LOL, as I said, sooner or later, it would happen.

Also ... I think the latest Idle change just broke my strat . . .

New Markets
This update changes the way markets work. Instead of selling items at a fixed cost, they now start off cheap and get more expensive the more you buy from them.

DAMN !!

@functor

Thanks for the replies - they were all good additions to my initial commentary, especially the drafting component since I had forgotten to account for it in my comparisons.

For mines before hospitals (an ordering I debate about a lot), I typically have estimated that most early-to-mid game mines (those that produce ores up to aluminum or possibly silver) tend to easily pay for the extra armies they cost to conquer if you have decent mine upgrades and they aren't obnoxiously out of the way (i.e. you don't have to acquire many other territories to reach them). But do note that I have to make these estimates frequently with incomplete knowledge of available hospitals since this is my first play-through and exploration is tricky if you have limited fog busters (e.g. Reconquest 1065).

Another tip I have is on where to use DT/QS/TS/FH. I do not think it is a good idea to apply them to a random territory. Instead, we can use them on important territories, such as the ones containing very good recipes, or some huge stack like the 401B one in the last level Europe Huge.

I'm guessing better opportunities become available on the later levels - I haven't seen much that's particularly enticing up through Europe 1066, though that level does start to make FH decent with some of the clusters of expensive territories in western europe.

Your updated calculations 0.20 for TMB and 0.19 for BMB look more likely to be correct.

I believe they are correct if TMB and BMB artifacts are multiplicative with the corresponding technologies (similar to how MB is multiplicative with mine output increase technologies). If they are additive instead, then the true benefits will be slightly smaller. This should be pretty easy to test for certain at the start of my next level.

I would like to remind you that there are other good artifacts which do not need to occupy a slot constantly, and you may also want to have a look at them.

Fair point - those are a little trickier to quantify but certainly worth doing!

Adding some additional analysis for upgrading Uncommon -> Rare for someone partway through 1st Ascension (stopped after Europe 1066 before update 5.14, then switched to re-beating old levels for the ore bonuses while waiting for IOS release). So slightly into Phase 2 upgrades.

With the latest nerf to mercs (a substantial decrease in the total number of mercs available), I've started running out of mercs on each level (+20% merc availability from AP) and had to spend a few hours waiting for army camp production to catch up at the end of the last two levels (Sengoku and Copper Creek Castle). So I was curious as to which of my uncommon artifacts would help the most with that problem. For simplicity, I've assumed that any money generating artifacts would have substantially smaller impact since I had plenty of money during the level. All values below are for Copper Creek Castle.

TLDR:

    Increased Army Camp Production: ~160M
    Hospital Boost:                  ~98M
    Supercharge Army Camp:           >95M
    Draft Boost:                     <61M
    Army Cache Boost:                ~48M
    Quad Strike:                     ~48M*
    Triple Strike:                   ~46M*
    Time Warp:                       ~27M*
    FH:                              ~25M*

At end of level rates, each 1M armies represents about a 1 minute faster level completion time.

Active artifacts denoted with * are worse than described because they would have been competing with an existing artifact slot, so there is opportunity cost to using them (and hence true benefit is substantially lower than the number shown, likely negative). SAC does not have such an impact because I was using it when playing.

Level Breakdown:

  * Total Armies:     11.385B
    - JS Armies:       1.921B
    - Hospitals:       3.332B
    - Earned Armies:   6.082B
      > Camps:         1.518B
      > Mercs:         2.273B
      > Caches:        1.284B
      > Draft (Fixed): 0.104B
      > Draft (Slide): 0.903B

AP comparison:
Just for comparison, here's how up to 300 additional AP would have helped via Additional Mercenaries (currently +20%) and Increased Army Camp Production (currently +90%):
Additional Mercs:

  60AP:   48
  130AP:  95M
  210AP: 142M
  300AP: 189M

IACP:

  90AP:   81M
  190AP: 161M
  300AP: 242M

Takeaways:

• IACP really is a strong artifact for new players.
  
• HB is a clear second-best and will likely be my next upgrade since it will fully scale onto future levels.
  
• Apart from SAC, the actives are quite bad at this point.
  
• Going back and investing additional AP in IACP is looking tempting, though competing with Mercenary Discount, Speedy Crafters, Additional Mercenaries
  

If you're curious about any of the assumptions I used when computing the numbers (there's a lot of them), I'll be happy to elaborate further.

Edited 8/23/2021 00:34:27

As you are explicitly talking about artifact upgrades: the Hospital Boost artifact got nerfed with the latest update. Rare is still twice the effect of Uncommon, but beyond that point HB isn't doubling in effect anymore. So, you should take this into account when estimating the effects of upgraded artifacts. Or in general, always look up what an upgrade gives you if this information is available. The number of artifacts that don't double in effect (anymore) seems the increase with each update (unfortunately).

Phoenix makes a good point regarding HB. It's unfortunate that the game doesn't tell you much like it does with the mine/army camp/hospital upgrades what the new stats will be post Artifact upgrade. It's deceitful imho to have a system where most but not all items 2x with upgrade, but that some items like SC & HB just don't.

I've assumed that any money generating artifacts would have substantially smaller impact since I had plenty of money during the level.

Can you elaborate on this?

If you have "plenty of money during the level", to me this means you could have further upgraded your hospitals, army camps, mines or bought more mercs. Having "too much money" is only ever possible if you've exhausted all of it on these and the next upgrade costs more than you have and/or the cost to benefit ratio just isn't worth it. If you have money left over, you likely don't have enough mercs to use the money on, which unfortunately artifacts can't help you with, only Advancements can, but you'll need that money for when you do get more mercs.

Thanks for the reminder about HB's nerf, @phoenix. This does bring up one downside of it that (at least until Fizzer updates HB's progression into something more reasonable) that HB won't provide any further efficient upgrade opportunities beyond the immediate uncommon->rare upgrade.

Can you elaborate on this?

Sure! All hospitals were maxed except the first which was upgraded a lot, but not fully since the final upgrades have absurd cost to benefit ratios (> $100/A saved). Similarly, I had purchased all mercs. If I'd had enough mercs to finish the level (via AP advancements), I also could have easily purchased the extras. Army camp upgrades were similar to the hospital one in that they provided absurd benefit relative to their cost (e.g. the next upgrades were around $1B each, for only about 2-300A/sec). Mine upgrades were what gave me the large amounts of money in the first place - you can easily get $300K/sec from mines alone on CCC.

A few other stats that may help get context:

• My final session time was 2days, 9hours without any time-warps used. The last 3-4 hours was purely waiting for army camps, so the session time I was attempting to achieve was say 2days, 6 hours = 54 hours.
  
• I used 2 FB's as soon as I had naturally uncovered enough territories that that would complete the map (I remembered the basic layout from my first playthrough; this is more for my next one during Ascension 2. My point here is that I didn't have to waste many armies exploring and hence was able to get strong value from the hospital upgrades).
  
• I used 1 MR partway through the level (testing my understanding of the MR mechanics), which did provide quite a bit of money, though a substantial fraction of this was unused after all hospital upgrades and buying all mercs.
  
• Total money earned was 55B, of which 28B came from selling ore, 18B from selling items, and 6B from caches (1.5B from bonuses & .5B from territories).
  

So, given this, I don't see a clear way in which more money would have helped substantially. Of course, it would have had some impact (upgrade camps / hospitals / mines slightly earlier), but the change due to a single artifact upgrade seems extremely small there.

If you have money left over, you likely don't have enough mercs to use the money on, which unfortunately artifacts can't help you with, only Advancements can, but you'll need that money for when you do get more mercs.

Yup, that's pretty much the state of the game for newer players - many inefficiencies easily solved by more AP, but you don't (yet) have access to more AP :( You do have some spare uncommons that could potentially be upgraded at this point, though and the idea of my previous update was to add data from a new point to help provide a more full picture of artifact comparisons.

One other thing I realized - if the ad bonus of 20% is multiplicative, that would have also enabled me to finish the level "on-time" so maybe someone is telling me to watch ads =D j/k

But, I was playing on PC, so alas, this isn't an option (plus the general undesirability of having to see a glimpse of an ad to play a game)...

@Earl
I used to have that same experience (lots of money, not enough armies, nothing useful left to buy). And when that happens . . . you wait for armies to accumulate from camps, b/c that's really all you can do. I thought that this was no longer a thing due multiple updates & changes, but perhaps it's just b/c I have better Advancements now... I solved my 'excess money problem' by providing things to buy (mercs).

For a while thereafter I had an excess army (mercs) but not enough money problem (which just means craft as long as is necessary to get the required money, then win).

Now I have a good balance of money & armies . . . with +100% mercs, +50% hospital buff & +70% army caches, just about the right amount, and with +50% crafter speed, +100% bonus money, +85% item sell values, +100% resource & money caches, I don't have to do nearly as much crafting (real-time) as I used to in order to clear a level.

@krinid

One day I'll have enough AP... for now, I'm still thousands away from unlocking Phase 3 advancements.

The balance seemed pretty good to me before the latest patch that reduced the number of available mercenaries, but now seems a bit off for newer players since additional mercs are quite expensive in terms of AP, which you collect pretty slowly at the beginning. The patch also buffed mines pretty considerably and I finished maxing out the ore sell value bonus, which is apart of why I'm at the state I am. I expect (hope) that in a few more levels I'll start to become money limited again and start caring about things like speedy crafters more.