Summer of Math Exposition

Randomly playing chess

In this video, we explore what happens to chess pieces when they randomly move around the board. In particular, we explain a simple formula for a somehow complex question: if a single knight starts from a corner of the board and randomly moves around, how long will it take to return to its original location?

Analytics

6.1 Overall score*
32 Votes
12 Comments
Rank 41

Comments

Really solid video ! The topic is not the most interesting in my opinion, but you managed to share it in a way that made it entertaining. Everything is really easy to understand, it was a pleasure to watch.

5

Very good animation style. But I believe the conclusions of the math are wrong. The corner most likely has the greatest chance of being reached

3.5

Awesome video: good animations, novel & interesting topic, good explanation. Some quality improvements in audio and subtitles are possible. Engagement was great.

7.1

Hi ! I have not noticed any obvious possible improvements to your video. Beautiful animations, sound quality was great, and explanations are very clear. Maybe you could provide a little bit more motivation at the beginning ? Like why is this problem of counting the average return time important or complicated. Other than that, very very good video. Thanks for submitting and keep at it. :)

7.8

I would suggest using an easy problem to build intuition and then explaining why the chess board has that property

6.9

Would have loved to see the specific formulas used. Good explanation!

7

Rating as "Better than most" I really enjoyed this one. Its a nicely paced video and the subject is explained well. I thought that this was a neat way of looking at the problem. I wouldn't have thought of this approach so it has taught me something new.

7

The video does not adequately explain the leaps of logic it uses. Why is the likelihood of being on a given square proportional to the number of valid moves from that square, without any weighting for the likelihood of being on *those* squares? There is a reason, but the video does not provide it. Why is the expected return time equal to the long-term average probability of being on a given square when taking random moves? Again there is a reason, and again the video does not provide it.

5.7

I really liked this video. The only thing that I missed was a bit of more math in it. Maybe not a rigourious proof, but at least some intuitive justifications.

6.1

Very nice introduction-by-example to random Markov chains.

7.3

Short and sweet. Was expecting more based on the title but very clean delivery and easy to stay engaged.

7

Good problem but less applicable but still lot enjoyable

7.1