10 catapults is a reasonable amount to start the war. However, given we will sacrifice some of them when we're at bad odds, we might need more.
Handling OF is a pain... if you keep a calculator handy though, you can keep track of it and decide what to build next.
Take Tours for example:
T133 -- start sword: 12 OF + 2 base = 14 * 1.25 = 17
T134 -- start rax: 2 base = 2*1.5 = 3
T135 -- whip rax: 1 base + 60 whip = 61*1.5 = 91+3 = 94;; 94-50 = 44/1.5 = 29 OF
T136 -- resume sword: 17 + (29+1)*1.25 = 54;; 54-40 = 14/1.25 = 11 OF
T137 -- (11+2)*1.25 = 16 H -- put in either a new sword
T138 -- start catapult (2H)
T139 -- whip catapult 2 + (1+2*30)*1.25 = 78;; 78-50 = 28/1.25 = 23 OF
T140 -- OF to finish sword...
And so on...
T141 -- rax + 2 swords + Cat done. 4 builds in 8 turns is optimal.
If you want 2 Cats instead, try whipping sword into cat. Not sure if it works as well since I didn't try it.
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I believe we could start considering Markets over libraries.
- the cost is 100H vs 36H (so 2 more pop)
- we get the improvement later
- no ability to run specialist for longer
+ we get 1

+ merchants
+At the moment 3g = 4b* research multipliers ::: ~3g:5b
+1C = 1.32b, 1C = 1g (but 83% of our gold goes to expenses)
I'll fiddle with cities a bit to see if what I'm thinking makes any sense
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X-Post with
Duckweed
Whipped on T133 (10)
T134 (9)
T133 + x = (10-x)
T143 (0)
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EDIT: for fun, I removed all of ours libraries, and placed 2 markets instead (7*36 - 2*100 = 52H conservative) in Dijon and Chartres (not to skew too much)
With libraries, sustainable tech rate is 82b @ 0 g/t
With 2 markets, sustainable tech rate is 83b @ 0 g/t
Basically, even if we get more beaker multipliers, we can't really sustain a high slider anyway... what's the use.