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Since resource 3 doesn't have beards associated to it, most people neglect the bars quite a bit, just getting enough to get to your cap in under 60 minutes is considered fine for many.
Other than that, you tend to follow a ratio similar to the one you use for energy or magic between power and cap, maybe favouring power a bit more if you want.
There is no set ratio for resource 3 compared to energy and magic, mostly because until you can cap all evil NGUs you probably want to focus primarily on energy and magic while only spending a bit on resource 3 to get a few levels from hacks.
After that, you transition to mostly resource 3 and a bit towards energy and magic, it will help both hacks and wishes that you will have unlocked by then.
If you absolutely want to follow a ratio between energy and resource 3, you can use the one from the exp costs, 100k energy for 1 resource 3, but the "ideal" ratio is something that varies greatly depending on your progression (in sadistic after reaching the hard cap for energy and magic cap you tend to have resource 3 higher (cost-wise at least) than the other two combined for example but going for a ratio like that early wastes a lot of exp for a minimal increase in bonuses.
After that, ratio 100k energy to 1 R3 is very viable as it supports the next feature best. Hacks "don't matter", despite their look they are not cumulative feature. Levels don't matter, only milestones do. And milestones are multiplicative to each other so every milestone gives the bonus mentioned in description to the total! And every 90 levels no matter hack requires double R3. As such hacks levels are directly bound to your current R3 power/cap (not time spent in hacks).
Considering everything above it is good strategy to not focus on hacks at all. Instead focusing on EM. And time to time plan for "hack run". You will spend all XP to R3 to reach double your ratio, along with perks/quirks/... related to R3. Then you will run hacks (with the dedicated equip), ideally with both boosters, this justifies even 2 days long rebirth (or even better: plan this for your challenge run and the 4 days banks refill period). After that you may turn hacks off and catch with E/M, doing NGU and ... .
This way you will get much more then just trying to keep ratio and run hacks all the time.
This is what will work well up to sadistic.
Oh, and the R3 ratio is strictly 1: 37.5k, no deivation there. As for bars.. 1:1 with power will hardly get you 1h refill so it's a good target. (Keep in mind bar upgrades (PP/QP) will be sliding one tier behind the power/cap. It's cheaper to compensate with XP most of time.)
PS. If you are looking around internet be VERY careful. Most of what I've found predates 2020 and is quite different to what applies now. People back then were required to rely on excessive hacks to move forward to sadistic. That no longer applies. We, as a new generation, are reaching sadistic much sooner (like half XP sooner), without any XP spend on adventure stats. 100k:1 R3 ratio will make your ... be very well and E/M ready for sadistic as best as it can. Don't try to compare stats with 2019 posts anymore.
Altough it isn't that bad, for now that's enough to level up my hacks quite a bit and NGU still feels like the right way to go.
Wait, am I much heavier on R3 than I ought to be right now? 435B base energy cap and 41M base R3 cap. That's a little over 10k energy for each 1 R3, and you just said 100k energy for each 1 R3.
Progress: Exile v3 autokill stats quickly reached every rebirth, not near v4 autokill yet
Base energy stats: 80M / 435B / 15M (custom purchase fields set to 500k / 1B / 50k for 83M exp)
Base magic stats: 45M / 330B / 10.5M (custom purchase fields set to 250k / 500M / 25k for 124.5M exp)
Base R3 stats: 2300 / 41M / 2300 (custom purchase fields set to 5 / 100k / 5 for 155M exp)
You work on base ratio 1:2000 while it really should be 1:37500. This alone would keep you at around 33% efficiency. In NGU and wishes alike.
E:M should still be 3:1 at that point. I don't know where the 2:1 keep coming from. But all NGUs are loong capped. So 3:1 for wishes.
And concentrating on R3, will hold you back.
Not sure what's your total XP or total time played. But since I'm near you I've spent 2/3th of XP you did on base EMR (zero on adventure stats) and I'm at Exile V4 finishing last evil wishes.
For comparison day 220, 85B EXP
Base E: 48M : 1800B : 48M
Base M: 16M: 600B : 16M
Base R3: 1200 : 45M : 600 (on double time as I'm preparing for strong hack run at the start of sadistic)
The 2:1 at least for me comes from the fact that I want quite a bit of extra magic beyond NGU and/or wishes in order to fuel blood magic, energy in augments for the whole day is not exactly crucial but with blood magic you can squeeze some extra, and for me it is definitely worth the exp.
If you want to min-max everything you obviously skip that but at the same time you already cut corners everywhere you can and your base stats at the same point of progression end up lower (because it took you less time to reach it).
I took into account the long discussions we had on the kongregate forums about this when answering him and only based it on resource 3 power compared to energy and magic power.
Of course if you want to apply the math to his stats they are all sorts of wrong, but that is by choice from him knowing that it is not optimal (like me and my 2:1 energy and magic ratio).
For the ratio between power and cap, I frankly stopped caring about what is the most optimal and stuck to the base from exp costs after people came up with the "truth" guide that has so many very arguable ratios and "proof" to make it seem like 1:20k is the most optimal somehow, that beards are absolutely not worth investing into and so on.
At this point I have seen so many people throw their math without context that even if someone came up with 1:10k being the best because X and Y reasons I wouldn't even try to argue against them.
(I mean, I understand arguing about bars because beyond beards it is convenience versus min-max, it is worth it losing 20-30 minutes worth of "work" from your cap per rebirth if you can raise both power and cap for the same cost)
Ratios.. they are subject to personal strategy. There is no universal ratio through the entire game. And adapting it is a matter of what features you want to support, but beyond that it's quite clear and comparable. If anybody doesn't care, then they choose anything between 1:20k to 1:40k and call it. Never bother with it anymore.
But in no way I will believe anybody "not caring" would willingly "chose" 1:2000. That's way off for someone who simply don't care (but care to ask/read guides). It doesn't produce any "more rounded" numbers or anything. It feels like simple (significant) mistake that could be easily fixed. And he asked.
And the nice thing about Exile is everything is capped there. There is no question about ratios anymore at that phase. You don't need to "choose" features. You have them all for free. Only wishes and hacks remains and they follow the same ratio so the answer here is really that simple :) Unlike the very beginning of game where beards are complicating everything :)
His stat ratio is most likely at least partially my fault for not doing a quick check on it and only checking "power" after the first few times where he explained not caring about optimal ratios.
I went back to the topic on kongregate forums where he posted his stats recently and while not as bad as now it was already way out of the normal ratios and I had not even noticed.
EDIT:
On the topic of 2:1, it is not limited to evil, it also allows you to get blood and magic NGU going sooner in sadistic.
I am well aware that 3:1 would most likely allow me to get slightly better results overall but I found that weirdly enough this allows me to keep a consistent pace through all of the features without having to sacrifice one in order to run the others.
But since it comes from someone that was running NGU, hacks and wishes all at the same time you can probably guess that I was more after an aproximation of somewhat optimal that happens to allow me to use as many features as possible at the same time.
There is also the fact that I have been pretty close to the end game pretty much since evil was introduced so rushing ahead and getting stuck grinding with no target so it does colour my view on what is "good enough".