tldr: split the purge 'job' into active purging and passive purging where only actively purged pops decline or produce resources.

The current purge mechanic is utterly ridiculous. Consider the math:

Suppose you have a number of pops, p, distributed over a number of worlds, w purging at a given rate, r.

To minimize purge time you'll want to distribute your undesired pops over as many worlds as you can. For a purging situation with pops equally distributed over your worlds you get a purge time, t, in months of:

t=(100*p)÷(r*w)

This somewhat makes sense as having multiple planets in general should afford you more facilities to purge undesirables. I think it would be best if purge rate also depended on the number of non-undesired pops or districts a planet has, as a fully developed ecumonopolis would reasonably have more facilities for purging than say a backwater rural planet. This problem isn't urgent or gamebreaking, but the next is.

For purge types that produce resources there is what an unintended consequence involving purge time. An undesired pop is treated as having the 'job' of being purged. Which as all other jobs do yields a monthly production. However this incentives the purger to make it take as long as possible to maximize reward. If a given pop yields a value of v resources per month while being purged the math is as follows.

Output=v*t*p

recall that t=(100*p)÷(r*w)

output=(100*v*p2)÷(r*w)

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Take a moment to consider the implications of this equation. Value and purge rate, v and r, aren't under player control and can be treated as constants, however worlds purging and pops purged is under player control. This means that a player should optimally decide to purge as many pops as possible over as few worlds as possible. Which makes no goddamn sense. If a player were to have 100 undesired pops spread over two planets then he'd earn half the resources a player with 100 undesired pops concentrated on one planet would. A player with 200 undesired pops on one planet would earn 4 times as much as the previous player and 8 times what the first would. This is insane. Essentially the resources you get per pop increases as you add pops and subtract worlds. A player with 1000 undesired pops on one world would yield 25 times the resources as the previous player and 200 times as much as the first. He will only have purged 10 times as many pops as the first player but yield 200 times the resources. That's not fair and makes no sense mechanically or within the logic of the game.

Ideally to solve both problems there is an elegant solution. Split purging pops into two categories: actively purging, and waiting to be purged. Actively purging pops would produce their v resources per month, but all decline at once. Pops waiting to be purged would be treated as a special type of unemployed. They would produce no resources and a nominal amount of unrest per pop. The number of job slots for actively purging pops would depend on the development of the world so an empire could ship undesired pops off to a purge center to be expediently processed. The number of active purging 'jobs' could also be deprioritized to allow the empire doing the purging to 'titrate' the rate at which they receive resources from the purge. This solution should fix purging being painstakingly slow and the current meta of super broken super tall nihilistic acquisition. Of course there will be some slight caveats to any math in this post as I didn't bother to account for the slight perturbances of purging being a discrete process, but the conclusions should hold. Tell me what you think. The only problem I can think of with this solution is that I'm not sure whether paradox intended pops to be able to decline faster than one at a time. I'd imagine this would be a rather trivial problem to fix, but I'm not a game dev.