Let us complicate the situation a little bit more.
Define 5 variables
- the production needed to complete the project (X)
- the city-per-turn production (Y)
- the production modifier bonus (A). So Y is the basic production part, A*Y is the bonus production part.
- the overflow from previous production (O)
- the chop value (C)
- The Magnus modifier 0.5
1. Do I understand right the chop with Magnus and Agoge will result in=
30*(1+0.5 (Magnus)) * 0.5 (agoge) = 67.5?
2. Do I understand right that TOTAL city production per turn = (O+Y) + (O+Y)*A
If we chop then TOTAL per turn I get = (O+Y) + (O+Y)*A + C*1.5 + C*1.5*A
So X is compared with (O+Y). If it is not enough, then
X compared with (O+Y) + (O+Y)*A. If it is not enough, then
X compared with (O+Y) + (O+Y)*A + C*1.5. If it is not enough, then
X compared with (O+Y) + (O+Y)*A + C*1.5 + C*1.5*A.
3. If it is right, then following conclusion (to max chop*bonuses) can be made:
A. chop at the beginning of production heavy projects (e.g. wonders). You can apply bonus card to max the effect. Magnus will help to max the effect
B. chop at the end of non-modifiable production projects (granary) and then choose production with bonus card applied (e.g. archer with agoge). Magnus will help, since his amplifier is added to the base
C. multiple chopping with Magnus will help only at the beginning of production heavy projects
Sorry, I couldn't fully follow point 2.
I agree with your A and B conclusions. For C though, I think it depends on the unit/building.
The way I visualize it:
- if the chop amount with the policy bonus is less than remaining project cost -> policy is 100% effective
- if the chop amount is not enough to complete the project, the policy bonus will give you at most enough to complete it, no extra overflow -> policy is 1 to 99% effective
- if the chop amount is equal to remaining needed production -> policy card is useless, 0% effective
- if the chop amount is more than the remaining needed production -> policy card is useless for the current project, but any base overflow remaining can be modified based on the next project policy modifier
example:
200 cost project, 50 base production chop, 2x policy modifier
example 1: start 0-100/200, then chop -> 0 overflow from chop, (50 base / 50 bonus from policy)
example 2: start 101-149/200, then chop -> 0 overflow from chop, (50 base / 49 to 1 bonus from policy)
example 3: start 150/200, then chop -> 0 overflow from chop (50 base / 0 bonus from policy)
example 4: start 151-199/200, then chop -> 0 overflow from chop, 1 to 49 modifiable production for next project (1-49 base / 0 bonus from policy)