Can a Chess Piece Explain Markov Chains? | Infinite Series

In this episode probability mathematics and chess collide. What is the average number of steps it would take before a randomly moving knight returned to its starting square?

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Previous Episode - When Pi is Not 3.14

Mathematician Kelsey Houston-Edwards explains Markov Chains and how they can be used to determine the probability of random chess moves, as well as the likelihood your favorite music will pop up on the radio.

Sources include:

Probability: Theory and Examples

Markov Chains

Markov Chains and Mixing Times

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux

Comments answered by Kelsey:

Taylor Kinser

Huy Dinh

Funky Tom

Steve’s Mathy Stuff

[nathanisbored]

im surprised how this series is touching on concepts that aren't as popular as topics for math videos on youtube. i was expecting it to just be another take on the same kind of topics seen on numberphile and the like, but it seems like it's really kinda doing it's own thing. really fascinating topics ^^

[amicloud_yt]

I love how you guys actually get into some real mathematics in this series. It's not your usual Youtube surface level stuff.

[djbslectures]

Thank you for doing this without dumbing things down

[petemagnuson]

Re: The challenges

Knight in the corner:
1/(2/336) = 168, by the same logic presented in the video.

Rook:
First, we note that a rook has the same number of moves anywhere on the board (14), so the stationary distribution is 1/64 everywhere. From there, just take the reciprocal and find the answer to be 1/(1/64) = 64.

[Promatheos]

Starting on their original squares:

King = 84
Queen = 69
Bishop = 40
Knight = 112
Rook = 64

[Ermude]

Can a chess piece explain Markov chains? No, but PBS Infinite series can explain Markov chains with chess and radio stations.

[ColinJonesPonder]

168 for the knight.
As the rook can move to the same number of squares from every square (14), the stationary distribution is 1/64, so the average number of moves is 64.

[kingnabeel]

I'm studying industrial engineering and am taking a stochastic process class so this was a nice surprise as we covered markov chains last week. However, we also used linear algebra to make the math easier and delved a lot deeper.

[Tral]

I'm so happy I found this channel. Only 8 uploads so far, yet they are already of such high quality! Your explainations are stellar, and the visuals make this higher mathematics stuff really accessible, even for someone who doesn't study it. To me this is absolutely fascinating, and I love it. It's gonna be exciting watching this channel grow!

[nO_dNAL]

Wow, this makes so much sense! I think this is the best way to explain Markov Chains. But 6:30 confused me as the derivation wasn't clear.

[zubmit]

Love your videos. Keep up the good work.

[veloxlupus]

Omg, these videos are amazing!!! They explore actually interesting topics, rather than boring old basic math. Please keep up the good work!!

[psaini]

Came back to this channel after 5 years, from some chess content that I'm really into nowadays. One of the best channels on YouTube

[bwill]

The production value is crazy good on these, all of the diagrams are very well done. I wish they were still making them.

[BetoAlvesRocha]

Wow! I think it's the best video explaining the usage of Markov Chain in a very playful way I've ever seen. What a amazing job you are doing here, guys!

Greetings from Brazil!

[jesusthroughmary]

The important question is, what is Kelsey's FIDE rating?

[yourfellowcommuter]

Loved this video! Haven't seen any of the older ones... let the binge begin.

[fourzin]

I feel alive each time I watch an episode from this awesome channel !!!

[testerpce]

I have never heard of Markov chains. All I knew was basic probability and little bit of state space in control systems. but this makes a lot of sense and I felt like I actually understood this. this is truly amazing.

[chrisdock]

Can't get over how amazing this channel is. Seriously thank you.