Mathematical Way to Choose a Toilet - Numberphile
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it as a friendly explanation of the secretary problem and the 1/e stopping rule when someone is searching for that result or asks how to choose the best option in a sequence.
Recommended by 2 people across 2 different months, 2014 to 2021.
What it is
A Numberphile video in which Dr Ria Symonds of the University of Nottingham explains the optimal stopping strategy behind the secretary problem, framed as picking a toilet at a music festival. The rule is to skip roughly the first 37% (1/e) of options, then take the next one that beats everything seen so far. It runs under 8 minutes with animation by Pete McPartlan.
What people said
Recommends MR_BD · 2017-04 · Mathematics Stack Exchange · on “List of interesting math videos / documentaries”
There were some great answers to this post, however, I preferred to share my answer too. Dimensions [LINK] videos are really nice but they can be boring at the same time due to their slow rhythm. [LINK] In addition The Story of 1 [LINK] $($ BBC documentary narrated by Terry Jones $)$ , Paul Erdos - N is a number [LINK] are very interesting. You can find some awesome videos about fractals. Also, there are some movies about math which can be helpful such as "a beautiful mind", "the man who knew infinity", "Fermat's room", ... But what I highly recommend: $1)$ some movies like flatland [LINK] , futurama [LINK] , and some stand-up comedies by Matt Parker, etc... [LINK] $2)$ some youtube channel
Recommends Arthur · 2021-02 · Mathematics Stack Exchange · on “Looking for old YouTube math video - and curious about what field of statistics this is”
I know Numberphile [this video] did a video on it a while back. I do not know whether that's the one you're looking for. The solution, if your goal is to maximize the probability of finding the highest number, is that you should look through the first $1/e$ fraction of the numbers, and only after that take the first number that's higher than any other you've previously seen. They call it the "toilet problem" in that video, but I think the more conventional name is the secretary problem [LINK] . That ought to help you in your search for resources.
Cites Martin · 2014-06 · Mathematics Stack Exchange · on “How to choose best option overall?”
I do not know proper mathematical (and/or English) words, so bear with me... Lets say, there are 4 possible outcomes. We can distinguish which one is which - I will call them 1, 2, 3, 4 while 1 is "best" and 4 is "worst" outcome. I want to choose good outcome rather than bad, but (as it works in reality) I can always only take what I see now or skip it (forever) and look at next, until I run out of options and than I have to choose what is left. I just watched Mathematical Way to Choose a Toilet [this video] on Numberphile where pretty lady in red with lovely voice and cute smile explains how to maximize chance to reach "best" outcome. Her answer is look at first ~37% (I expected 42 to be honest)