The Hot Potato Problem Solved 2 Ways - from Algebra to Math Major!

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The problem goes like this: you're playing hot potato on a cube. You're at one vertex, and a hungry monster is at an adjacent vertex. You throw the potato to one of the neighboring vertices with equal probabilities. People standing at each other vertex act the same way. What's the probability you feed the monster?
Let's analyze this problem two ways - first with algebra, and then as a Markov Chain!
00:00 The problem
00:31 Hot Potato on a Square
01:26 Algebra Solution
04:11 Markov Chain Solution

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1 авг 2024

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Комментарии : 19

@chemicalbrother5743 3 месяца назад

I would definitely use Markov Chains bc it doesn't need to be symmetrical.

@huhuboss8274 2 месяца назад

I love the idea of giving an intuitive solution and the solution a mathematician would use.

@YourWealthCome 3 месяца назад

Not sure what the probability of me just finish reading the Dunwich Horror and the Call of Cthulhu (2 hours ago) and having this video pop up on my feed right after..

@RSchrE 2 месяца назад

I am most concerned about the probability of the monster dodging the hot potato and crossing the vertex to eat me in stead.

@erin_rose0 3 месяца назад

see what they don't teach you in high level maths is I actually just eat the potato instantly with p = 1 and burn my mouth a little because it's too hot still

@konradkaranowski6553 2 месяца назад

This is by far your best video. Please more content on probability!

@TRex-fu7bt Месяц назад

I knew about exponentiating a transition/adjacency matrix from all the Advent of Code programming puzzles about walks through networks, but the stuff about the structure you can use for the exact solution was really cool.

@jamiepianist 2 месяца назад

You would be great teaching a math show on cable television, similar to Bill Nye (who my entire elementary school and middle school peers loved)

@oafkad 3 месяца назад

From potato to Cthulu? I'm intrigued. Edit: Yep, neat!

@DrSeanGroathouse 3 месяца назад

Glad you liked it!

@wernergamper6200 3 месяца назад

Very nice problem. Question: My simulation shows that the average number of throws is 7, until the monster gets the potato. How do you calculate that?

@DrSeanGroathouse 3 месяца назад

It turns out we can use the matrix (I-Q)^(-1). The entry in row i and column j tells us if we start at i, how many visits there will be to j before the potato is eaten. If we add up the 6th row of this matrix (corresponding to starting at Y), then we'll get the average total number of steps until the potato is eaten. And I also got 7 from that calculation!

@wernergamper6200 3 месяца назад

@@DrSeanGroathouse Great. Many thanks for your reply. The use of the matrix is still a bit too advanced for me, but interesting anyway.

@Qermaq 3 месяца назад

MONSTERS EAT POTATOES

@S-payanage 3 месяца назад

K’ulu!

@compositeboson123 2 месяца назад

no, I'm hungrier so I eat the potato and the monster( and maybe others but thats optional)

@Exachad 3 месяца назад

First

@Erotemic 3 месяца назад

It bugs me when people write sums with "..." notation. It is ambiguous. It relies on contextual knowledge and the assumption that the pattern is going to be "simple" to know what the "..." means. The expression: sum(S * Q^i for i in [0,n)) --- or whatever explicit summation notation you like --- is more concise and unambiguous. I'm sure others will have differing opinions, but I prefer to avoid pattern recognition problems when I'm reading an expression.

@PhucNguyen-vf1zt 3 месяца назад

this is so cool The etymology of the word “matrix” is quite fascinating! While it doesn’t directly trace back to the word “mother,” there is an intriguing historical connection. The term “matrix” has its roots in Latin. In Latin, “matrix” originally referred to a pregnant animal, particularly a female animal carrying offspring I guess mathematicians know their way around words.