The balls in a Galton board fall down randomly. Any time they come to a junction they can take any number of paths and it's almost impossible to accurately predict every ball's trajectory.
The problem with individual stock prices is that they do not follow a "random walk" because the next price in a sequence is NOT independent of its previous movements.
It is a fundamental restriction in the definition of "random walk" that each movement is completely independent of all previous states.
It's also a good way to explain the particle/wave duality. There's no way to track and predict the path of one particle but the end result of all the particles together follow a predictable wave pattern.
This is how you teach statistics, in college and highschool I was taught statistics and probality theory as if it was a recital I never understood what a distribution is and how it works or hoe itreflects on real world applications, thank you for this
We actually made a Galtonbrett (Brett is German for board) as a gift for our math teacher for high school graduation. It was made out of wood with many nails, plastic balls from a BB-gun, behind a PMMA cover. It showed not quite a normal distribution, our nails were a bit crooked 😅
So don’t be fooled by flashy lights and cool peg boards with neon pachinko boards! If the middle stuff is low and only the ends are the jackpot, dont even try it. You’re way more likely to walk out broke than to go out of there a millionaire.
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It is a fundamental restriction in the definition of "random walk" that each movement is completely independent of all previous states.