Talk:Galton board

message: A picture of a bean machine would make this article much clearer. Michael Hardy 02:10, 16 May 2004 (UTC)
replies: text: (Obviously, pictures have been added since Michael posted his comment. - dcljr (talk) 07:19, 20 October 2015 (UTC)
thread_title:  Pic 

message: I had not come across Galton's box before.  It would have been helpful to point out that balls are fed to the machine centrally at the top.
Tony.payton (talk) 10:41, 15 September 2008 (UTC)
replies: text: Actually, given the wide "bowl" (or "twin ramps") shape at the top of Galton's diagram and then the narrower "bowl" below, you should be able to feed in the bean anywhere at the top, not just in the very center. (Unless you just meant that it's not fed in from the side of the box. In which case, yeah.) But come to think of it, he probably did that so he could pour in lots of beans at once (in which case the beans start interfering with each other's movements, and the motions are no longer independent). Perhaps I'm overthinking this… - dcljr (talk) 07:53, 20 October 2015 (UTC)
thread_title:  Clarity of machine description 

message: The article states "If a ball bounces to the right k times on its way down (and to the left on the remaining pins) it ends up in the kth bin counting from the left."  Surely this cannot be correct?  If the ball bounces right k times and left l times it will end up (k - l) bins to the right of the central bin? 
Tony.payton (talk) 10:47, 15 September 2008 (UTC)
replies: text: In the second picture (photograph), if a ball never goes to the right, you can see it would end up in the "zeroth" (leftmost) bin; if it goes to the right every time, it would end up in the last (rightmost) bin. You don't need to keep track of both left and right movements. The top picture (drawing) suffers from the fact that a ball can actually reach the left or right side of the box and get bounced back towards the center (thus every once in a while, the sequence of random movements is interrupted by a non-random movement towards the center). If the box were made wider, the balls could be prevented from hitting the sides of the box, avoiding that problem. - dcljr (talk) 07:19, 20 October 2015 (UTC)
thread_title:  Distribution of the balls 

message: I am preparing a paper in which I use the bivariate binomial distribution proposed by Aitken and Gonin (1935), which is based on a fourfold sampling procedure in contrast to the twofold sampling procedure in the ordinary bean machine. For a demonstration one actually needs a three dimensional bean machine. In the traditional bean machine, after the ball has fallen on the first pin, the ball can fall on one of two pins with probabilities p1 and p2 with p1+p2 = 1. In the case of a fourfold sampling procedure according to Aitken and Gonin after the ball has fallen on the first pin, the ball can fall on one of four pins, arranged as the corner points of a square, with probabilities p1, p2, p3, p4 with p1+p2+p3+p4 = 1 and so on. Does one know of such three dimensional bean machine. 
Reference
Aitken, A.C. and Gonin, H.T. On fourfold sampling with and without replacement, Proc. Roy. Soc. Edinburgh 55, 114–125, 1935.  — Preceding unsigned comment added by Ad van der Ven (talk • contribs) 18:51, 30 January 2012 (UTC)
thread_title:  Three dimensional bean machine 

message: Imagine you ran a machine like this 1,000 times. Each run, you note how close the distribution is to an actual proper binomial one that the odds predict. Measure this by how many balls are in the "wrong" location compared to a nice graph that's printed on the front of the machine. How many runs of the 1,000, would be out by only 1 ball? How many would be out by 2? Graph that. I've got a funny suspicion what the graph would look like, but I'm not smart enough to figure out how to calculate it, short of writing the code to actually simulate it. But surely there's an equation that could do it. Ta for help, I really don't know the answer to this. 
84.67.73.190 (talk) 18:15, 15 January 2021 (UTC)
thread_title:  Probabilities of 1000 runs of the machine 

message: What's the WP:COMMONNAME for this, "bean machine" or "Galton Board?" Firestar464 (talk) 05:19, 24 March 2021 (UTC)
thread_title:  WP:COMMONNAME 

message: Is this usually called a bean machine?  And does bean machine usually mean this?  Online searches suggest this is more commonly called a Galton board or Galton box or Galton quincunx (though quincunx usually means five points: four in a square and one in the middle). Bean machine usually seems to involve making coffee, or perhaps somebody who eats a large amount of beans.2A00:23C7:7B0E:7400:BC5F:152F:8ACC:7C (talk) 15:16, 28 October 2021 (UTC)
replies: text: Moved to Galton board Rumping (talk) 15:27, 28 October 2021 (UTC)
thread_title:  Bean machine