This playground needs JavaScript to run experiments. The story is still here.
A ball, not yet fallen
Eight independent choices lead to nine possible endpoints. A path records what happened once.
Left. Or right.
At a fair fork, each direction has a one-half chance. Earlier left turns do not make a right turn due.
More paths than places
Four choices make sixteen direction sequences. Six lead to the central endpoint.
The middle has more ways in
Eight choices make 256 sequences. Their endpoint multiplicities are 1, 8, 28, 56, 70, 56, 28, 8, 1.
Small samples have character
Two sets of sixteen balls can look different. The expected central count is 4.375, not a promised result.
A different leaning
Changing p changes the chance of turning right at every level. It starts a separate experiment.
Same rules. Different evenings.
Independent rounds differ. Larger samples are usually more stable, but each added ball need not move the shape closer to theory.
A portrait of 256
Every ball in the portrait belongs to the same saved teaching round. Each retains its own path.
Give chance a set of rules
The interactive workbench can use 4, 8 or 12 choices, right-turn probabilities of 0.25, 0.50 or 0.75, and 16, 64 or 256 samples.
Still worth watching
Many journeys reveal a shape. The next one has not been promised.
This is an ideal independent probability model using replayable pseudorandom samples. The animation is not measured collision physics.