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A cute probability fact
🕑 Added 2024-09-02 21:52:34 +0000 UTCOn a recent UK trip, Matt Parker shared this little fact with me. He was making a video about it, so I made an animation to help explain it, which I figured would make for a nice short video.
This is an early view for patrons, I'll likely put it up on various social media sites when Matt posts whatever he's working on.
Comments
David Terr
Wow, this is a very interesting result I never would have expected, and also simple to prove. Nice job!
John T. Draper
Where can I watch Matt Parker's video - whats the link or name of the video?
Sophia Wood (Fractal Kitty)
lovely
dcy665 .
I watched Matt Parker's video yesterday, so this was pleasing to watch, but was not a surprise. I did like the elegance of the solution. And there wasn't even a hint of hail of dice.
Poker Chen
...I actually guessed the topic of the video the moment I saw your thumbnail.
Poker Chen
I loved figuring this out on my own when I was writing a dice simulator some years back. I did an epsilon delta style proof by increasing the numer of faces and showing that the number of combinations (1,3,5,7... in the 2-dice case) converge to the required result. The idea also lets you generalise the concept of "lucky" in some table-top systems to a more fine-grained mechanic where you can now throw a non-integer number of dice and then take the maximum thereof.
Rion Boom Crabhands Keon
That's really handy and satisfying! Can you make an extended video that now explains the https://en.wikipedia.org/wiki/Gumbel_distribution? :D
Sven Codes
This is how I've been creating biased random values for my games for 30+ years :)
Walther
Reminds me of this video: https://www.youtube.com/watch?v=4y_nmpv-9lI In computer graphics, square roots can be expensive to compute, so figuring out creative ways to get random variables from a desired distribution can be beneficial. The equivalence of distributions coming from seemingly different methods comes up!
Owen Wang
So cool!! This is what I pay monthly on Patreon for hahah
Lech Mankiewicz
Very nice! :)
Yonatan Zunger
Well, that's just lovely!
Miles
That's a nice one! Thanks for sharing, Grant
Daniel and Rebekah Slonim
Cool stuff! Thanks for sharing.
Michael Chui
Wikipedia's explanations of math things tend to be pretty bad, sadly. And I'm not sure it's improvable, because IMO, math concepts are kinda orthogonal to an encyclopedia entry. I think using Wikipedia to understand math is best for if you have a good sense of something already and want to follow links to other related topics, which you can then research somewhere else.
Seth Arnold
That's so satisfying!
dcy665 .
that was left as an exercise for the reader
LK
This reminded me of something similar from a SoME1 video: https://youtu.be/4y_nmpv-9lI
Kevin
I have to say, I like this presentation a lot better than Wikipedia's (which just spells it out in formulas with no derivation given). Like, yeah, it is useful to know that statisticians refer to this distribution as Beta(n, 1), and I suppose it is also useful to know that this fact about the CDF is a special case of the incomplete regularized beta function, whose general form is far more complicated, and sure, inverse transform sampling is also a nice technique to keep in your back pocket, but... the way they present it, it's just a bunch of formulas on the page, and you really have to work to understand how all those things fit together.
Michael T
Imma need this restated in terms of D&D advantage (and disadvantage), where you take the higher (or lower) of two dice.
Timur Sultanov
Sneak peek... nice
Jesse Thompson
But they come from different nations 😁
Luke de Wet
That is very interesting, thank you for sharing!!
Naked Jeff Tamer
min((Matt Parker), (Grant Sanderson)) >= (a national treasure)
