Dota 2 Mods - LEGION TD

Play Sweet Dreams Alex on Steam! Thank you! store.steampow...
Check out Stories of Dota! / @storiesofdota
Subscribe!!😡 www.youtube.co...
I stream on Twitch every day: / baumiandcats
Join the Community Discord! / discord
Chroma: Bloom and Blight is a digital card game I created: store.steampow...
Disastles is a physical card game I created: www.disastles....
Social Media:
/ baumiandcats
/ baumiandcats
/ baumiandcats
Business Mail:
[e-mail]
#Baumi #dota2 #DotaBut

[@muhamaddaffaridwan4380]

Definitely need 3 hours version of this❤

[@itamarneto5851]

Hell yeah!!

[@robinroth5063]

I think it already exists, just search for it

[@nightknight3414]

hell yeah

[@maxweber06]

Oh boy, here we go. One of the most space efficient ways to write big numbers is Knuth's up-arrow notation. Basically, if you want to write a stack of exponents you can denote the length of that stack with nested arrows. For an example 2↑↑↑4 would be a stack of 2's to the power of 2 with a height of 2↑↑4, which is a stack of 2's 4 separate times, which is 65,536! Imagine writing 2 to the power of 2 with the stack of 2's reaching up many thousands high. Now imagine *that* ungodly number being the height of the exponent stack for 2↑↑↑↑4. Now, for an unrelated reason, lets denote this iteration with 3↑ⁿ3, then when we set n to something like 3↑↑↑↑3 (which is 3 to the power of 3 with the height of the three's being whatever 3²⁷ is), it's a chain of arrows with the length that is simply unimaginable, 3 followed by more arrows than you can possibly write in your lifetime, an ever exploding value, each arrow denoting bigger and longer iterations of iterations of exponentiation. There you have G₂ but wait, what about G₃? You guessed it, it is a chain of arrows with length G₂! And this continues until... Graham's number, which is G₆₄ a number that defies time and space by being too big to write out in power tower notation or even up-arrow notion, the universe is too puny. And then there's TREE(n) which is comparatively, effectively ZERO compared to G(n), but I'm not well versed enough in the fast-growing hierarchy of functions to explain TREE. What I do know is that Rayo's number blows _both_ numbers completely out of the water. It is the GOAT of big numbers, bigger than even TREE(G₆₄). I suggest you watch Numberphile's video on the subject, it would be cool to see it played during stream.

[@IExistSometimes]

Tree(n) grows much larger than G(n) for all n greater than 2

[@IExistSometimes]

Actually apparently you can only choose positive integers, is there any guarantee that rayo's number is an integer

[@jeremylakeman]

TREE(1) = 1, TREE(2) = 3, TREE(3) ... has so many decimal digits that you can't visualise them. If you stored the digits in a volume the size of your brain, it would collapse into a black hole.

[@UmbrellaExile]

I respect the math knowledge, I want to flex the MtG knowledge. While the rules on this are vague, there are important points to consider. The first is that if you were to defer to a judge, their discretion would be the final say. If you aren't deferring to a judge, you'd need a general consensus. Now! The rules state that you can only choose a positive integer or zero when instructed to choose a number. While exponents are expressions that represent integers, they aren't strictly speaking integers themselves. This brings us to our first stop; Either a judge might rule that your exponent isn't an integer which disqualifies it as an answer, or they allow it. However! The second rule is that if anything is using a number that can't be determined, it uses 0 instead. So! If you had an impossibly high number, and you are determining the difference to see whose number is larger, a judge could simply say your number is too unwieldy the other numbers from and is therefore treated as 0. This means if you're relying on general consensus, you also have to pick the largest number that your play group feels is calculable, so actually drawing a really big 9 on a piece of paper might win you the game if all your friends go too hard into mathematics.

[@ekinkus795]

"At least im getting a story from it" bro is doing it for the vine

[@Uptoyouthen]

Man legion TD, i still remember back in Warcraft 3, half of warnet cafe playing this game

[@4KR0S]

10:13 like interruption scared the hell out of me. 13/10 left like

[@rroygreen8013]

Look up tetration. Trust me. Its basically writing 9^9^9, but waaaay more space efficient. Think powers, but to powers by that many times. 3^3^3^3 is basically 3 tetrated 3 times if i understand it correctly. Pentation is even more crazy.

[@mikahyakuya3542]

Those videos are so much fun, will never get bored of em

[@davidlayman901]

Well, if we assume factorials are valid for the big number thing, then since even adding on one more factorial is more important than getting in an exponent, for extra space, go across your paper diagonally! It'll look super goofy, but the extra space could be a lifesaver if someone else at the table had the same idea you had, but wrote in a straight line lmao

[@EmergencyTurkey]

Fold the paper into a mobius loop and just write 9s all the way around so it goes forever

[@IExistSometimes]

This is genuinely clever and doesn't need shorthand

[@patrickb6862]

the way to write the biggest number is to right a 1 diagonally from corner to corner it is bigger than everyone else number :P

[@AdianAntilles]

Look up Ackermann or Busy Beaver functions. They are so fast growing, they are regarded as non-computable.

[@beastboy1712]

Graham's number.

[@hartonigio69]

I guess one way to write some of the big number is TREE(TREE(3))

[@Dr.Death8520]

"The biggest number" You can all go home now

[@thehonestdude1067]

5 hour version would be nice

[@danyavernik4498]

let's go some more legion td, it was very nice

[@Amendelwyr]

Biggest number: 42 The answer to life, the universe, and everything. Nothing can be bigger than that. :D

[@Picaboom]

Actually got jump scared by Miki xD

[@ashash2432]

Just write "your mom's waist size" and gaslight your opponent until you win

[@julgoe5493]

1 Googol! The exclamation piont means factorial.

[@PolitePlayer]

Biggest numbers: factorials 10000!

[@ekinkus795]

Ah the rare like interrupt. Always a fun change of pace

[@IvanIvanov-ej2wy]

If i can use powers and factorials, can I use special functions? Like zeta function of whatever. These evaluate as nicely as factorials or at least they need to be evaluated like powers and factorials.

[@hsandev8972]

Eyyy, Baumi finally played LegionTD

[@miconradon3570]

Ok time to flex some math knowlage ^^ The best way to reach a big number mathamaticly would be with factorials of factorials so to put that into numbers there is already a difference of multiple factors if you would compare 999!!! = 10^(10^(10^2568.013591096136)) to 9^(9^9) =4.28124773175747048036987115930563521339055482241443514... × 10^369693099 and it is even more space efficient so the resultung number would be even larger since you can fit in more ! then anything else.

[@Hinotori_joj]

Let me flex my math knowledge: factorials are worse than exponents for a simple reason: take 9^9 vs 9!: one is 9*9*9*9*9*9*9*9*9 vs 1*2*3*4*5*6*7*8*9. You can see that the exponential is greater or equal at every number. Additionally, multiple factorial signs together doesn't mean (n!)!, instead it means, "if theres two factorials, only multiply every other number, three factorials every third number" etc. So you would have to nest your factorials in parenthesis, but it would still be worse than building a power tower.

[@Vale-vc3ri]

@@Hinotori_joj but 9^9 uses 2 numbers, while 9! only one; to be fair you should compare 9^9 Vs. 99!

[@Hinotori_joj]

It's true that 99! is greater than 9^9, however, lets add more 9s. 999! has a magnitude of ~10^2567, while 9^9^9 has a magnitude of ~10^369693099. If we filled the page with 6000 9s (the most you can fit on a page at 12pt font), that would have a magnitude of roughly 10^(10^6000), which is still smaller than just 9^9^9^9, which has a magnitude of about 10^(10^100000000).

[@papuce2]

10:02 lmao :D

[@IvanIvanov-ej2wy]

seven uhh yes, big

[@IvanIvanov-ej2wy]

and all the nerds with arrow notation and tetration can suck on a lemon!!!

[@nicolascolaizzi2519]

can also break biggest number by writting 9E99 or something whenever using a constan causes the number after rperesoent extra zeros. where ever you would normaly right 9, could also probably right Z instead of 9 and just say your using base 36 number system.

[@33gazer33]

Probably RAYO(10^100) I think

[@TM-yw9uh]

Thank you for always releasing these absolute bangers! Long time fan Baumi. Keep up the great work!

[@ramzikhalaf5860]

infinity is a state of mind

[@GamesMidnight]

" the biggest number" and if that is no valid in the other side of the paper says X+1 when X is the number my opponent wrote

[@metacarpo10]

Are functions ok? If so, how about TREE(TREE(3)) ?

[@ReiruYT]

This is also such a fun gamemode in Warcraft3

[@leysonmose]

I think 16 is a pretty big number so I'm putting down 16

[@Emile50]

I think it's best to not think about their response. You know, let it be

[@her0gamer638]

I would write 1+ and theoretically it`s the biggest because the other half of peace of paper got cut off so it`s like shrodingers cat, yes or no, it`s the biggest, shortest or even middle.

[@her0gamer638]

Its a peace of paper, not a board...

[@chrisslive2561]

Nice not-baumi intermission... I like :v

[@Relmmag]

why is there no auto chess style td? Just smash legion td and auto chess together :D

[@Felix-pd6pt]

Uhhh Legion TD nice gamemode Btw did you try out "survival chaos devotion" Maybe this is also worth giving a try

[@sal0qwerty]

Aleph-infinity

[@formless000]

TREE(TREE(TREE(TREE(TREE(TREE(9)))))) Whoever stack more TREEs wins.

[@Adrian_Good]

The Biggest Number

[@stooooopad2206]

Boomi I think you need to write 9 to the power of 9 and so go on and at the bottom spam factorials and you get the best of both worlds

[@kevinkevin8569]

Force focal

[@paulb.437]

I this going to be the "new" 1x6!!

[@jeanrouxel4837]

that is a big number 3↑↑↑3

[@JohnRoux]

69e+69^69e+69 But yeah, Baumi, I'd guess there're better options but using using scientific notion + powers is pretty good.

[@koishiscrawfish958]

9.9999999999 * 10^10^10^78 (stacking exponents should work)

[@Deads_boy]

the biggest number

[@Abilidaran07]

Biggest number

[@kevinkevin8569]

Googolplexian

[@harshkhatri3075]

what happened to 1x6

[@MessedUpSystem]

Biggest number: \omega

[@keagan1639]

Rayos number

[@arturosanchez1513]

My immediate thoughts was 1^infinity, then you said infinity aint a number so while still not cheating according to your rules, my answer is 9^9trillion (dont know how to spell anything longer even i know there obviously is)

[@coololi07]

1^infty is 1 :)

[@arturosanchez1513]

@@coololi07 Right, sometimes I'm big dum dum

[@devinbreytenbach7775]

10^10100

[@croutier1272]

Lim(x->0) f(x) = 69/x

[@gracz10001]

9!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(...)!

[@gracz10001]

uch someone said it on stream xD

[@iTzMAS]

10^(10^(10^(10^(10^(10^(10))))))

[@Vale-vc3ri]

Hey Baumi, about the biggest number: your explanation was 9 to the power of 9, to the power of 9, etc... This is actually wrong, the biggest is 9 to the power of 99... Example: assuming your piece of paper fits 3 numbers: 9^9^9 as you said makes 9^81.. but 9^99 is bigger :)

[@plaintoutarf9066]

9 to the power of 9 is not 81

[@Vale-vc3ri]

@@plaintoutarf9066 9 to the power of 9 to the power of 9 is 9 to the power of 81

[@heragon13th]

What you're saying is (9^9)^9 Not 9^9^9

[@seriossuperman]

81 is 9^2, 9^9 is 387420489

[@Vale-vc3ri]

@@heragon13th they are exactly the same and the result is 9^(9*9) = 9^81; way below 9^99

[@ALKOOOL]

69E

[@vetteran1905]

∞^∞

[@vetteran1905]

fuck

[@keagan1639]

Not a number

[@GGKalthos]

0

[@picklechiken16]

ℵ0

[@stooooopad2206]

Cheater

[@farbodkhalili1486]

First

[@ostadkhanCE]

¹⁰10 this is called Tetration (en.wikipedia.org/wiki/Tetration), it translates to ((...(10^10)^10)^....) for 10 times this number is bigger than the number of atoms in our universe :)

[@samsoulpactum8409]

Oh, you mean you can use math operators. Than it's easy. en.wikipedia.org/wiki/Tetration

[@krikri8303]

Biggest number: 9999^9999^9999^9999^9999^9999^9999, have fun calculating thre result :)

[@MySuperHentai]

googol^100

[@samsoulpactum8409]

13199357 or 1

[@JaredJKOB]

Tetrations easily make a significantly larger number than exponents with half the time

[@SirTimidFlash]

Biggest number. Googleplex^Googleplex

[@telmah5721]

my highest number I could in theory count up to: 999 novemviginitillion 999 octovigintillion... this goes on for a long time, played too many idle games

[@MrGreg242]

42069^42069!

[@9fastcutman661]

Incase it was unknown to you Baumi, this game is a replica of Legion TD 2 (on steam)

[@robinroth5063]

Wanna explain to us plebs cause we ben watching Boomi play this mode since like 2020

[@robinroth5063]

@@LittleDanny9899 right i remember him talking about that a Year or tow ago. Involving some beef¿ it was a qile time when custom games began monotising or mabey when valve anounced (for the first time back then)that you wherent allowed to monotise. I dont remember the details, wondering why boomi plays the dota mod and not the steam app. He seems like he'd support indi devs, tho on the other hand, it started as a mod and kinda still is.