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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Scott
Massapequa, US
★★★★★ 5
Screamo for Creamo! Update on Sage and Citrus and Cologne
Scent: Bourbon Oak, Size: 16 Fl Oz (Pack of 2)
So first off the product came exactly as depicted. The smell was good but not strong or offensive. It has a pleasing woodsy smell. The name says it all. The lather is not particularly big but that doesn’t define how clean you get. I think it cleaned me up very well with one caveat. My face is a little oily so I did purchase the Creamo face wash. The body wash really didn’t do the trick for my face which is somewhat oily. The bottle is reminiscent of the past and stylish. It overall is a great product. I just bought the Sage and Citrus body wash. This is a great all season body wash with a more contemporary smell. It’s lighter than the Bourbon and Oak with, as stated, a citrus smell tempered with the earthy sage. Again it does not clean my oily face but I use the Creamo face wash and it does just fine. The rest of my body feels clean and the scent is light and not overpowering. Between both products I also use the shaving cream. I enjoy the original scent. I tried the Bourbon scent with the Bourbon and Oak body wash and felt it was a little overpowering. On a good note I combined all this with the Bourbon and Oak cologne. The shaving cream last a long time and should be used sparingly. The value is in the amount you use. It’s far less than a cheaper shaving cream but offers superior protection and excellent moisturizing elements. The cologne lasts all day and does not require but a single spray under both arms and a single spray on a wrist rubbed against the other. If you need an anti perspirant use one without a scent since this will conflict with the cologne. The value is definitely there as this cologne albeit simple in appearance has very delicate notes reminiscent of my more expensive cologne. I use Creed Vetiver for going out. This cologne has a very similar quality but is, of course, a different bouquet. Overall the whole line of Creamo products seems to be well thought out and outshines many higher end products such as Clinique or Brickell which I have also used. It comes down to value and quality. That’s where it really wins. It’s made in California where I live!
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Reviewed in the United States on August 23, 2019
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BRANDON MCCOLLOUGH
San Leandro, US
★★★★★ 5
Smooth Lather and a Balanced, Refreshing Scent
Scent: Sage & Citrus, Size: 32 Fl Oz (Pack of 1)
This body wash delivers a rich, consistent lather and a scent that’s both clean and uplifting. The sage adds a subtle herbal note while the citrus keeps it bright. It rinses off without residue and doesn’t dry out the skin. A well‑crafted formula that feels premium without the premium price tag.
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Reviewed in the United States on February 26, 2026
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BarabbaOr
Pawtucket, US
★★★★★ 4
Does this beat Anthony Invigorating wash in the long last smell
Scent: Seagrass & Driftwood, Size: 32 Fl Oz (Pack of 1)
Anthony Invigorating wash (check out my review of that) has a very strong pine scent to it and is a very long lasting smell. How does Cremo's products stand up to it! I put deodorants, shampoos, and body washes through the same rigorous tests. I run 14+ miles 4-5 times a week, swim 20+ lengths (or laps) in a junior Olympic pool 3 days a week, use a Sauna 2-3 times in fifteen minute intervals 4 times a week, and use weights 4 days a week. All of these body washes and shampoos that I try out not only go up against Anthony's but also getting rid of that chlorine smell. I always will finish a product before reviewing it I'll be honest here as always, the Blue Cedar and Cypress at first whiff smelled weird. I can't explain the 1st whiff smell though you have my warning. I thought this was going to be my least favorite of the 3 different Cremo products (bourbon and oak, seagrass and driftwood, and this one) that I received. I have the policy to use all the products up in their entirety, so you don't have to. After using it up, I actually like the smell of it. The cedar smell comes out once applied. I actually use this with Anthony Blue Sea Kelp Body (check out my review of that). This goes great with it. So on my buy, borrow, or bury review rating system, this is a buy. The issue I have with it, is that Cremo products don't seem to be that moisturizing their smells are good and lasting. This beats the off the chlorine smell of the pool and works great in combination with Anthony's. Try it out, just get past that initial smell, you won't be disappointed. Now for Cremo's seagrass and driftwood. The First smell test of it is very pleasant. It's once you've put it on does that wood smell really come out. The smell is good and does last long though the issue I have that it is not moisturizing. This goes great with Anthony's other 2 products that I have viewed (please check those out). So on my buy, borrow, or bury rating scale, this is a buy. If they could make their products more moisturizing it would be fantastic. I'll be back here to review the Bourbon and Oak, I have not finished it yet though it's probably going to be my favorite of all the 3 Cremo products I've tried out. Please check out all of my other reviews!
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Reviewed in the United States on February 20, 2020
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Steven P Nelson
Houston, US
★★★★★ 5
Great buy!
Scent: Palo Santo, Size: 16 Fl Oz (Pack of 2)
This is my favorite brand and the lather is second to none! The smell is amazing and the quality is worth the extra price. It leaves my skin feeling moisturized and soft.
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Reviewed in the United States on March 4, 2026
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Mitchell
Dallas, US
★★★★★ 5
FINALLY. THIS IS ACTUALLY WHAT YOU WANT.
Scent: Seagrass & Driftwood, Size: 32 Fl Oz (Pack of 1)
I’ve tried all of the soaps. All of them. Molten brown sucks, 18.21 sucks, Blackwood sucks, and brickell sucks. All I wanted is a premium soap that doesn’t suck. All I wanted is to feel good and smell good. I work in kitchens, so I’m not some desk monkey needing to wash off the stale air, I have to actually clean myself. I don’t even know how these soaps stay in business, you might as well be using Irish spring and save the money. Nothing moisturizes, I’m always left with dry skin, or the smell lasts all of 6 minutes. Until now. This stuff is actually the luxury brand I’m swearing by. It lasts on my skin, it lathers well, it cleans well, and it doesn’t give me itchy skin just to smell nice after a shower. Also, it doesn’t cost $36 per bottle like molten brown does for 2 teaspoons of soap with gold flakes in it that smells great for 6 minutes. It’s cheaper, and you get more.
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Reviewed in the United States on September 14, 2024

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