Thanks for replying!
A simplification that happens to support your preferred outcome. Each tier of industrial tech introduces a sizeable boosts to MIC output, devaluing early game production.
As you can see in the graph by the output bonus B, the output granted is a (relatively) minor factor in the resulting pay off.
Changes in economy laws/production efficiency/etc. can all be fit into B as they apply a bonus to MIlitary factory output after the initial Mil's or Civ are constructed.
Another simplification that happens to support your preferred outcome. For CG a CIC counts as much as a MIC, meaning per construction day you rack up CG faster while building MIC due to their lower cost.
Inaccurate. For Case #1 to output more than Case #2 you would need to build
more factories (to catch up).
This would mean that, at the very least (if case #2 built 2) you would need to build 3 to match and 2+ more to catch up and overcome in military production.
Case #1 hence depends on more factories (and resources) -> Adding more CG and resource requirements than Case #2.
If I were to account for CG it would only penalize Case #1 (which already gives a poor result)
If you are focusing on building Civ's, the end result is you will have more factories for a shorter period of time.
This generally forces more of a penalty CG wise and resource wise.
I can guesstimate that you'd have around 30%+ more factories with Case#1 than Case#2, at the very least.
Hrm, on further thought.......you would have more CIC/day by going Case#1 in the earlier part of the game.
The problem is that this doesn't seem to be enough of a factor to affect any simulated runs I've done (to a noticeable extent)
Another simplification that happens to support your preferred outcome. CIC are worth more later in the game which would work against your hypothesis of getting ahead using early game production and staying low on factories.
I think you misread here. The laws are constant
until the Civ finishes building. The switchover happens immediately (for the maximum discrepancy/benefit for Case #1)
So once you finish building the single Civ in Case #1, you will switch to the most beneficial economy law/production boost/etc. all at once.
(Changes at d = C)
In the graph, X == The military construction bonus at time D > C, or when the Civ in Case #1 finishes building.
Another simplification that happens to support your preferred outcome. This simplification alone invalidates your integral because M is not constant, not even close. Your available CIC go down as you build more MIC due to CG. The maximum ratio of CIC: (CIC+MIC) your economy law supports is the CG percentage and M converges towards infinity as you approach this ratio.
I'm simply assuming that you are using the full 15 civs per factory at that given point.
The case comparison is at a single point in time, where you chose to do Case #1 or #2.
So, at a given point in time, where you decide to do Case #1 or Case #2, M is a constant
For future decisions M will gradually decrease yes.....but I'm not measuring a causality chain.
In my game Japan starts with 21 CIC, not 90. If I had the latter, sure I'd also just build MIC/NIC.
The quantity of starting Civs does not affect or change the results, barring resource constraints.
Having more starting Civs is always better.
But it also adds flexibility. I could build a bunch of support equipment, motorized, etc. in the early game to skirt the resource issue during buildup. But can I be sure I will need them in those exact quantities much later on? Depending on the game scenario I might not even yet know who the enemy will be, who my allies will be, who I'll be able to trade with and where the war will be fought.
I'm assuming you know how much equipment you need for the usual basis of your divisions. E.g. 200 garrisons? 100? and what template? etc.
That should help with motorized/support equipment.
On most nations I don't find it too difficult to push mils onto something that would be of use later.