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Ancient Souls (AS) are another type of currency, just like Hero Souls (HS). Ancient souls (AS) are spent on Outsiders (Borb, ponyboy, chorgorloth, etc), which in turn are some kind of supercharged Ancients (Fragsworth, Siyalatas, Atman, Dora, etc).
How many AS you get when you transcend is a pretty straightforward function of how many hero souls (HS) you've obtained. In layman's terms, when you transcend you obtain a cumulative total of AS equal to five times your sacrificed HS "e" number, rounded down — technically speaking, floor(5*log(HS)). So if you finish a given transcension with 1e100 HS you will get a cumulative total of 500 AS. You will get to spend the whole 500 AS only if you respec on transcension, though (there's a "respec" checkbox close to the "confirm transcension" button). Now, how to spend those AS?
After december patch what you should do is drop a ton of AS on Borb. If you check Clicker Heroes' reddit page and hover your mouse cursor over the "clicker heroes" logo you will see it swaps to a "Borb Heroes" joke logo. It's a joke that makes a lot of sense, given the power shift from AS and HS to hero upgrades —since december patch, mid-to-late game progress is based on purchasing hero upgrades, whereas before december patch hero upgrades were borderline anecdotical. With solomon gone and ponyboy reworked to a solomon-wannabe, what matters now is transcendent power + HZE, and HZE equals Borb.
By design, progressing to further zones faster is what yields the best AS / time ratio, and nothing helps more in this department than Borb, since Borb maintains the 2 mobs / zone limit, up to current max zone (circa 1.2 million) at Borb level 238 (called "soft cap", vs Borb "hard cap" which is at 250 if I'm not mistaken).
Even if you've got a 5% boss chance —lowest possible value ATM—, "5%" equals 1/20, or in layman's terms again, it averages to one boss each 100 zones, with merc hero souls missions allowing you to make up for extreme bad luck with your 5% primal boss chance.
There are online Ancients calculators that behave quite differently before you can hit your 238 borb cap than afterwards - once you can hit Borb 238 they will go for it even if it leaves your other ancients at <30 levels all across the board. Borb is _that_ good.
TL; DR: Your AS cumulative total is five times your sacrificed hero souls "e" value (1e500 HS equals 2.5K AS for instance). Regarding how to spend those, a player that reaches a highest zone ever (HZE) of 50K is going to run circles around any player that's at 40K (provided reasonably similar transcendent power values ofc) regardless of Ponyboy / Phandoryss / Chorgorloth / Rhageist etc. levels, with a 5 minute hero souls merc quest yielding magnitudes of order more HS to this higher HZE player. Since HZE = Borb, Borb is the main outsider ATM, hence reddit's "Borb Heroes" joke.
- You progress through zones until you can't do so efficiently any longer. Usually this means 3 or more mobs per zone, though not on your first "playthrough" - before transcending for the first time;
- Once you can't progress efficiently enough you then ascend and cash in the hero souls (HS) by buying ancients, then levelling then as smartly as possible. This means focusing on your favorite playstyle. That said, active trumps passive by a landslide; passive should be done if you can't keep your game client open for any reason.
- Regarding smart spenditure, plenty of people follow the so-called "rules of thumb", and some people took the time and effort to create some nice tools such as this one (the one I use, albeit there are others just as viable): https://kepow.org/clickerheroes/
- After your first 3-5 ascensions (if you haven't transcended) you might want to transcend. After that, you want to allocate your ancient souls (AS) as smartly as possible. There are two steps come this stage: previous to Xavira (a certain hero), and post Xavira.
PRE-XAVIRA you may want to play "old-school" like. This is because heroes before Xavira have such weak improvements that your progress is mostly based on ancients and outsiders, just like it was before december. Still, don't neglect borb. Each level dropped on Borb will increase the number of zones you can beat by taking down only two mobs. This is good.
POST-XAVIRA it all boils down to how many transcensions you want to run before cap, if you want to go to a great HZE before new heroes are added to max out your available AS when new heroes hit the board, etc. If you want to transcend as few times as possible (because post-Xavira ascensions take way too long unless you spend a massive amount of rubies) you want to hit Borb soft cap ASAP. If you don't mind doing a couple transcensions along the way you may want to lower your Borb value in order to boost the other outsiders (they are useful, though none as much as Borb).
Hope this helps.
Before december patch you used to have to ascend, then transcend, but the devs realised this needed some love and happily obliged. :)
* Realistically speaking, not spending any HS is not a good idea but I want to get that single point across.
Borb is important to get forward in a good time, but I hold the "Level per Stage"-Cap at 2 until I need over 60secs to kill a boss... so where I do an Ascension (or Transcension).