Falling balls (plinko) demonstrate the normal distribution.

"St. Petersburg Paradox" (Niklaus Bernoulli).
Flip an even coin, continue until you land on "heads".
The payout is $2^n (that is the payout doubles each toss).
The average/mean payout approaches infinity (.5 x 2) + (.25 x 4) + (.125 x 8) + ... = infty.
However, there is a 50% chance you will win $2 (median).
Is the "fair" wager $4 or more than all the money in the universe?

The view that emerged was that the universe
itself was a machine, perhaps like a gigantic, complex clock.
If we could understand the motions and connections be-
tween all its wheels and gears, we could predict their future
positions throughout all of time...
To mark his 60th birthday on January
21, 1889, Oscar II, King of Sweden and Norway, proposed to
give a prize to the best mathematical essay on this question.
Of the 12 essays received, the winning essay was submitted
by the French mathematician Henri Poincare´ [12]. He
showed that if we have three bodies in space, even though
we know the law of gravity and the conditions under which
the three bodies start, we still cannot necessarily predict the
future locations of the three bodies. It is as if we have ex-
amined all the gears in our great-grandfather clock in the
parlor and so we know how each one works and how each
is connected to all the others. We set the time on the face of
the clock. But we still can’t correctly predict the time that
will be on the face of the clock the next day. About 70 years
later this behavior was given the name “chaos.”

https://onlinelibrary.wiley.com/doi/epdf/10.1002/1099-0526%28200003/04%295%3A4%3C34%3A%3AAID-CPLX5%3E3.0.CO%3B2-3
[12]: Barrow-Green, J. Poincare´ and the three body problem. American Mathematical Society: Providence, RI, 1997.