Jet Lag probability video ? I'm sold. Also after the intro I immediately thought of the Adam coin flip challenge, glad you covered it as well Also team Sam (I like to be a contrarian)
As someone who studied a bit of this stuff and also enjoys jet lag this is so cool and smart! Market Flow poisson process analysis for strategy would be so cool I've done exercises like that in school a while ago but didn't even think about that when I watched that episode 😭 Shoutout to youtube for recommending, just gained you a new subscriber!
tbh it's less of the process itself and more the act of estimating the parameter based on their observations, but yeah I'll definitely have to make that video now with how well this one is doing hehe
Hah, love seeing this video and approach. When Adam got that 7-in-a-row challenge, I had found my way to the same Markov chain model, and hadn't found anyone else taking a similar approach in any of the discussion I read online (or really not many doing a complete analysis, rather than a rough heuristic). However, I brute-forced the solution from there via a transition matrix, multiplying it by itself until the 0-to-8 probability just exceeded 0.50. (A very compressed explanation for readers, the transition matrix of a Markov chain model gives the probability of a state A-to-state B transition, for any pair of states (A, B) in the model; if you then take the matrix to a power N, the resulting matrix values give the probability of passing from state A to state B after exactly N events.) Neat seeing the mean-hitting-rate derivation. Nice and simple.
@@cadaeicstudios I imagine this scenario is a very good foundation! I never took stochastic processes in uni, unfortunately, but I've picked up some basics over the years. Should pick up a book or course at some point - prob and stats is way more interesting to me now than it was in uni, especially undergrad.
I think walking speed is a lot less random than you would think. Our brains (especially unconcissous portions like used in walking) naturally fall into a tempo and stick to it + our bodies naturally have a more comfortable speed to walk at due to the dimensions of our bodies. It does kind of surprise me that his walking would not slow noticeably by the end though.
Nebula subscribers should check out the Layover podcast episode for Adam's coin flips. They got a lot of feedback saying Adam lost because he kept interrupting "his flow" and they appropriately lambasted it. ("It is LIT ER AL LY a coin flip!")
oddly enough, the probability of him failing all 3 of the coin flips is still higher than the probability of him failing to get 7 in a row at all across the 694 flips
To be perfectly fair, coin flips are, strictly speaking, not actually random. They’re entirely deterministic, but in a way that is, typically, too hard for humans to predict. But you can build a coin-tossing robot that gets the result you want every time, because it just depends on the precise way you flip it. It is possible that in those situations, Adam DID get into a kind of “flow” where all the flips were excecuted essentially the same way, causing them to repeatedly land on the same side, until he changed it back up to random on the last flip when he interrupted. It was, of course, still a 50% chance each time then, and so he did get quite unlucky, but it’s possible that he could’ve had a near guaranteed victory if he had not interrupted his flow, as they say.
In head-to-head competition (like S10), I tend to root for Badam, but in turn-based competition (like tag), I root for whoever's currently in the unique role (so runner in tag, hider in H&S). The exception was Sam in S11, where I really wanted him to get another run to get to his end location.
oh hey it's my fellow math nerds! I also stopped mid Jet Lag S11E1 to analyze the probability of the 7 consecutive coin flips and came to the conclusion that Adam is the top 7% unluckiest player (with some terrible python code lol) I hope Ben wins, not because he deserves it (he absolutely does), but because he is a silly goose.
From what I can tell, it's how many results out of the 100,000 were in that range (i.e. at x=450, it shows how many attempts took between 400-450 throws to first win)
I'm usually just team "whoever's behind at the moment", except in tag and hide and seak, where I'm team "runner/hider". I've never felt a strong calling to go for any one specific person.
I think the original design on the 30 min timer challenge assumes you’d be counting in your head, which I’m sure is impacted by the time it takes to say the numbers (even in your head). Adam was genius for translating his walking tempo to time as it’s clearly way more consistent
but how would you analyze the markov model without using a simulation? i guess like a weighted sum of all states branching outward for 3312 state transitions would be the expected time?
the expected time is actually right in the middle, pretty easy to prove with symmetry. but the variance is huge. it's been a while since I've done stuff with detailed balance and no way was I going to attempt to explain it in a video that aims to be introductory
cool! small nitpick, at 5:19 it seems like you set tau_7 = 1/2 tau_0 + 1/2 tau_8 = 1/2 tau_0 + 1, because of not adding +1 initially, which is a contradiction
I feel like the probability of increasing the step frequency should decrease the higher the frequency is, and oppositely the probability of decreasing the frequency should decrease the lower it it is.
I root for Sam usually. Ben is lovely but his inability to run has held him back so many times. Adam has a great competitive energy, but he can be a bit miserable. Sam though is usually upbeat enough but also puts the effort in.
A Jetlag video that uses Manim? Of course the algorithm is going to show me this 🪙
Queen Toby!
Yo Toby!
7:11 she's the goat after all
why hello there
It's a Cadaeic Studios video, not a jetlag video
Very well made video, I hope the Jet Lag team sees this
Jet Lag probability video ? I'm sold. Also after the intro I immediately thought of the Adam coin flip challenge, glad you covered it as well
Also team Sam (I like to be a contrarian)
Is team Sam contrary? I guess I'm contrary
if it makes you feel better I am usually Team Sam too, especially when he's with a guest
As someone who studied a bit of this stuff and also enjoys jet lag this is so cool and smart! Market Flow poisson process analysis for strategy would be so cool I've done exercises like that in school a while ago but didn't even think about that when I watched that episode 😭
Shoutout to youtube for recommending, just gained you a new subscriber!
tbh it's less of the process itself and more the act of estimating the parameter based on their observations, but yeah I'll definitely have to make that video now with how well this one is doing hehe
Great video! Surprised it doesn't have more views. Please do analyze the customer estimation challenge next!!
Hah, love seeing this video and approach. When Adam got that 7-in-a-row challenge, I had found my way to the same Markov chain model, and hadn't found anyone else taking a similar approach in any of the discussion I read online (or really not many doing a complete analysis, rather than a rough heuristic). However, I brute-forced the solution from there via a transition matrix, multiplying it by itself until the 0-to-8 probability just exceeded 0.50. (A very compressed explanation for readers, the transition matrix of a Markov chain model gives the probability of a state A-to-state B transition, for any pair of states (A, B) in the model; if you then take the matrix to a power N, the resulting matrix values give the probability of passing from state A to state B after exactly N events.)
Neat seeing the mean-hitting-rate derivation. Nice and simple.
we actually solved almost the exact same problem in my stochastic processes course lol (just with only 3 or 4 states)
@@cadaeicstudios I imagine this scenario is a very good foundation! I never took stochastic processes in uni, unfortunately, but I've picked up some basics over the years. Should pick up a book or course at some point - prob and stats is way more interesting to me now than it was in uni, especially undergrad.
great video! used to be team sam, now i feel like i root for everyone because they’re all so fun to watch
I think walking speed is a lot less random than you would think. Our brains (especially unconcissous portions like used in walking) naturally fall into a tempo and stick to it + our bodies naturally have a more comfortable speed to walk at due to the dimensions of our bodies. It does kind of surprise me that his walking would not slow noticeably by the end though.
Nebula subscribers should check out the Layover podcast episode for Adam's coin flips. They got a lot of feedback saying Adam lost because he kept interrupting "his flow" and they appropriately lambasted it. ("It is LIT ER AL LY a coin flip!")
oddly enough, the probability of him failing all 3 of the coin flips is still higher than the probability of him failing to get 7 in a row at all across the 694 flips
To be perfectly fair, coin flips are, strictly speaking, not actually random. They’re entirely deterministic, but in a way that is, typically, too hard for humans to predict. But you can build a coin-tossing robot that gets the result you want every time, because it just depends on the precise way you flip it. It is possible that in those situations, Adam DID get into a kind of “flow” where all the flips were excecuted essentially the same way, causing them to repeatedly land on the same side, until he changed it back up to random on the last flip when he interrupted. It was, of course, still a 50% chance each time then, and so he did get quite unlucky, but it’s possible that he could’ve had a near guaranteed victory if he had not interrupted his flow, as they say.
I was not expecting this video to be as interesting as it was. Which is to say it was very interesting.
Thanks for making this! Team Ben all the way
i just took my intro to ai final exam, and to see markov chains applied in real life? google is listening to me
In head-to-head competition (like S10), I tend to root for Badam, but in turn-based competition (like tag), I root for whoever's currently in the unique role (so runner in tag, hider in H&S). The exception was Sam in S11, where I really wanted him to get another run to get to his end location.
toby the 🐐 indeed
oh hey it's my fellow math nerds! I also stopped mid Jet Lag S11E1 to analyze the probability of the 7 consecutive coin flips and came to the conclusion that Adam is the top 7% unluckiest player (with some terrible python code lol)
I hope Ben wins, not because he deserves it (he absolutely does), but because he is a silly goose.
Hi, I'm not sure i understood what the y-axis numbers represent, could you elaborate?
From what I can tell, it's how many results out of the 100,000 were in that range (i.e. at x=450, it shows how many attempts took between 400-450 throws to first win)
I'm usually just team "whoever's behind at the moment", except in tag and hide and seak, where I'm team "runner/hider". I've never felt a strong calling to go for any one specific person.
Is the walk time process not the result of a random walk? That's a very amusing coincidence of terminology. A random walk walk time.
yo another jetlag viewer??? team sam lol. great video btw
I am #TeamBen all the way
Can someone explain why the simulation result is different to the expected value? Why is it sooo much lower, or what am I missing?
I think the original design on the 30 min timer challenge assumes you’d be counting in your head, which I’m sure is impacted by the time it takes to say the numbers (even in your head). Adam was genius for translating his walking tempo to time as it’s clearly way more consistent
but how would you analyze the markov model without using a simulation? i guess like a weighted sum of all states branching outward for 3312 state transitions would be the expected time?
the expected time is actually right in the middle, pretty easy to prove with symmetry. but the variance is huge. it's been a while since I've done stuff with detailed balance and no way was I going to attempt to explain it in a video that aims to be introductory
Never heard about the jet lag game, so clicked this video really curious what having jetlag had to do with markov chains
great video
cool! small nitpick, at 5:19 it seems like you set tau_7 = 1/2 tau_0 + 1/2 tau_8 = 1/2 tau_0 + 1, because of not adding +1 initially, which is a contradiction
perhaps I should have made it more clear earlier on, but the +1 accounts for the time that you spend inside the state before you transition
team ben but I love everybody
4:10 that also very much looks like a state diagram in digital logic...I just finished my exam in logic design so it's very fresh in my mind lol
yeah, markov chains are a kind of state machine I believe
Hmmm. I just gave an exam in my digital logic class. I wonder what the probability is that you are my student?
I feel like the probability of increasing the step frequency should decrease the higher the frequency is, and oppositely the probability of decreasing the frequency should decrease the lower it it is.
Per your request: in 1v1v1 seasons, I root for Ben. In 2v2 seasons, I root for Sam and Guest.
And I always pause for giant chunks of text
team adamben
In 2 v 2 I root for Ben and Adam. In 2 v 1 I root for whoever the solo person currently is (hider/runner)
I root for Sam usually. Ben is lovely but his inability to run has held him back so many times. Adam has a great competitive energy, but he can be a bit miserable. Sam though is usually upbeat enough but also puts the effort in.
3:01
I root for Ben