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I'd be curious to see a video about gacha probabilities. To be more specific, Infinity Nikki which just came out has quite a few variables AND it has a little coin machine to use in game money for a set of items. I was trying to figure out how many tries it would take to get all like ten of the rare items from the machine, which I did very roughly and I'm not sure if it was right or how it worked for sure. But then there are more slightly less rare ones too so that adds another percentage to deal with and I just ignored that. So it would be interesting to see how these kind of combined probabilities work for getting at least one of each item. Likewise the main system gives certain low percentages of a four or five star item but you're guaranteed a four star after ten and a five star after twenty so usually people will just brute force and say the absolute maximum tries it would take to get them all, since in this game you get a new one each time. Other games have different pity systems but will do for example a 50% chance of the new character when you either get lucky or hit that guaranteed pity drop, and then the next time you get one it's guaranteed to be the new one. Genshin Impact, one of the biggest games, also added a weird system where if you lose that 50/50 chance there's then another small chance that's rolled to give you a sparkly animation and give you the new one anyways, which feels like they basically just slightly changed the overall probability but it's weird to factor in. Anyways it might be a bit niche in terms of what your audience would want to see but maybe the math is interesting?

I love this video, studying for my probability final atm, its nice to see what im interested in and what i need to learn to combine together to give me a refresher

Noice

On predicting 30 minutes, I think it's more complicated than this because your model assumes (i think) that every step is independent from each other. But they aren't independent since every step is more likely to be of equal length to the previous one. So if you start undershooting, then you're more likely to keep doing it for the whole duration instead of having equal chance to overshoot as well.

Great video man just out of curiosity what would be the MTTF for the coin flips?

as a nebula subscriber, this is a legendary algorithm pull.

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

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

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.

Never heard about the jet lag game, so clicked this video really curious what having jetlag had to do with markov chains

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.

Can someone explain why the simulation result is different to the expected value? Why is it sooo much lower, or what am I missing?

team adamben

I was not expecting this video to be as interesting as it was. Which is to say it was very interesting.

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.

great video! used to be team sam, now i feel like i root for everyone because they’re all so fun to watch

3:01 I root for Ben

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 am #TeamBen all the way

A Jetlag video that uses Manim? Of course the algorithm is going to show me this 🪙

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.

great video

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?

Very well made video, I hope the Jet Lag team sees this

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

yo another jetlag viewer??? team sam lol. great video btw

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!

i just took my intro to ai final exam, and to see markov chains applied in real life? google is listening to me

toby the 🐐 indeed

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!")

team ben but I love everybody

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

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.

Great video! Surprised it doesn't have more views. Please do analyze the customer estimation challenge next!!

Hi, I'm not sure i understood what the y-axis numbers represent, could you elaborate?

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.

Thanks for making this! Team Ben all the way

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)

Great video, please turn the music down, it’s distracting, subbed

I wonder how De Lijn Limburg mainlines would work (not counting 3 digit lines because they practically dont exist)

Okay but as someone who as a bit talked in base -4 (not base 4, base -4) for a few months I can tell you that balanced bases (which are different but share a lot of properties) are gonna be extremely intuitive to any child that grew up using them, It took me very little time to estimate the value of a 5 digit number, And while it takes a while to figure out the exact value, That's not because the base is unintuitive, But because I'm converting to base 10 instead of base 12.

This is awesome! Algorithm, do your thing.

This came at exactly the right time, planning on how to explain probability best to high schoolers!

This is a well-made video! I appreciated the more in-depth look into the Monty Hall problem - I'm not sure I've seen that way of thinking of it before. I also appreciated seeing the two ways of handling the birthday problem, it highlighted something I hadn't thought about properly before.

💖 *Promo SM*

Great video. I'm not at all a math guy but I've been playing with balanced ternary on my own quite a bit (since resources on it are scarce) and its been one of my favorite learning experiences. Love that you actually crunched the numbers on carry rates, something which I could never prove but just came to expect while using it.

Base 1 is good too

how does addition/subtraction and multiplication/divison work in balances ternary? i cant find any videos related to that. addition and subcration i can figure out, but multiplication i struggle

FWIW, I wonder if one possibly neat and aesthetic way to write numbers in this format would be to use color coding, like how it is done on banks today. You use a black "1" to represent positive, and a red "1" to represent negative, while "0" is always black. I also thought of this because negative numbers were first created in China, and the Chinese used black and red rods to represent positive and negative, though actually it was the other way around (i.e. red as _positive,_ not negative).