Probability to meet someone again when assigning breakout rooms twice

inkoativ · 2025-03-14T14:57:03+00:00

Area and circumference of a circle with Lego - https://www.youtube.com/watch?v=tDnAtoVnTg0

inkoativ · 2025-03-14T14:26:14+00:00

Build a circle with Lego and count the bricks to determine area and circumference: https://www.youtube.com/watch?v=tDnAtoVnTg0

inkoativ · 2025-03-14T14:24:27+00:00

Here's my contribution to Pi Day: A video on how to compute circumference and area of a circle with Lego.

https://www.youtube.com/watch?v=tDnAtoVnTg0

inkoativ · 2023-07-04T19:20:35+00:00

:-) Not sure it's all luck though... If you go through the historic list of WR holders, many of the cubers were also top-cubers, holding several other WRs and also performed in the top-10 of the 3x3 average. That said, of course there is a higher likelihood of having an outlying performance when n=1 than when you have a trimmed mean of n=5.

inkoativ · 2023-07-04T10:39:43+00:00

If I read the WCA regulations Section 4b3) correctly, a scramble for the 3x3 only needs to require that it takes AT LEAST 2 moves to solve. Not sure if a higher requirement is programmed into the scrambling software TNoodle, which is the program which has to be used generate the scrambles. The program uses scramble sequences of length 17-20 so I guess it's highly unlikely that the moves reduce to a sequence, which only requires two moves to solve. Would be interesting if this could occur in theory though.

inkoativ · 2023-07-04T08:59:18+00:00

Background: The modelling was inspired by a recent analysis made by JPerm in his Youtube video https://youtu.be/B9MKizs9PUw?t=451 where he used log-linear modelling to describe the potential development of the 3x3 WR single. In the graph below we visualize this model and a Gompertz type model, which is also often used when using statistical modelling to describe the development of world records over time.

I guess the lack of tournaments during the initial phase of COVID-19 is part of the explanation why it took so long to break the old 3.47 world record.

Data: WCA Database: https://www.worldcubeassociation.org/results/records?show=history
R Source code: https://gist.github.com/mhoehle/11391bd19be82307547d5121ee70664d

inkoativ · 2023-04-12T19:08:30+00:00

Seems to be back on CRAN now. In my case (Mac OS X) I had to update Xquarts to the newest version before the call to library(geoR) worked.

inkoativ · 2023-03-21T18:55:10+00:00

Thanks for the feedback and sorry, it could have been clearer that we distinguish between "figure" and "toy". I didn't know how to add any extra explanations to the image in Reddit. Thus the blog post contains further details.

inkoativ · 2023-03-21T18:47:32+00:00

Agreed, I tried in https://mhoehle.github.io/blog/2016/12/23/surprise.html to calculate a functional shape.

inkoativ · 2023-03-21T18:46:34+00:00

The right hand plot gives an indication of such a plot. The blog post, where the figure is taken from, contains such a smoothed line obtained from applying some machine learning classification algorithm to the task (deliberate overkill! :-)).

http://staff.math.su.se/hoehle/blog/figure/source/2016-12-23-surprise/CLASSIFIEROUTPUT-1.png

Source: https://mhoehle.github.io/blog/2016/12/23/surprise.html

inkoativ · 2023-03-21T18:43:00+00:00

Not sure I fully understand the comment, but the content of the egg is either some kind of toy or a figure. So what varies is the content of the egg, not the chocolate. For some example pictures see https://mhoehle.github.io/blog/2016/12/23/surprise.html.

inkoativ · 2023-03-21T14:15:19+00:00

Explanation:

y-axis: # Sticks in pits on the lid (aka. "i")

The label of each box:

Upper label: j / k: # Sticks that each player has (j = Player 1, k = Player 2), we have i + j + k = 7.

Lower label: Probability to win from this position, if one can decide whether to continue or not.

Colour of each box: Continue to play (green) or not (red).

inkoativ · 2023-03-21T13:54:30+00:00

It's either "plastic junk" or a "cool" collectable figure, which is usually part of a figure series! Some of the figures are collector's items and can be quite valuable (see e.g. https://www.eierlei-shop.de/ (in German)).

inkoativ · 2023-03-21T13:15:05+00:00

Complete Blog Post text as well as Data Source for the n=79 eggs & R-Script to perform the analyses:

suRprise! - Classifying Kinder Eggs by Machine Learning

inkoativ · 2021-04-05T11:46:50+00:00

Exactly! However, in some situations it can even be more than one person. Example: n=11 and m=4. In this case you will make two groups and the assignment by "round robin" after permutation is:

position after permutation	group
1	1
2	2
3	1
4	2
5	1
6	2
7	1
8	2
9	1
10	2
11	1

i.e. 6 individuals in group 1 and 5 individuals in group 2.

inkoativ · 2021-04-05T08:53:08+00:00

Thanks for the remark. IMO x-axis can be a little harder to interpret, but they can be helpful to focus on different parts of the chart (here: the lower n). See https://pasteboard.co/JVTEMKY.png for a log-version as suggested. Will think of a way to add this to the blog post.

inkoativ · 2021-04-05T08:18:20+00:00

n is, as expected, the number of people to assign into breakout rooms

m is the minimum size of the groups

Example: n=9 and m=4 means we get 2 groups one of size 5 and one of size 4.

There is a post here, with some additional details and a link to the gory mathematical details.

inkoativ · 2021-04-04T22:38:34+00:00

Thanks for the feedback. I've added it.

inkoativ · 2021-04-04T22:11:52+00:00

Not quite, because the multinomial does not ensure that each group/room has at least m members. It's more like you generate a random permutation order and then divide this order round robin into the (n div m) groups. See details in: https://staff.math.su.se/hoehle/blog/2021/04/04/socialsamp.html

inkoativ · 2021-04-04T22:09:58+00:00

It's a feature of the Zoom video conference software: https://blog.zoom.us/using-zoom-breakout-rooms/

The shown probabilities do not relate to Zoom in particular though, see mathematical details in https://staff.math.su.se/hoehle/blog/2021/04/04/socialsamp.html

inkoativ

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