0, 0, 4, 4, 4, 4),
B = (3, 3, 3, 3, 3, 3),
C = (2, 2, 2, 2, 6, 6),
D = (1, 1, 1, 5, 5, 5).

- Unlike the calculation of expected value, the calculation of "probability of winning" involves a nonlinear function that says "win small, lose big, win/lose once", which can be used to create a die with the same expected value but with a higher probability of winning.

• The probability of winning a gacha with probability 1/N drawn N times is rather low.
• In backgammon, throw two dice or throw one and go twice as far, and the latter will finish first.
  • Deviation from the mean and sample size
  • Low incidence in rural areas, but also high incidence in rural areas
• Uniform random numbers added together approach a normal distribution
  • [/prog-exercises/generate normal distribution](https://scrapbox.io/prog-exercises/generate normal distribution).
  • The public doesn’t seem to understand the “shape of the distribution,” as evidenced by the “random number cock” response.
  • How to experience it? → A game to get under the skin of probabilistic events.
• Repeated seemingly equal transactions create a gap between the rich and the poor. - Not a natural occurrence of disparity.
  • 5a56c7bcaff09e00000cb8d0
• Random distributions do not look random. - Distribution of random points
  • What humans naively imagine as a random distribution is more uniform than a truly random distribution
  • Because what humans usually observe, such as the distribution of trees in the mountains, is not a truly random distribution, but a homogenized distribution due to the effect of “too close together and they exclude each other”.

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