Nobody can predict this ball
The short answer
Nobody can say where one ball dropped through a board of pegs will land, but a thousand of them always pile into the same bell-shaped mountain. On a board of 12 rows there is one path to each edge and 924 paths to the middle, so the middle fills fastest. A casino works the same way: it cannot predict one spin, but over many spins its 1 in 37 edge on European roulette shows up.
Chapters and transcript
- 0:00
Where will this ball land?
A ball drops into a board of pegs. At each peg it bounces left or right, and nobody can say where it will finish.
- 0:06
Same drop. Different ending.
Drop another ball from the same spot and it finishes somewhere else.
- 0:11
Now drop a thousand. What shape?
Before a thousand balls fall, guess the pile: flat, jagged, or a mountain?
- 0:16
A thousand balls
A thousand balls fall through the pegs, each one bouncing at random, and the pile begins to grow.
- 0:32
A mountain.
They form a mountain: tall in the middle, thin at the edges.
- 0:38
Run it again. Same mountain.
Sweep the board clear and drop another thousand. Every ball takes a new path, and the same mountain comes back.
- 0:45
One ball: nobody knows.
For one ball, nobody knows the answer. For a thousand, you already knew it.
- 0:52
924 ways to the middle.
On this board of 12 rows, only one path reaches each edge: every bounce the same way. The middle bin can be reached by 924 different paths, the number of ways to choose 6 bounces out of 12.
- 1:04
The supreme law of Unreason
In 1889 Francis Galton wrote that this curve reigns amid the wildest confusion, and called it “the supreme law of Unreason.”
- 1:10
A casino can't predict one spin.
A casino has no idea where the next spin will land, and it doesn't need to. European roulette has 37 pockets, which gives the house an edge of 1/37, about 2.7%, on an even-money bet. The climbing line is a simulation run by this film, not casino data.
- 1:24
Luck is only random up close.
One more ball falls, as unpredictable as the first. Luck is only random up close.
Sources
Every figure in the film comes from these. The animation is illustrative.
- Galton, F. (1889). Natural Inheritance, Macmillan, chapter V, p. 66.
- Path count: the binomial coefficient C(12, 6) = 924, calculated. House edge: 37 pockets on a European wheel, 18 winning and 19 losing for an even-money bet, so (19 − 18) / 37 = 1/37, calculated.