this post was submitted on 17 Oct 2024
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While I disagree that "billions is beyond being halved", there is some truth to the idea that numbers can get so big that halving doesn't make much difference. That seems very very counter-intuitive, so I'll try to briefly explain.
Consider (10^10 + 2). That's 10000000000+2. I think it's fair to say that the +2 doesn't make a lot of difference. It's still approximately 10^10.
So then, consider 10^(10^10)×100. That's a huge number, too big to type here, then multiplied by 100. So the result is 100 times bigger than the huge number. But... writing it down we see this:
10^(10^10)×100 = 10^(10^10+2) ≈ 10^(10^10).
So although ×100 does make it one hundred times bigger... that just doesn't really make a lot of difference to a number as big as that one. As numbers get bigger and bigger, they start to take on properties a bit like 'infinity'. Addition stops being important, then multiplication, then for even bigger numbers exponentiation doesn't huge much of an impact either.
Mathematically, I think this is really cool and interesting. But I don't think 1 billion is that big. 10^9 is big enough that +2 doesn't matter much, but not so big that ×2 doesn't matter.
[edit] (I'm struggling to get the nested powers to look right... So hopefully my meaning is clear enough anyway.)
Interesting concept, thank you!
Have you ever played idle champions of the forgotten realms? At some point you start to get this feeling.
Happens in MMOs too, world of Warcraft was bad with it over the years on and off.
They've reduced the numbers down multiple times so that people start to feel progression again.
I'm not too familiar with WoW, but I think it's a bit different.
In the idle clicker, you quickly get to exponential numbers, so when you're optimizing the party and you have a choice of say, something that doubles your base damage or something, it really feels irrelevant because after all the other multipliers your hero is already dealing 2x10^(102), and going to 4x10^(102) is nothing
Yeah I think that can happen at different scales, and of course MMOs didnt just increase the numbers higher and higher, they added more damage sources per second, per target.
It gets to the point you need a meter and graph to really tell much of a difference with anything, but you won't be able to create enough data points to make a real determinstion.
So the end result I think is the same you are describing. You get a new upgrade and it looks like it will be a substantial difference but you end up not being able to tell.
The game you are talking about, is the exponential increase a feature of the game? It sounds like it goes up very quick from what you described.
Oh yes it's intended, there's even a setting where you can choose between abbreviations or scientific notation, because everyone knows K, M or B, but ain't nobody gonna remember Ovg for "Octovigintillion" (10^87 apparently), much easier to just keep track of the powers.
It's decent fun for what it is and it's f2p, give a spin if you want - https://idlechampions.com/