The Beautiful Math of Snakes and Ladders - Numberphile

Featuring Marcus du Sautoy. Book details below. The game is also widely known as Chutes & Ladders. More links & stuff in full description below ↓↓↓
Around the World in Eighty Games (Amazon): amzn.to/3snW2bD
More about the book: www.simonyi.ox.ac.uk/books/ar...
Marcus du Sautoy books: amzn.to/3QkSjnf
Marcus du Sautoy website: www.simonyi.ox.ac.uk
More videos with Marcus: bit.ly/Marcus_Numberphile
Dice videos on Numberphile: bit.ly/Dice_Videos
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We're also supported by the Simons Laufer Mathematical Sciences Institute (formerly MSRI): bit.ly/MSRINumberphile
Our thanks also to the Simons Foundation: www.simonsfoundation.org
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Video by Brady Haran and Pete McPartlan
Thanks Debbie Chakour for helping with error spotting!
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[@numberphile]

Around the World in Eighty Games (Amazon):

[@Sam_on_YouTube]

What can be more British than assuming something from India is yours?

[@Georgie_thedog_]

who else came from the 301 video

[@bigpopakap]

LOL! I love that his takeaway was "it pays to behave badly" instead of something inspirational like "even a setback might be a blessing in disguise" 😂😂😂

[@mscha]

I ran a simulation of Marcus' small board version of the game, and over 1,000,000 games, the average number of turns was about 8,59. Quite a bit less than 10.

[@tonyzang2344]

Wth As an Indian I can tell you that most people don't know this nirvana thing in game and we too play to reach 100

[@PaulsPubAndBrew]

Years ago I was playing this game with my daughter who was five. She learned about counting and how being ahead in the game didn't necessarily mean she would win. Later that day, I showed my son who was 14 how to write a computer program to simulate the game. The computer played 1 million games and found that it took 42 moves to win on average. It's the answer to everything! It was crazy that this exact game provided two separate opportunities for two completely different aged kids to learn something

[@MathsMadeSimple101]

You mean eels and escalators?

[@romanvolotov]

the fact that they made Trump play the bongcloud is nuts

[@macronencer]

This was very interesting, but I'm missing a crucial piece of explanation... WHY is the total of the top row of the matrix equal to the expected number of turns?

[@SophieBK]

It's really neat that the algebraic identity 1 + q + q^2 + q^3 + ... = 1/(1-q) also holds for matrices!

[@ChefSalad]

One way that you can add a bit of strategy to this game is to roll 2 dice at a time and choose one of them as your move. This adds quite a bit of strategy to the game without taking away too much of the randomness.

[@alphageek101]

Love the “bong cloud” opening and the crashing eval bar.

[@minitbnn]

18:40

[@LobanRahman]

I think the surprise realization at the end - that removing a snake can actually increase the expected number of turns to win - sets up a wonderful bit of advice for life: Don't get too upset or give up when you face an event in your life that seems to have set you back a lot - it might be just what you need to achieve your goals faster! ❤

[@danodet]

Me and my son played this game so much when he was young. He learn to add numbers with it. And me I ended up analysing probabilities and expected values of the two players version. I wrote and publish a paper on this. I am now cited on the wikipedia page. My, now teen, son loves math. He compete in international math competitions and has a better intuition on probability than mine. And he loves Markov chains...

[@Oznej]

When I played this as a kid, it did have an element of agency: It had question cards. Whenever you landed on the bottom of a ladder, you'd have to get a question right in order to climb up; and when you hit the head of a snake, you'd only fall down if you got the question wrong.

[@oskarekberg3704]

That chess game at

[@hannibal1991]

If the dice's number is too big, you go up to the finish and then start going down until you "advanced" the right number of cases. At least that's what we did in my family.

[@NataliaBazj]

Beautiful. I do not comprehend how this sum of probability matrices shows the number of moves.