Fun fact, the growth was more than generic exponential growth :) The base of the exponent (the percentage with which the tower stats increase) grow as well (with roughly square root growth but exactly sqrt(x*sqrt(x))). This means the function describing your growth will be of the form x^x. Absolutely insane growth.
Its even more beyond that, not only does the princes increase the percentage growth, it also increases how often the slime tower can eat, and the princes scales how quickly it scales these 2 towers futher up
@@rysea9855 yeah, thats why we use big O notation when comparing functions with large inputs to simplify them. grossly simplifying: as both the base and the exponent grow, this function would be O(x^x).
I got lectured about the use of exponential in the Path of Achra discord, here's how he explained it. "Quadratic is x^2. Exponential is n^x, where n is a constant. The growth rate of quadratic is linear. The growth rate of exponential is also exponential." Quadratic, x=1 incementing: 1,4,9,16,25,36,49 etc. Exponential, same but n=2: 2,4,8,16,32,64,128 etc. Same number of operations, you can see the gap grows quickly. He described x^x as "even faster than exponential", I'm not sure what the proper term would be. But with the same number of operations as above... 1. 4. 27. 256. 3,125. 46,656. 823,543. I think you can see the difference lol.
So i was watching sifd's video the other day where he got 70k stats, i was like "wow that's amazing" Now me watching Dex completely decimate the game beyond any reason "the 70k was nothing after all huh"
in the end you would have needed one million hits to defeat the boss. then 1000 times more. Soon the fight against the boss would taker longer than the age of the universe.
I tried to end the run so it counts as "highest floor reached", i did end the next fight with a 1000 times speed up (no clue how fast it actually got), but the one after that ran for half an hour and no numbers changed, so yea
omg Dex, that was amazing. you managed to grow numbers, not linear, or exponential, but to the power of itself and increased further by princesses. amazing stuff XD
What you saw here is just exponential scaling. In the form of statMultiPerRound= (towerBaseStat * towerGrowthMulti^n)/towerBaseStat, where n is the number of times you can consume the tower. So when the malignant tower had 200% stats after coming back and let's say it's at 1M stats,^eaten 5 times, the new stats would have been sometihng like. 1M * 2 ^ 5 = 32M, which is very close to what you see happening in the game. He had some other effects that increase the towerGrowthMulti a bit but it's just some constant in the end. The missing variable here is time, so let's add that in statsCurrentRound+nRounds = statsCurrentRound * (statMultiPerRound^nRounds) And as you see it's just a regular exponential, it just increases a bit faster as you add more consumes to the slime and levels to the malignant tower. Specifically what it is NOT, is a function in the form of x^x, so it's NOT to the power of itself.
I am quite surprised to see a game that actually expects the numbers to get this big. The highest number most programming languages can work with by default is roughly 1.8e308, or 2^1024. The fact that it has a safeguard for this totally surprised me though, I did expect the game to just let you hit that max and break it.
That's just default behavior for the adder/multiplier in the CPU for numbers, code won't blow up, it'll just keep computing with incorrect values unless you explicitly try to detect it.
@@woobilicious. Not in my experience. In c# at least, you can keep increasing a double until it hits 1.8e308 where it becomes infinity. Unless you're talking about something else, in which case please do elaborate
Yeah, interesting that they programmed in a safeguard to cap the max base tower power a good way from the maximum 64-bit float value so that even with other temporary modifiers it shouldn't reach the limit. Usually only idle games with exponential scaling bother doing anything with the cap like either unlocking new difficulty/content and scaling things to keep away from it, or by treating is as a milestone to break infinity and using something like the BigNumber library to go way past that value using software workarounds to the hardware limitation.
The e308 limit is pretty common since that's where a float64 maxes out... but it's awesome when games put in the extra effort to allow scaling beyond that. Like SwarmSim uses its own number library so e308 is still small potatoes in that game. The natural progression lasts until about e500 or so, but the player can use alternate strategies to get up to e100,000. And at that point, the main limitation is just that each number takes ~40 kilobytes of RAM and a whole bunch of CPU cycles per computation, so the game gets really slow.
I am guessing the reason why the stats capped at e288 has nothing to do with the dev putting in a cap manually. I think it has to do with how doubles (a type of comma number in code and probably the type used, as it is the only commonly used type that is able to produce numbers this large) are calculated. For those who don't care for a detailed explanation, basically the numbers got so big the additional stats were too small to make a calculable change for the computer, while the boss scaled enough to overcome this mathematical error. For those who wish to know the details, it's a bit complicated but here is as simple as I can think of. Here is how doubles are represented in computers. Doubles are 64 bits (ones and zeros) long. The first bit is the sign (+ or -), the next 11 are used to calculate the exponent (I will call the number you can get from these bits e) and the last 52 are used to calculate the fraction. The last 52 are bits are bitshifted (bassically move the coma but in binary) 53 bits to the right (that means less, it is called right because of how it looks in binary, shifting 2, 2^1, 0b010, 0b means in binary, 1 right would be 0b001, 1, 2^0, shifting it 1 left would be 0b100, 4, 2^2) eg. 2^52 would become 2^-1 (I will call this bishifted number f). This is the formula to calculate the number: (+/-) 2^(e-1023)*(1+f) Doubles lose precision as they grow larger constantly requiring larger changes to actually make any changes. Either that or the dev actually capped the number to avoid a buffer overflow, as that could in some cases crash your pc and in the very worst cases entirely brick your pc (though modern OSs should prevent this). I still believe it is the former though as doubles behave weirdly as they grow very large and you were still able to increase it. None of this weird behaviour is on the dev btw. These calculations are done at a hardware level with the only way around it being writing custom binary operations, which would be actual madness, as well as it being a lot slower.
yeah i asked chatgpt at what point a multiplication by 5 (500 something% stats kept) of the number would not change any binary digit and it said around 10^291 which was exactly the highest point reached. i was amazed how quickly dex figured out that he had to increase the stats gained by a factor of 10 to register and how he assumed the dev wouldn't store the number as a double but rather as an abstract representation calculating only on exponents (which wouldve been the right choice)
@@DexTag It seems then the dev actually did put in a max to avoid a buffer overflow, which is probably what froze the game. The exact highest number for a double is 2^1024x0b1.111111.., 52 1s after the comma basically or 1.79769313486232E308.
the reason he can not do it is because anytime he gets close to it grass just pick on her roots and starts running that how op DEX is, even real life grass run over the hills
The correct terms are: Decillion Undecillion Duodecillion Tredecillion It's based off of french numbers: Un, Deux, Tres, etc. When you reach 20 (vingt), it becomes vingticillion and starts again
For every 1 scientific notation the bosses health was over your tower's attack it will take 10x more hits to defeat. (In base 10 adding a zero is multiplying by 10, scientific notation is how many zeros follow the number). Meaning just 3 notations higher and you're looking at 1,000 headbutts ---> 4 is 10,000 ---> 5 is 100,000 and so on. Meaning it would start taking days, then weeks, then months, then years for the boss to go down.
One thing to note is, for your next runs, you could use the ancient tower´s ability What it does is that it replaces all commons with ruin towers, all uncommons with defender towers and rares with a moai that I cant remember the name of The first two arent that important, but the rare version works like a shop for tokens, each level granting acces to another token trade. 2 of them are very good, one gives percentage based stats and the other one makes a part of all temporary buffs permanent I dont know if there is a unique interaction with the malicious towers sooo you will have to try I guess
I love how dex always says “sorry guys this is my 2nd time playing so i will make a lot of mistakes” the. Proceeds to absolutely wreck everything like he developed the game for himself
When you have more towers in the shop than it can display, there is an arrow at the top of the shop which can be used to scroll back and forth through them.
So because the game seemes to cap the stats at 1e291 the numbers shouldn't break because the upper limit on numbers that most computers can handle is in the e308s (limits of double precision floating point) also fun fact if the difference is greater than about 20 exponents the tower would be taking 0 damage due to rounding errors
Man dude what the hell did I just see . . . bro I played this game myself and I thought you were joking with E288 numbers . . . But oh dear oh dear God no . . . It was actually real in a game that I have never seen it have even a million in number when I played it . . . Dude this is a bit beyond breaking the game
in Version 0.62b there was an implementation of a limit E290 to not get close to the real limit of double type of E 308. so to get as high as possible you shout get close to it with good towers. before you cude brack it with it like some streamer did.
I find the obsidian tower with a flower and honey tower is way more broken. By the time I get to the final boss the obsidian tower has 15k health and 20k damage
Na, I dont think it can compete, at least not scaling wise. It's more reliable I'd say cause you can do it earlier, but I'd say once you get past the early early game, the next time you can lose is when bosses scale up quickly, so quite late
Hey :D Good to see you play some EAT aswell :D We want to be greedy :P Nice transition from Cat into the bears with the grand final of an insolent tower :D Well done :DD
Yea it definitely hooked me (for myself), but i wished I found your videos before I recorded this, then I wouldve known that second main tower can give tokens to speed up scaling temporary stats xd
@@DexTag Nice :DD There is plenty of time to go for more rounds :D And there are always improvements to make but you did great!! :D Thank you for watching my content aswell :D
I made the same build yesterday and got the same problem. Let the game half an hour run... nothing happens.. the first beartower hold the line. Round 175 does not end. 😅
Es gab einen bug dass sich ab E308 stats das Game aufhängt und dann abstürzt, deswegen wurden die stats auf E288 gecaped. Das Update ist erst 3 oder 4 Tage alt
IMO thats wasted money if not needed, but upgrading the milk tower just throws out milk further, so to a tower in front of the cat. You can put another tower in, but space is an issue and it costs 9 gold to buy them
I just want to make Dex suffer with this one: NUMBERS! after Decillion it goes like this: Undecillion, Duodecillion, Tredecillion, Quattordecillion, Quindecillion, Sexdecillion, Septendecillion, Octodecillion, Nondecillion, Decadecillion Unvigintillion, Duovigintillion and so on and so forth...
Fun fact, the growth was more than generic exponential growth :) The base of the exponent (the percentage with which the tower stats increase) grow as well (with roughly square root growth but exactly sqrt(x*sqrt(x))). This means the function describing your growth will be of the form x^x. Absolutely insane growth.
The base grows because the princess upgrades he tower btw
Its even more beyond that, not only does the princes increase the percentage growth, it also increases how often the slime tower can eat, and the princes scales how quickly it scales these 2 towers futher up
It's probably even more nuanced than that when you consider all the factors into play, but it's definitely still insane. I love this sort of stuff
@@rysea9855 yeah, thats why we use big O notation when comparing functions with large inputs to simplify them. grossly simplifying: as both the base and the exponent grow, this function would be O(x^x).
I got lectured about the use of exponential in the Path of Achra discord, here's how he explained it.
"Quadratic is x^2.
Exponential is n^x, where n is a constant.
The growth rate of quadratic is linear.
The growth rate of exponential is also exponential."
Quadratic, x=1 incementing: 1,4,9,16,25,36,49 etc.
Exponential, same but n=2: 2,4,8,16,32,64,128 etc.
Same number of operations, you can see the gap grows quickly.
He described x^x as "even faster than exponential", I'm not sure what the proper term would be.
But with the same number of operations as above...
1. 4. 27. 256. 3,125. 46,656. 823,543.
I think you can see the difference lol.
So i was watching sifd's video the other day where he got 70k stats, i was like "wow that's amazing"
Now me watching Dex completely decimate the game beyond any reason "the 70k was nothing after all huh"
i've tried hitting this and for the life of me cant get it right :I
in the end you would have needed one million hits to defeat the boss. then 1000 times more. Soon the fight against the boss would taker longer than the age of the universe.
I tried to end the run so it counts as "highest floor reached", i did end the next fight with a 1000 times speed up (no clue how fast it actually got), but the one after that ran for half an hour and no numbers changed, so yea
@@DexTag need to keep some tokens to remove the carry towers so you can lose in the end
Dex got stuck in game world with no exit 😢
he becomes an anime protagonist
"I reincarnated in a auto towers game and became invincible"
omg Dex, that was amazing. you managed to grow numbers, not linear, or exponential, but to the power of itself and increased further by princesses. amazing stuff XD
What you saw here is just exponential scaling.
In the form of statMultiPerRound= (towerBaseStat * towerGrowthMulti^n)/towerBaseStat, where n is the number of times you can consume the tower.
So when the malignant tower had 200% stats after coming back and let's say it's at 1M stats,^eaten 5 times, the new stats would have been sometihng like.
1M * 2 ^ 5 = 32M, which is very close to what you see happening in the game. He had some other effects that increase the towerGrowthMulti a bit but it's just some constant in the end.
The missing variable here is time, so let's add that in
statsCurrentRound+nRounds = statsCurrentRound * (statMultiPerRound^nRounds)
And as you see it's just a regular exponential, it just increases a bit faster as you add more consumes to the slime and levels to the malignant tower.
Specifically what it is NOT, is a function in the form of x^x, so it's NOT to the power of itself.
hey the boss only needed to attack 471 000 times to kill itself
I am quite surprised to see a game that actually expects the numbers to get this big. The highest number most programming languages can work with by default is roughly 1.8e308, or 2^1024. The fact that it has a safeguard for this totally surprised me though, I did expect the game to just let you hit that max and break it.
That's just default behavior for the adder/multiplier in the CPU for numbers, code won't blow up, it'll just keep computing with incorrect values unless you explicitly try to detect it.
@@woobilicious. Not in my experience. In c# at least, you can keep increasing a double until it hits 1.8e308 where it becomes infinity.
Unless you're talking about something else, in which case please do elaborate
Yeah, interesting that they programmed in a safeguard to cap the max base tower power a good way from the maximum 64-bit float value so that even with other temporary modifiers it shouldn't reach the limit.
Usually only idle games with exponential scaling bother doing anything with the cap like either unlocking new difficulty/content and scaling things to keep away from it, or by treating is as a milestone to break infinity and using something like the BigNumber library to go way past that value using software workarounds to the hardware limitation.
A recent update added the limit Dex hit, it used to keep going, but the game would crash when you hit over 1.8e308.
The e308 limit is pretty common since that's where a float64 maxes out... but it's awesome when games put in the extra effort to allow scaling beyond that. Like SwarmSim uses its own number library so e308 is still small potatoes in that game. The natural progression lasts until about e500 or so, but the player can use alternate strategies to get up to e100,000. And at that point, the main limitation is just that each number takes ~40 kilobytes of RAM and a whole bunch of CPU cycles per computation, so the game gets really slow.
Some rumors say that the boss is hitting the tower to this day…
I would be so funny if a dev watched this thinking how badly could he break it and then being like oh, he broke it that badly.
I am guessing the reason why the stats capped at e288 has nothing to do with the dev putting in a cap manually. I think it has to do with how doubles (a type of comma number in code and probably the type used, as it is the only commonly used type that is able to produce numbers this large) are calculated.
For those who don't care for a detailed explanation, basically the numbers got so big the additional stats were too small to make a calculable change for the computer, while the boss scaled enough to overcome this mathematical error.
For those who wish to know the details, it's a bit complicated but here is as simple as I can think of.
Here is how doubles are represented in computers. Doubles are 64 bits (ones and zeros) long. The first bit is the sign (+ or -), the next 11 are used to calculate the exponent (I will call the number you can get from these bits e) and the last 52 are used to calculate the fraction. The last 52 are bits are bitshifted (bassically move the coma but in binary) 53 bits to the right (that means less, it is called right because of how it looks in binary, shifting 2, 2^1, 0b010, 0b means in binary, 1 right would be 0b001, 1, 2^0, shifting it 1 left would be 0b100, 4, 2^2) eg. 2^52 would become 2^-1 (I will call this bishifted number f).
This is the formula to calculate the number:
(+/-) 2^(e-1023)*(1+f)
Doubles lose precision as they grow larger constantly requiring larger changes to actually make any changes. Either that or the dev actually capped the number to avoid a buffer overflow, as that could in some cases crash your pc and in the very worst cases entirely brick your pc (though modern OSs should prevent this). I still believe it is the former though as doubles behave weirdly as they grow very large and you were still able to increase it. None of this weird behaviour is on the dev btw. These calculations are done at a hardware level with the only way around it being writing custom binary operations, which would be actual madness, as well as it being a lot slower.
It used to be higher apparently at E306, but then the game would apparently completely freeze and you wouldn't be able to do anything anymore at all
yeah i asked chatgpt at what point a multiplication by 5 (500 something% stats kept) of the number would not change any binary digit and it said around 10^291 which was exactly the highest point reached. i was amazed how quickly dex figured out that he had to increase the stats gained by a factor of 10 to register and how he assumed the dev wouldn't store the number as a double but rather as an abstract representation calculating only on exponents (which wouldve been the right choice)
@@DexTag It seems then the dev actually did put in a max to avoid a buffer overflow, which is probably what froze the game. The exact highest number for a double is 2^1024x0b1.111111.., 52 1s after the comma basically or 1.79769313486232E308.
Nah Dex, you dont goofed around you absolute madlad. Keep the insanity in your Videos going, but dont forget to sometimes TOUCH SOME GRASS!!!
the reason he can not do it is because anytime he gets close to it grass just pick on her roots and starts running that how op DEX is, even real life grass run over the hills
The correct terms are:
Decillion
Undecillion
Duodecillion
Tredecillion
It's based off of french numbers: Un, Deux, Tres, etc.
When you reach 20 (vingt), it becomes vingticillion and starts again
its based ob latin numbers but yes
Three in French is 'trois' ;)
For every 1 scientific notation the bosses health was over your tower's attack it will take 10x more hits to defeat. (In base 10 adding a zero is multiplying by 10, scientific notation is how many zeros follow the number). Meaning just 3 notations higher and you're looking at 1,000 headbutts ---> 4 is 10,000 ---> 5 is 100,000 and so on. Meaning it would start taking days, then weeks, then months, then years for the boss to go down.
One thing to note is, for your next runs, you could use the ancient tower´s ability
What it does is that it replaces all commons with ruin towers, all uncommons with defender towers and rares with a moai that I cant remember the name of
The first two arent that important, but the rare version works like a shop for tokens, each level granting acces to another token trade. 2 of them are very good, one gives percentage based stats and the other one makes a part of all temporary buffs permanent
I dont know if there is a unique interaction with the malicious towers sooo you will have to try I guess
"replaces all rares with a moai that I cant remember the name of"
heh, fitting for the name "forgotten tower"
The game puts a hard cap on the player to ensure defeat,
Dex: Hold my 5 beers + keyboard + sunglasses.
The Irresistible Number meets Immovable Notation.
What a legend Dex is. I’m honored to be able to see all this road since beginning, when Bible Evolved just start and talk about Dex in he’s videos
"oh Scheiße" hab ich gefühlt xD
I love how dex always says “sorry guys this is my 2nd time playing so i will make a lot of mistakes” the. Proceeds to absolutely wreck everything like he developed the game for himself
"That's not even a wall... That's a whole universe waiting for them!"
Dex just wanted to exit but it won't let him. That's what happens when he plays with all shafts and no balls.
yet another game that got dexstroyed
Geiler build😊. Hab jede Minute genossen. Danke für den upload.
Two uploads in 1 days, what a blessed life
Wow, it's been a while since I've last seen someone *actually* break a game. Looking forward to watching some of your other stuff!
I can always count on Dex to find some ridiculous way to break these games
Only 4th or 5th time he's played, and already working his magic.
When you have more towers in the shop than it can display, there is an arrow at the top of the shop which can be used to scroll back and forth through them.
This gave me flashbacks to those hyper stacking poison runs in clawler you did a few months back. Exact same vibe on this one xD
Epic auto towers is a perfectly balanced game with no exploits
Stairway to heaven turn princesses to queens
More of this game would be awesome ❤️
It hurt when you deleted the bear.
The bear wants to be strong too!
Chop chop little german boy this aint brotato
Jk much love ❤
Seem like the numbers get so high that both the tower and the boss hp lost can't even be calculated by the game engine
you litherally smash the game in first video . who needs seasons
If it is a game where you have stats, dex can make it explode.
So because the game seemes to cap the stats at 1e291 the numbers shouldn't break because the upper limit on numbers that most computers can handle is in the e308s (limits of double precision floating point) also fun fact if the difference is greater than about 20 exponents the tower would be taking 0 damage due to rounding errors
Legend say Dex is still begging the game to let him quit while the boss smashes it`s own head against the insolent tower.
in the description it says its a brotato game might want to change that but this video is goated
Thanks!
Man dude what the hell did I just see . . . bro I played this game myself and I thought you were joking with E288 numbers . . . But oh dear oh dear God no . . . It was actually real in a game that I have never seen it have even a million in number when I played it . . . Dude this is a bit beyond breaking the game
Dex, you were butting up against the hard limit of double precision floating point numbers.
in Version 0.62b there was an implementation of a limit E290 to not get close to the real limit of double type of E 308. so to get as high as possible you shout get close to it with good towers.
before you cude brack it with it like some streamer did.
I find the obsidian tower with a flower and honey tower is way more broken. By the time I get to the final boss the obsidian tower has 15k health and 20k damage
Na, I dont think it can compete, at least not scaling wise. It's more reliable I'd say cause you can do it earlier, but I'd say once you get past the early early game, the next time you can lose is when bosses scale up quickly, so quite late
Pfanner Eistee ausm Tetra Pack :D
Danke dir jetzt hab ich Durst
Trendy Eistee aus dem Tetrapack
sag mir bist du ein Göttergeschenk 😂
Hey :D Good to see you play some EAT aswell :D We want to be greedy :P Nice transition from Cat into the bears with the grand final of an insolent tower :D
Well done :DD
Yea it definitely hooked me (for myself), but i wished I found your videos before I recorded this, then I wouldve known that second main tower can give tokens to speed up scaling temporary stats xd
@@DexTag Nice :DD There is plenty of time to go for more rounds :D And there are always improvements to make but you did great!! :D
Thank you for watching my content aswell :D
You can get another shop to buy tokens through the ancient towers tower...1 is 10% stats to scale a bit faster
do find it a bit lame that it's an "endless mode" where there is a soft end by artificially capping player scaling so the boss can outscale you.
The boss at the end:
"LET ME INN, LET ME INNNNN"
And this is why you put points into your luck stat before being born :^)
Insane and crazy, thats what im here for.
You should do a video named : learn number with dex
I have a feeling that Dex is german xD
Harter deutscher Akzent:D
I want to see what he does with the towers of defense
Wait, what do you mean Tetrapak doesn't exist anymore lmao
you managed to win infinite mode lmao
I made the same build yesterday and got the same problem. Let the game half an hour run... nothing happens.. the first beartower hold the line. Round 175 does not end. 😅
to maximise your board covering everything els with bear would add a little more power
good work in braking the game
Bad News, i broke the Game complitly, at Boss Level 174 the Boss has so much Life That he will attack you around 1 Year before he will be killed.
If dex not broke something, its not dex)
*mass pretend* SUCH A SHAME... Big Shaaaame *gigglesnorts* BREAK THAT SYSTEM!!! :D
Es gab einen bug dass sich ab E308 stats das Game aufhängt und dann abstürzt, deswegen wurden die stats auf E288 gecaped. Das Update ist erst 3 oder 4 Tage alt
Hey dex, if you want an addictive game to try and try to break it, Balatro is for you.
i think you reached the interger limit, so even tho the game said u upgraded, it couldnt go past it
yeah stairways to heaven is the best item in the game btw it litterly allows for infinite scaling
The eternal battle.
watched the whole vid 🔥
ohh iam early i didnt notice until i read the comments
If I remember correctly the number after letter E is the ammount of zero's there is
Yes, that's why it goes up in batches of 3. Thats a 1000 progression like thousand million billion trillion, 3 zeroes
Wouldn't the milk give more stats if you upgrade the Milk Tower the Cat could have scaled more
IMO thats wasted money if not needed, but upgrading the milk tower just throws out milk further, so to a tower in front of the cat. You can put another tower in, but space is an issue and it costs 9 gold to buy them
Dex I just got the dex-troyer in brotato
i hit it too * - * but my full bord has the stats from the slime :D
Number go up
We happy
Tetrapack-Dikadillion xDDD
This excited to see
100-speed boss go brrrrrrr
Crazy tetrapack
Digga was??? Verrückt
the game crashes at E303
hi
51:45 alt+F4
Hey kann es sein das du deutsch kannst dieses scheiße im video war sehr verdächtig 😅😂
Min 49:30
Unplayable... I had high hopes for the game
69 Dextillion DMG
Geiles Deutsch
⭐⭐⭐⭐⭐
Day 11 of asking Dex to play Utopia must Fall.
Yea i did the same hours ago, still in boss fight...
I just want to make Dex suffer with this one: NUMBERS!
after Decillion it goes like this:
Undecillion, Duodecillion, Tredecillion, Quattordecillion, Quindecillion, Sexdecillion, Septendecillion, Octodecillion, Nondecillion, Decadecillion
Unvigintillion, Duovigintillion and so on and so forth...