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To figure out which is better, you'll need to compare your production rates in common time units (put them both in per-minute timeframes, for example) between your increased click entries in each category, versus the increased production from workers / buildings in that same time unit.
So figure out (in any given minute) for each of those two breakdowns, which produces more of what you need: base worker & building production per minute before multipliers and then triple that, or twelve clicks on each of the production buttons. That's the one you should probably increase for short-term gain.
Having those two apples-to-apples numbers for comparison purposes in each of the five production resource types will likely help inform what your longer-term choice should be.
Here's an example from my current challenge-format game: I'm constrainted by medicine right now. It's the only thing holding me back. I have exactly 25 scientists to spend. I have almost 61k ambulances and no nurses giving me just over 3E12 medicine per minute. But I have a 12x industry multiplier on that, so I'm getting base production of 2.5E11. I triple that and get 7.5E11 increased medicine per minute if I buy another Proper-ganda.
My click value for producing medicine, on the other hand, is currently at 2.6E12 per click. Buying my first auto-clicker would give me 12 times that per minute, or 3.1E13 more medicine per minute. I get almost 42 times more benefit for my constrained value if I buy the auto-clicker, making it the no-brainer choice for me.
Hope this helps.
I've definitely confirmed that I've gotten progress on resources with the auto-clicker experiment while offline, with no workers or production buildings at all. If you have a counter-example, please report it as a bug. There may be a condition that interferes with it.
Earlier in the game, when I was trying to buy Plantations (I have 6 hives now and 1 colony) I ran into the issue of not having enough Medicine. When I noticed, that if I had the auto clicker, I would be gaining lots if not tons. So, I invested... I'm not sure how many at this point into the auto-clicker but it's doing the trick and I'm slowly progressing and might even have my Colony #2 by tomorrow if I'm lucky.
My state multiplier is x15 and if I were to guess around 10-15 auto clicker purchases, it seems to be kinda quick.
Still, better than having no Scientists output, imo.
At what point do you believe auto-clicker becomes useless? I'm seeing a linear increase of 12 clicks per minute from each upgrade purchased...
That would imply that the availability of clicking upgrades would decay towards a linear rate (the extra tripling of resources should happen on average over the same time period), which should generally be acceptable performance assuming the base projected value is high enough.
Then optimal strategy would be to keep resource banked until you can allow 2-3 clicking upgrades for that resource to let multiplication do its job... and clicking (or any production for that matter) is useless.
Do you mind explaining how you got to those numbers?
For me the text on auto-clickers reads "Auto-clicks all resource buttons once every 5 seconds. Stacking cuts the time in half" which would mean 5*(0.5^[Number of clickers]) which would result in way more than 12clicks/min as soon as buying the 3rd one.
At 10 auto-clickers that would mean 6144 clicks per minute and not the 120 you claim.
All of these were verified with weapons and medicine prior to buying any workers or bulidings for that resource, so the math was very consistent and uncontaminated. All resources in those categories were coming only from clicks.
There are staggeringly few things in this game that actually do what they advertise on the tin, so this is just one more to add to the list.