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Simulating the Evolution of Rock, Paper, Scissors
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- เผยแพร่เมื่อ 12 ก.ค. 2024
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Source and further reading on the common side-blotched lizard:
Sinervo, B.; C.M. Lively (1996). "The rock-paper-scissors game and the evolution of alternative male strategies". Nature. 380 (6571): 240-243.
en.wikipedia.org/wiki/Common_...
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key takeaway from this video: the best strategy in life is to do random stuff and hope it works
E
This is an undeniable truth since Fredderick (a Goldfish) outperformed NASDAQ.
no the key is not to be to extrem in one property. I believe this would be healthier like that but economy forces us to be imbalanced to get rewarded
I think that sounds about right, because like, isn't that what evolution is? Very slowly sexually selecting for the strategy that survives? Be that random or just, hey it's easier to get seeds than bugs? (Like in birds)
I just do everything I can think of (good and bad ideas) and hope they all work. I think it has so far?
as a geologist, you see these ternary plots literally everywhere in literature
I’m a geologist too 🎉
Ternary plots are so handy. More people should use them.
L O A M
I had to look this up, because, as a computer scientist, we use "ternary" as a conditional operation - that is, choosing a value based on whether another value is true or false. yay for engineering consistency!
Who is sandy loam and why do you keep talking about her?/j
When I learned about side-blotched lizards, one of my first thoughts was "this sounds more like a Primer video than a real organism."
finally, a comment about those guys.Deep look made a video about them pretty please watch it when you have the time.
all I know is them lizard are throat goats
@@hopepope6573 Clint's Reptiles also did a video including them recently!
@@b1bbscraz3y what.
In some countries, they play _"Janken pon,"_ totally different! /s
"0:04 If you're unfamiliar with Rock, paper, scissors" What are the things that people who don't know rock, paper, scissors have been living under??? It's certainly not rocks.
Perhaps they are the lizardfolk and live under Spocks
They are geologists. Covered in papers Studying rocks.
@@John-gr5tx what they do wrong is licking the rocks, crumbling the papers, and digging with the scissors.
@@John-gr5tx nice a tbbt reference
5:33 "Let's actually skip drawing the blobs"
Me: 🥺
5:36 "Okay, still some blobs"
Me: 😊
he knows his audience too well :D
real
lmao fr
LITERALLY ME
For the last part the saying "A jack of all trades is a master of none, but still often better than a master of one." rings very true
One thing interesting about this quote is that I would consider the jack of all trades a master of something - a master of versatility, which is kind of what this full version of the quote is going for.
that saying is false, specialization overwhelmingly dominates biologically and economically
@@mrosskne only in specialized environments. If the environment changes, like which is the case here with scissors alleles transforming into rock alleles, then versatility (and the ability to adapt, in a biological point of view) seems to have the upper hand.
@@xMysticMia In all environments.
@@mrosskne The saying might imply the master of one to be completely inept in anything else, which just gets you extinct in the evolutionary context. Baseline capabilities are required to reach your specialization's potential.
13:05 "I was confused in front of ALL twenty people who were watching"
You're a gem, mate! hahaha
I mean, imagine being in public and doing something embarrassing in front of 20 whole people😭
That’s like classroom size
I think the blobs would make perfect stress balls, can that be a thing?
Agreed
take my moneyyyy
Nooooo why would you squeeze them! Make it a huggable 3ft tall plushie instead :D
There's a plushie on the website!
He already did the plushies, was expecting whether or not I'll see a comment like that lol, people think alike
"Okay, maybe some blobs" and then there's 3 blobs (the blobs are really cute by the way) just kind of sitting there, relaxing.
that blobs enjoy watching how others fight for live
He knows we come for the knowledge and stay for the blob
5:36
Way too many blobs to count: 💥💥💥⚔⚔🪨📰✂
🔴🟡🔵:🍿🍿
I do absolutely love those little blobs
@@VonThallis Or possibly the other way around!
When are we getting the sequel with Rock, Paper, Scissors, Lizard, Spock?
I thought about this, but a 5-simplex plot is a little hard to draw. :(
@@PrimerBlobs scissors cut paper, paper covers rock, rock crushes lizard, lizard poisons Spock, Spock smashes scissors, scissors decapitates lizard, lizard eats paper, paper disproves Spock, Spock vaporizes rock, and rock crushes scissors.
@@PrimerBlobs Do you think it'd follow the same pattern? From what I got in the video, I assume it would, but I'm curious as to whether the added variables might influence it in some way.
@@PrimerBlobs It's technically a 4-simplex, also known as a Pentachoron (you know, 1D digon, 2D trigon, 3D tetrahedron and 4D pentachoron)
@@merlijnfolkerts3066 I love the wording on this
Something about the phrase "If you want to use fancy words, which I do" just felt so relatable to me
Who said we dont use rock paper scissors to compete for food in nature? Thats like the most common method seen in my school cafeteria
Same
There are few places more _unnatural_ than a school cafeteria...
the brown blob waving at the end was so cute my heart melted
hello mine turtle
Yeah! Absolutely adorable!
Timestamp is 14:33 🤎
Today I learned normal type pokemons can be useful
well, there isnt anything implying normal types are the neutral strategy. normal types are stuck in their own rock-paper-scissors triangle, theyre only neutral in the face of unrelated triangles like fire-water-grass
@@knopfirNormal isn’t super effective to anything, so technically they aren’t even in a rock-paper-scissors relationship. They do get better move-type diversity, but it’s not really that useful.
Just like the brown blobs, they do nothing particularly well and suck to use, but (besides fighting) nothing does particularly well against them so they're a pain to deal with.
Not quite true a "normal" type blob would infact send it self to extinction as it would function the same way the brown blob does except that is always copies the opponents choice resultsing in it always get 0.80 every encounter until it should eventually drive its self to extinction.
A better anolgy would probably be dragon since it "beats" the presumable type triangle by not being able to lose.
So ez 4 me- Machamp 2024
This is also a perfect example of analyzing eigenvalues to evaluate stability of a system. Assessing your matrix (with all values subtracted by 1 to make the matrix a proper system of ODEs that tracks *changes* in population) pre- vs. post-tie punishment, you can see that the real eigenvalues go from 0 to negative, which indicates a shift from unstable (spiraling towards and around the edges forever) to stable (spiraling towards the center and staying there). Though, for the 0 eigenvalue case, a perfect system maybe should have forever spiraled around the middle of the triangle without reaching the edges. I think the introduction of noise and random fluctuations makes the system less stable, spiraling outwards instead. Thanks for a cool video!
Linear differential equations are used for predator-prey calculations. Eigenvalues are used in those 2d cases. This is the same problem expanded to three dimensions where there are coupled predator - prey relationships
warning at 1:10, almost got hit by a rock, barely dodged
Barely saw it in time, thank you
Dayum thanks bro, I can't imagine what would've happened if it wasn't for yuh😱😳
I mean, I gotta go to work on Monday, can't die from some random rock rn🤧
Fun fact, the "brown" strategy is actually an evolutionarily stable strategy specifically because it is a Generalist one that can take control of all the niches when they pop up! Abundance of Scissors? Generalists have the tools to exploit them by going Rock. Abundance of Paper? Generalists can hit them with Scissors pretty much immediately. Abundance of Rock? Paper usage wallops them back down from the Generalists. They win out because they are prepared for any situation, and as a result, can win in any situation.
Which, incidentally, is why humans are the best animal by far. Because we are the most generalist, we can actively think of new strategies to compete in nature, rather than having it ingrained in us.
That's also why brain and consciousness was created. Learning during time and adaption during life time are beneficial@@brutusthebear9050
I think you missed the point. The browns never won nor lost against the specialist strategies because they could only win 1/3 of the time, draw 1/3 of the time, and lose 1/3 of the time. This is true against any opponent they fought, and therefore their population didn't depend on the others. It's not like they could exploit all niches, it's that they didn't exploit any niche, but weren't hurt by any special strategy either.
@@ethanrutevillarreal1506 the browns couldn't exploit any niches, but they didn't have the problem of tieing often, which all the niches had, which resulted in niches being worse than the browns.
@@brutusthebear9050 You're underselling animals a lot. They're pretty smart and learn and adapt well. They just don't have written language to accumulate institutional knowledge with, which is what lets us do science.
I've been waiting for this moment for years... a new Primer video on Rock Paper Scissors of all things! Love it!
One thing I'm especially interested in is if more gestures were added. Imagine Lizard or Spock in blob form!
Fr
E
a new Primer video on blobs is enough to make my day
your feelings are irrational
0:09 Not for some reason! paper beats rock because it used to be cloth. the same cloth which flung stones from slings, stayed stones as embroidery, and dragged heavy stones in a process called heaving.
Oh, never knew that! Interesting
I only knew about paper covering rock not the whole cloth thing lol
@@TheSadster yeah me too
papercut
In my language (swedish) it's rock, scissors, bag (translated to english obviously). The bag can hold the rock but the scissors cuts the bag. Bags being primarily made of cloth, it makes sense I guess 😊
I would add in behaviors to each one. Rock could play it safe only playing against those who have 1 or less paper choices at a penalty to its food intake, paper could go for food above all else searching specifically for wins and ties, and scissors could play aggressive seeking out the nearest opponent no matter what they throw. Id love to see that simulation.
See you guys again in a year.
Happy Primer day! 🎉
Commenting to remind me when it’s a year from now.
😭😭😭
💀
Who else attending Primer Day Anniversary next year?
4:35 Rather than skewing the graph, realize that it's *already* an equilateral triangle, just in 3 dimensional. It's the plane that goes thru (1,0,0), (0,1,0), and (0,0,1), with every position containing any negative values cut away.
It's a right triangle, not an equilateral.
@@wrpen99 no no, it's equilateral. But from the projected angle it looks like a 2D right angle.
In 3D space it's equilateral.
@@jursamajI had never noticed that! it's an incredible way to visualize this graph
@@Endless-fire It's still a 2D triangle, there's no projected angle here. Measure the distance from points (0,1) and (1,0) on a graph, it will be longer than the lengths of the other two sides
@@wrpen99 what they're is saying that you can imagine a 2D right triangle as a projection of a 3D equilateral triangle. The distances between the points (1, 0, 0), (0, 1, 0) and (0, 0, 1) are the same. When projected to the xy plane these points become (1, 0), (0, 1) and (0, 0) and takes the appearance of a right triangle. it's really quite simple
I'm glad when you mention being surprised by results. It makes me more confident making guesses and engaging with the video more attentively, because I don't feel as stupid when I'm wrong most of the time knowing even someone who does this all the time could get it wrong.
At least you know you are some people don’t know they are.
A simulation about product quality would be interesting.
If high quality products cost more but last longer, will the seller gain or lose market share?
What about planned obsolescence, is it beneficial?
The reason why "paper beats rock" is usually, "because it envelops it and rock can't move".
Implying that rocks normally try to move lol
i have always imagined a piece of paper simply slipping on top of the entire rock, but not enveloping all the other sides
I'd say "it wraps around it, making it softer"
Paper covers rock.
@@Vospi yes.
If you want to play with the system yourself. Here's a desmos calculator that does the pure-strategy simulation and puts it on a ternary plot. It's a little different because it assumes an infinite population, and so you will see some subtle differences in the results.
www.desmos.com/calculator/lmx7hy2dai
I love that you share such things! Definitely worth checking out
Thank you!
I never thought I could have fun with Desmos...
Not sure if this eventually happens at lower speeds, but if you crank the speed up to near 1, the population just shoots off the graph in the direction of on of the ends (I’ve had it fly off after going from scissors to rock and going down the x-axis away from paper, and do the sam from paper to scissors and flying away from rock). It was funny.
Thx
I think it's interesting how much farther this simulation went than most of your other ones. Such a simple premise having so many iterations and tweaks, I admire your commitment and and I enjoy your work.
I'm always both amazed and inspired by the clarity of the visualisations on this channel, and how they perfectly enhance the understanding of the narration.
The 'winner take all' strategy almost looks like a logarithmic spiral (or almost a golden spiral) with some bounds. Interesting.
It is actually a solution to a set of linear differential equations. The eigenvalues of the reward matrix decide the shape of the population graph
It's 11:48 at night, I have to be up in the morning, but here I am watching Primer as soon as I got the notification
Damn for me it’s morning 😅
Like really early for me-
It's 10:20 in the morning, I should've been asleep two hours ago (my schedule is 27 hours long, so it drifts per day), but here I am watching Primer as soon as I got the notification.
10:20 here...
What time zone are you in?
@@user-fc3jq5cm5w GMT+10, Australian Eastern Standard Time.
Awesome video! I remember seeing this kind of stuff in dynamical systems, but your presentation is so much more approachable while still preserving the key takeaways about how these systems behave!
Lots of effort went into this video. Fascinating stuff you crazy man
Great video! Cannot wait for the plushies to be restocked. I need all of them!
I also cannot wait
@@PrimerBlobs also you said stuff about how you dont want ur computer to explode, what are the specs of your pc
@@PrimerBlobs 65rgf
I only have one
@@PrimerBlobsSame! I can’t wait to act out some physical simulations with them!
Babe wake up primer uploaded!
E
Yay 🥳🎉
I'm up! Im up!
It's been 84 years
🎉
These videos are always so relaxing and fascinating to watch! Keep up the great work!!
These videos are so cool! Really interesting and I love the pretty design and colors and the cute blobs :D Thank you!
i just found your channel 5 minutes ago and seeing that this video was posted 37 minutes ago after 6 months is insane. i love your videos man, thanks
One thing I'd consider is adding in some form of 'territory', where related blobs are more likely to interact with each other. Perhaps this could increase stability by limiting how effective a small change could reach the entire population. It would be cool if we got to see cyclic fronts of population change.
You could probably do that with location as an explicit parameter - the blobs live in a 2D plane and there are a finite number of mango trees.
Maybe the blobs live for 2 or 3 days total, and each day, can choose to either eat at the current tree or move to a different one nearby.
@@thehans255 This has interesting applications for the prisoner's dilemma, too. Which, I suppose, is almost the same problem as this one already.
If you make interactions local, the game becomes a cellular automaton.
If I remember correctly, you can create a grid of squares with multiple states, where each state beats and replaces the previous one, loses to the next, and draws (no change) with everything else. When you get about 6 states or more, you usually see spirals that cycle through all the states, and gradually spread and overwhelm smaller spirals.
@@tulliusexmisc2191 I think I remember seeing that. You would probably end up with different, more stable behavior if you factored in the slight penalty for getting a tie, since that makes ensuring that fights have winners is better for the total success of the population than getting ties is.
These are pretty cool, so I hope you're able to continue making these! I started watching these a few years ago when I was just interested in the blobs and the mathematics, but now I'm very interested in biology, plants specifically, and I LOVE seeing when plants evolve and mutate (leaf variegation, changes in petal shape & color, etc). I can't afford to donate yet, so for now I'll comment and then go browse the shop
No matter what colors anyone eats, all that is left is brown.
That was more intuitive than I expected.
Coincidences can be funny, can't they... Just last night, I was watching a video about the UK election that mentioned one of your videos, so I spent this morning watching back all your stuff, and then you upload this just a couple of hours later!
Our of curiosity, what video about the UK elections was that? 😀
@@kvmilos.tomaszek Matt Parker's bad election charts video.
You don't have a slithest idea how interesting this videos are. They helped me so much!
PRIMER IS BACK!!!!
Thank you for your videos! I learn something new everytime I watch them
This is the perfect video at the perfect time for me to procrastinate to. Thank you Primer!
No way, thats the same topic I got for my bachelor thesis in math. (without mixed strategies tho)
Got to combine evolutionary game theory, which was a really fun topic, with stochastics (approaching the model with Markov Chains). The theory from Markov Chains gives a lot of explanations for the phenomena seen in the video, for example the absorption probabilities (one strategy reigning supreme) aswell as the expected time until that happens in the non-mutating scenario, and the repetitive cyclic flow as a stationary distribution in the mutating scenario.
Another really interesting thing without mutations is "Survival of the Weakest". In the Markov Chains model, but also in reality, for example with E.coli microbes, the strategy that "punishes" its "prey strategy" the least (for example if scissors would only keep 1.5 mangos and give 0.5 mangos to paper, while paper and rock keep the 2 mangos on their wins), usually wins out in the end due the predator strategy being extinguished by the prey strategy they left alive. Perfect example for "The enemy of my enemy is my friend".
(The article about the E.coli microbes is called "Survival of the weakest in non-transitive asymmetric interactions among strains of E. coli", if anyone is interested)
wow! survival of the weakest is an interesting term. having just finished a couple linear algebra courses, i kept guessing changing the parameters would change the outcome due to "something something determinant < 1".
i've added the paper to my reading list, but can i ask how you handled reproduction? curious if they can also be modeled with markov chains or similar structures.
Bachelor's thesis? Did you go to Reed College?
@@downloadjpg Reproduction wasnt really important in the article I got for my thesis, it instead dealt with it in the way that the individuals would swap strategies and turn into an individual of another strategy, leaving the total population unchanged throughout the whole simulation. It basically functions the same as with offsprings, as long as 2 offsprings are born for each "battle for the mangos". :D
@@michaelwalpole2208 Nope, I studied (still study) in germany
@@KunoichiLoL Ah, that makes sense. It's unusual to be required to write a thesis for one's bachelor's degree in the U.S., hence my inaccurate guess, but I presume it's normal procedure in Germany.
I love this channel - one fun bit after another. Thanks for the video. Cheers.
your videos are always so interesting, thank you for making them
14:32 You could also call it a Nash Equilibrium. A Subgame Perfect Nash Equilibrium, to be extra fancy.
It's always a good year when primer uploads 🔥🔥🗣🗣🗣🗣🗣🗣
love your videos glad to see another one is finally out
Great Video! Really cool seeing those patterns emerge!
When I first found this channel I basically binge watched all your videos
Haven’t we all 😂
Primer's back with a new banger
your video editing skills are incredible, what a treat to watch!
Very intuitive visuals, great work! Huge fan.
1:19
No mango? 🥺
No offspring? 🥺
This is literally what happened in the Rock, Paper, Scissors tournament lol
Aaaa, I love your vids, they’re the best! They are so informative and really teach me lots of cool things!
Glad to see another Primer video
In my local version of the game, you have a "well" instead of a "rock". It makes sense that paper beats well, because it can cover it up, while scissors fall down. Guess it makes sense with paper "hiding" a rock too
i've never heard of other versions! can i ask where you're from or what language you speak?
В странах СНГ тоже, бывает, говорят и про камень и про колодец =)
I'm curious as well. Where I come from (France), we also sometimes have a well, but it's an "additional" move that is usually considered unfair, cause it beats both the rock and the scissors, and is never played because of that.
@@artsenor254 In an instance of incredibly stereotypical behavior, the American equivalents for this are "gun" or perhaps "bomb." Or at least that's what kids did on the playground when I was little.
@@life-destiny1196 At my playground, kids slowly got more extreme with what they play.
7:14"Game Theory"??????!!!!!
IKR
It’s a section/field in mathematics
Is Springlock Breedable?
I am so glad to see another primer video is out.
this was fascinating thanks for creating it!
14:34 Did my mature adult a** just wave to an animated blob irl?
Worth
Friend shaped and rocking a smile, really good combo
No.
ass
HE LIVES! THE LEGEND LIVES!
This was super entertaining and educational, great video!
I learnt about those lizards recently in a recent Clint's Reptiles video that talked about crazy reproduction methods. It was a really fun video and I would thoroughly recommend it. I would recommend his channel in general, but I did especially enjoy that video, and I also think it would be fun for a wider range of audiences than his other videos.
5:53 is that the golden spiral?
Is it just me or is 5:17 looking a little Fibonacci?
always great seeing your videos!
these are the most interesting graphs I've seen all day. Thank you for sharing your experiment
0:32 All I'm thinking of right now is Rock Paper Scissors Lizard Spock.
Cancel your plans, a new primer video just dropped
Your videos are always awesome!
You know it's a good day when Primer posts a TH-cam video.
Did earth just revolved a full. Hiya😂
the reason paper beats rock is because paper covers the rock up
but how is that supposed to be a "defeat" paper gets cut, a rock breaks scissors but... paper covering a rock?? that's it?
@@AubreyMK the rock actually suffocates in the paper
@@sushicat1make sense to me, rock do breath fr (joke)
These videos are just amazing. Great job
Gosh, I really love your videos. Thank you
Yearly uploads
Hey hey. *Bi* yearly.
An important distinction
amazing video, very
good explained and
nice GFX\animation.
Interesting evolution.
Paper goes on top of the rock and COVERS it. That’s the reason.
Always a great day for a Primer video
thank you so much for making these videos
Love when you upload
It’s a new Primer!!! I’m excited and I haven’t even watched the video yet!!
so glad primer is making vids :)
that was awesome, thanks for making this :)
oh crap, it's Primer! I haven't seen you post in ages, I hadn't realized you were still making things.
Wow this is a beautiful video with a lot of commitment thank you
Fascinating to see how the population spirals and how the different rewards effect it. Great video!
Thank you so much for these videos, and this one in particular. I've been recommending the MIT OpenCourseWare course for Game Theory for a long time, and there's still a ton of value there, but introducing ideas like nash equilibria and ESS to a broader audience is so important. :)
1:38 im so happy you decided to use the fancy name for multidimensional array ♡! /srs and happy
I thought this channel was dead! Thank you returning, frendo!
WOOO, it's been too long without a Primer video!
An amazing explanation as always ❤
Seeing the paper comically cut the rock in two at 1:40 is hilarious
As usual, excellent and interesting video! My predictions were quite wrong! I appreciate the reminders sprinkled throughout to encourage people to actively predict and not passively watch the video! :)
the title honestly gave me a weird expectation of what was in this video and its way better than i expected i hope there's nobody passing it up (esp if they dont know the channel) cuz of that and missing this awesome video this has helped me understand population dynamics way better