[GS] Is chopping overflow overcorrected?

That's right, and you can see it's as same as you chop it without policy card.
Seems to me that "burst" production should not be seen as so much more valuable than "stream" production that it should lend itself to the notion that building a production stream is a dead-end meta. As that seems to be the case--not just from chopping, but also gold and faith purchasing--I would say there is an issue to address. Partially by nerfing chops a bit to create less efficient bursts, and partially by buffing the stream.
 
Civ 5 and 6 in a nutshell.

To be fair Firaxis' knee-jerk reaction to wall whip/chop overflow with protective in Civ 4 led to it being bugged/broken and not fixed back then, too. There are lots of good practices that Civ 4 used which 5/6 inexplicably abandoned but when it comes to overflow Firaxis has a much more storied history of nonsense than just 5/6.
 
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)
 
Thanks for all of this. When I watched the live stream and overflow was addressed, I got a much different understanding of how it was going to work.

I thought that overflow from a policy card would be pre-GS applied to production of the same type. So, if you chopped a forest with a builder to complete a legion that had just one hammer left and had the agoge card active, you could apply that extra overflow from the chop + anything gained from the agoge policy to say ... an archer (which also benefits from agoge).

I think my idea is better to be honest. The issue I had with overflow production was chopping boats and applying the overflow to a wonder. Or chopping boats and using the overflow to put up universities ... that kind of thing. So, yeah, I think there's a bit of an over-correction here. If you want to chop a boat and make another boat -- go for it! Or if you want to chop ancient walls to build medieval walls -- go for it.

On the other hand, it does slow things down a bit and maybe that's good thing in the end.
 
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