SKU: 96433863130

Galton Board: Probability Demonstrator

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Description

Galton Board: Probability DemonstratorUser Guide Check out the new Galton Board app! The Galton Board with Pascals Triangle is a 12 by 9 (310mm by 218mm) probability demonstrator providing a visualization of math in motion and the powers of the probabilities and statistics. With the addition of the Stock Market Clip ons, the board illustrates the randomness and the probabilities of various market returns. The Galton Board displays centuries old mathematical concepts in an innovative,

 

User Guide

Check out the new Galton Board app!


The Galton Board with Pascal’s Triangle is a 12” by 9” (310mm by 218mm) probability demonstrator providing a visualization of math in motion and the powers of the probabilities and statistics. With the addition of the Stock Market Clip-ons, the board illustrates the randomness and the probabilities of various market returns.

The Galton Board displays centuries old mathematical concepts in an innovative, dynamic desktop device. It incorporates Sir Francis Galton’s (1822-1911) invention from 1873 that illustrated the binomial distribution, which for a large number of rows of hexagons and a large number of beads approximates the normal distribution, a concept known as the Central Limit Theorem. He was fascinated with the order of the bell curve that emerges from the apparent chaos of beads bouncing off of pegs in his board. According to the Central Limit Theorem, more specifically, the de Moivre (1667-1754) – Laplace (1749-1827) theorem, the normal distribution may be used as an approximation to the binomial distribution under certain conditions.

When rotated on its axis, the 6,000 steel beads and one large golden bead cascade through 14 rows of symmetrically placed hexagons in the Galton Board.  When the device is level, beads bounce off of the 105 hexagons with equal probability of moving to the left or right. As the beads settle into one of the 15 bins at the bottom of the board, they accumulate to create a bell-shaped histogram.

Printed on the lower part of the board is the normal distribution or bell curve, as well as the average and standard deviation lines relative to that distribution. The bell curve, also known as the Gaussian distribution (Carl Friedrich Gauss, 1777-1855), is important in statistics and probability theory. It is used in the natural and social sciences to represent random variables, like the beads in the Galton Board. You can also see the Y-axis and X-axis descriptions, and numbered bins with expected percentages and numbers of beads. 

 

Printed on the top of the board are formulas for the normal distribution, standard deviation and binomial expansions. 

Overlaid on the hexagons is Pascal’s triangle (Blaise Pascal, 1623-1662), which is a triangle of numbers that follows the rule of adding the two numbers above to get the number below. The number at each hexagon represents the number of different paths a bead could travel from the top hexagon to that hexagon. It also shows the Fibonacci numbers (Leonardo Fibonacci, 1175-1250), which are the sums of specific diagonals in Pascal’s triangle. Within Pascal’s triangle, mathematical properties and patterns are numerous. Those include: natural numbers, row totals, powers of 11, powers of 2, figurate numbers, Star of David theorem, and the hockey stick pattern. Other patterns in Pascal’s triangle not identified on this board include prime numbers; square numbers; binary numbers; Catalan numbers; binomial expansion; fractals; golden ratio; and the Sierpinski triangle.

Among the 6,000 steel beads, there is one golden bead, which demonstrates a single random outcome. Shown on top of each bin is the percentage estimates of the probability from Pascal’s triangle that a bead will land in that bin.  By following the golden bead, you can clearly observe those probabilities with each flip of the Galton Board. When a Stock Market Clip-on is in place, the golden bead can represent the likely range and probabilities of next month’s stock market return. The Galton Board’s probabilities as to which bin the golden bead will land in is a substitute for the prediction of stock market forecasters.

Embedded in this Galton Board are many statistical and mathematical concepts including probability theories, independent identically distributed (iid) random variables, the normal or bell-shaped curve, the Central Limit Theorem (the de Moivre-Laplace theorem), the binomial distribution (also known as the Bernoulli (1655-1705) distribution), regression to the mean, the law of large numbers, probabilities such as coin flipping and stock market returns, the random walk, the Gambler’s Fallacy, the law of frequency of errors and what Sir Francis Galton referred to as the “law of unreason.”

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SKU: 96433863130

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Lesley
Fort Morgan, US
★★★★★ 5
Withstands big dog
Color: Green Cactus
As a dog mom to two active pups, I’ve gone through a LOT of chew toys over the years and honestly, many of them just didn’t hold up. Some cracked, broke apart quickly, or became rough after only a short time of chewing. That’s why I was genuinely impressed with the MewaJump chew toy. Both of my dogs immediately loved it, and what stood out most to me was how durable it’s been compared to other toys we’ve tried. It’s held up really well with aggressive chewing while still seeming safe and comfortable for them to use. I also love that it keeps them entertained and engaged longer without constantly worrying about pieces breaking off. Definitely one of the better dog toys we’ve added to our home lately and Molly and Piper would agree.
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Reviewed in the United States on May 15, 2026
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THAILEI L SMITH
Draper, US
★★★★★ 5
Not recommended for strong chewers.
Color: Green Cactus
There was nothing wrong with this. But my dog is an absolute destroyer. She makes it her personal mission to annihilate any toy I buy. This did not last 30 minutes. Very cute and good for normal dogs that like to actually have toys to play with. Do not recommend for strong jaw destroyers.
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Reviewed in the United States on June 8, 2026
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DianaZ
Belleville, US
★★★★★ 5
Fun and indestructible!
Color: Green Cactus
The dogs love this toy. And so far it’s been indestructible with constant playing and chewing
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Reviewed in the United States on June 5, 2026
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Lauren
Houston, US
★★★★★ 4
Durable for light to medium chewers - not heavy
Color: Green Cactus
obviously cute. not super durable - lasted a good minute but disintegrates fairly quickly and eventually nothing was left - having to high monitor with a big chewer. (10 mo Great Dane)
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Reviewed in the United States on April 4, 2026
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Amazon Customer
Lake Worth, US
★★★★★ 5
Unbelievable toy for aggressive chewers
Color: Green Cactus
Great toy for aggressive chewers! I'm not one to hand out 5 star reviews but this one I 100% believe in. I bought the first one in 2023 and just replaced it because it broke. Now this is not a played with every once in a while, this was played with daily as it is his favorite toy. Very few toys last long but this one has went beyond my expectations. Could not be happier.
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Reviewed in the United States on May 28, 2026

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