What If God Were A Giant Game Of Plinko?

The holiest series on television is a game show with millions up for grabs. It’s called “The Wall,” and it comes back on the air for a third season Wednesday at 8 p.m. EST on NBC. In its glitzy, 42-minute episodes, we catch a glimpse of the face of God.

Its basic premise is simple. Glowing, beach-ball-sized orbs fall from one of seven numbered slots at the top of the titular four-story-high wall. Those orbs fall down through a gridded maze of pegs, eventually landing in one of 15 slots at the bottom. Each of those is labeled with a dollar amount from $1 up to, in the final round,$1 million. Some of the orbs are green and some of the orbs are red. If the orb is green, you want it to fall into a slot labeled with a large amount of money, which is added to your total. If the orb is red, you want it to fall into a slot labeled with a small amount of money, since that amount will be subtracted.1

As the orbs skitter and kerplunk their way down the wall, the contestants scream, beg and plead with the wall to deliver the orb into the desired slot. They beseech; they supplicate; they importune. Actually, the only really fitting verb for what they do is “pray.” They pray to the wall.

“Love on us!” screamed one contestant, addressing the wall.

Contestants get to choose from which slots they want to drop their orbs, which creates a new moment to consult the heavens. To wish them luck on their random plummets, the contestants channel dead grandmothers, dead fathers-in-law, children’s birthdays and model years of first cars.

In a review of the show for Vulture, Jen Chaney called it “a carbon copy of Plinko,” the popular game played on “The Price Is Right” where a disc is dropped through a similar vertical maze. Sure, but Plinko is to “The Wall” as a toaster is to a burning bush. Most obviously, the Plinko board is maybe 10 feet tall, whereas the wall is 40. A Plinko chip takes about five seconds to complete its random descent; a wall orb takes twice that — all the more time to contemplate the randomness. In Plinko, contestants drop their own chips; on “The Wall,” things are, quite literally, out of their hands. But the biggest difference is the location of the contestants themselves. On “The Price Is Right,” they are on a small landing atop the board, staring down at a foreshortened, stochastic journey. On “The Wall,” they stand at its foot, supplicants to its process, staring up at their future like Daniel out of the lions’ den.

But why the praying? The wall is of course just an enormous random number generator. But couldn’t the agnostic among us say that that is also exactly what, from a certain point of view, God is? Is the wall a merciful wall? Is the wall an awesome wall? Is the wall a vengeful wall? As the show’s host, Chris Hardwick2 (who is fantastic — priestly, even), says: “The wall gives and the wall takes away.”

And it’s precisely this deeply believed illusion — that you can fight fate, that you can control the randomness, that prayer works if you just pray hard enough — that makes the show so fascinating. Don’t get me wrong: When the show’s on, I, the supposedly cold, statistically minded viewer, deeply believe that I can control the randomness, too.

Governing the specific brand of randomness on “The Wall” is something called the central limit theorem. In your statistics textbook, it might look something like this:

\begin{equation*}\sqrt{n}\left(\left(\frac{1}{n}\sum_{i=1}^N X_i \right)-\mu\right) \xrightarrow{d} N(0,\sigma^2) \end{equation*}

In English, this says, more or less, that if you aggregate enough randomness — any kind of randomness! — you tend to find within it the lovely bell curve called a normal distribution.

Bounce enough orbs down the wall’s face — each going left or right as they meet each peg — and you’ll find a probability distribution that looks like that curve.

I watched every episode of the previous season of “The Wall” and recorded the fate of each orb — its color, where it began and where it landed. Exactly 400 fell. It’s not the biggest sample size you’ve ever seen, but it’s a start.3

With enough time, a graceful bell curve emerges from the chaos.

A few centuries ago, statistics was a divine science. Back then, a man named Sir Francis Galton, an 1800s scientist, polymath and half-cousin of Charles Darwin, was obsessed with statistics, sociology, anthropology and eugenics.4 He made an invention called a Galton board, which illustrates the central limit theorem physically. It’ll look very familiar to any loyal “Wall” fan. Many tiny balls fall from the top of the box down through a grid of pins, bouncing randomly as they go. They land, bell-curve style, in a series of bins at the bottom.

Galton was in awe of the central limit theorem. “The law would have been personified by the Greeks and deified, if they had known of it,” he wrote. Deified! Indeed, the central limit theorem often plays a key role in crackpot mathematical “proofs” of the existence of God. There is also serious academic debate on the topic. Some have argued that chance eliminates God, some vice versa, and some that chance lies “within the providence of God rather than outside it.”5

The type of central limit theorem acting on “The Wall” is called the de Moivre-Laplace theorem. A century before Galton, Abraham de Moivre, a French mathematician, introduced it in his book, “The Doctrine of Chances.” The book, often cited as the first probability textbook, was immensely popular with gamblers. But, at least on paper, de Moivre distanced himself from these readers. In a dedication in the book’s 1738 edition, he wrote: “This doctrine is so far from encouraging play, that it is rather a guard against it, by letting in a clear light, the advantages and disadvantages of those games wherein chance is concerned.” He trusted that the explication of randomness would keep people away from it. Tell that to Matt and Jean, who won $1,100,098 on “The Wall.” De Moivre was a steadfast Christian, imprisoned for his Protestant religious beliefs under Louis XIV. But Pierre-Simon Laplace, the theorem’s other eponym and the so-called French Newton, was not so devout. He worked on mathematics, statistics, physics and astronomy and, so the story goes, once had a run-in with Napoleon. Laplace had given the emperor a copy of his work describing the workings of the universe, in which Napoleon found no mention of God. He asked Laplace why. “I had no need of that hypothesis,” Laplace replied. But Laplace hypothesized something that, if not about God, was godlike. The Frenchman imagined a sort of superman, able to cut through any uncertainty like a saber through chèvre. In an 1814 essay, he described that entity: An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. This hypothetical intellect, one that could use math to see the future the way we can remember the past, is often called “Laplace’s demon.” Two hundred years hence, presumably this demon would know quite a bit about the future of orbs, too, since they’re sized snugly between the tiniest atom and greatest bodies. But without the demon, it’s difficult to know where any one orb may fall. The contestants on “The Wall” are hoping they can slice off individual pieces of the beautiful, divine logic of bell curves for themselves. But we can’t always slice off the piece of the bell curve that we want. Sometimes an orb is just an orb. Ardent televised appeals to God or demon about falling orbs notwithstanding, maybe those who became newly minted millionaires just … got lucky. Chris and Katie wanted lots of money, too, but they took home exactly$0 from their episode. Darnell and Dion took home \$0, too. So did Jeff and Jamie. And so did Erin and Rachael.

Only one thing is certain: the randomness. That’s why we pray. And that’s why we watch.

## Footnotes

1. Each round gives players a different number of orbs, and they can earn more green orbs by answering various trivia questions correctly.

2. Hardwick is also an executive producer, along with LeBron James.

3. NBC declined to share videos of the show’s first season.

4. He coined the term.

5. “God, Chance and Purpose: Can God Have It Both Ways?” by David J. Bartholomew.

Oliver Roeder was a senior writer for FiveThirtyEight.