Income and population mechanics

[Olm]

I am playing MA Man in CBM and follow the advice to maximize money.
I have Order 3 Growth 3 Sloth 1 Heat 1 Misfortune 1.
I try to have a Forrester patrol each province with a halfway decent income, and overtax them to 110%
Seems to work great. But how could I really maximize the gains? Where is the break even between killed population and more income?
Any experience?

[JonBrave]

Originally Posted by Olm

Where is the break even between killed population and more income?

Break even in what sense? Forgive me if I'm wrong, but hasn't it been established that patrol-killing is simply always worse overall, what it brings is only in short term.

[shatner]

From the wiki we know

Every 3% tax above 100% kills 0.1% of the population.

In CBM 1.92, each level of growth increases population by .3%. So growth-3 gives +.9% growth which is enough to negate 27% taxation. Since we can only tax in increments of 10%, if you run tax at 130% you'll lose .1% of your pop each turn.


However, this does nothing to mitigate the unrest which will build up over time. Specifically the 6 unrest/turn from 130% taxation:

Every 5% tax above 100% increases unrest by 1.

I can't find the source but I seem to recall you lose 10 population for every point of unrest you reduce via patrol. That means that every 10% taxation above 100 is going to generate 20 deaths/turn from patrolling, in addition to the roughly .3% pop-death from over-taxation. Since we're now dealing in absolute numbers and not percentages, the larger the province's population, the less the unrest/patrolling deaths are going to matter. In a capital with a population of 30,000, with a tax rate of 130%, you are killing 1% of the population from over-taxation plus .2% of the population (60 people) from patrolling to reduce the unrest. That's 1.2% lost and .9% gained at growth-3 in your capital, resulting in a net loss of .3% each turn. For every province smaller than that (i.e. all of them), the patrolling deaths will count for a larger percentage of the population killed, further reducing the efficacy of using growth+overtaxing for profit.

As such, you have two options:
1) Take Growth-3 and overtax at 120% each turn (for -.8333% death rate mitigated by your .9% growth rate for .07% overall growth... assuming capital-size populations)

or

2) Take Growth-3 and repeat the following pattern: run 130% tax for 3 turns (while patrolling) and then set the tax to 100% for one turn. That will keep your population roughly stable and give you an average tax rate of 122.5% which is > option-1's 120% tax rate. Of course, this will be a micro-management nightmare so I'd recommend against this option.


TLDR: with full patrolling, you can overtax at 120% with growth-3 and have a stable population. Anything more and you're population will be in decline. If this is ever "worth it" it would only work in provinces with lots of money multipliers (high-admin castle, high order scales, no money loss from temperature).

[JonBrave]

For the illiterate among us: The best you are aiming at above is stable population. Is it not the case that you would always be better (richer) in the long-run letting your population actually grow? I'm just trying to conform my understanding.

[Squirrelloid]

Money now is worth more than money later.

[shatner]

Omikron Warrior breaks down the income gain from population growth here. Granted it's from back when Growth got you +.2% pop-growth/scale instead of the .3% you get now. But if you pretend he says Growth-2 whenever he says Growth-3 then the math works out the same.

The reason I bring that up is that it allows you to do cost-benefit comparisons on the actual income brought in by the various scales. For example:

Order-2 gives you +12% income on turn 1, 2, 3, and so on. You will be averaging +12% income over all those turns. Growth-2 gives +4% income from turn 1 and an average of +12% income by turn 6 (+4% from scale, +8% from pop-growth). By turn 12 you have averaged +14% income, thus earning more money from an 80-point investment in Growth-2 over an 80-point investment in Order-2.

Of course, this all assumes you are allowing your population to grow. With overtaxing and Growth-2 you're are getting +24% income on turns 1, 2, 3, etc, for an average of +24% income each turn. That's as much as you would have gotten from roughly 42 turns of Growth-2 without overtaxing... and double what you would have gotten from just Order-2.

Since having a bigger income on turns 1 through 41 is usually more important than having a bigger income on turns 42+, there is definite merit in long-term overtaxing.

All that said, I'm not actually sure how all the money bonuses combine when determining your income. If I had those numbers I could math-hammer this problem and figure out the sweet spots. Does anyone know how Order-3's +18% + Production-3's +12% + Growth-3's +6% + Castle Administration + Overtaxation actually combine?

[Olm]

I'll do some tests in a spreadsheet this evening. Perhaps I can show up with some graphs.

[llamabeast]

Obviously, over an infinitely long game you would do best to tax at 100%.

However, in practice income during the first 30 turns is worth A LOT more than income during turns 31-60 (for example). This means it's hard to give a mathematically meaningful answer as to what the best approach is. Plotting some graphs and/or just playing with different strategies should give you some idea of what strategy you want to take.

Playing as Man you have powerful troops but weak magic. I think it might make a lot of sense to overtax at the beginning and create large armies in order to get a lot of territory early on. Hopefully you'll have enough gems and forts (for research mages) by the midgame that you'll be able to remain strong when magic becomes dominant.

[Olm]

I cannot reproduce the income in my provinces.
I am always somewhat higher than the game, regardless if I just add up all scale effects (Order 2 + Growth 2 = 12%+4%=16%) , add up one scale and multiply sequentially (Order 2 + Growth 2 = 1,12*1,04=1,165) or multiply even within one scale (Order 2 + Growth 2 = 1,06*1,06*1,02*1,02=1,169).
Has CBM changed more than just scale effects (basic income)?
Its even for provinces with no unrest and no admin.
Or any Idea how it is really done?

Example: Pop 5260, Basic Income 52,6 Scales: Order 3 Growth 3 Heat 1 Sloth 1, 100% tax no unrest.
Ingame Income: 57

1st case: 18%+6%-4%-5%=15%; 52,6*1,15=60,49
2nd case: 1,18*1,06*0,96*0,95=1,141; 52,6*1,141=60,01
3rd case: 1,06³*1,02³*0,96*0,95=1,153; 52,6*1,153=60,63

Nothing near 57. I am puzzled.

We are more in the region of a scale Effect of 8%: 57/52,6=1,084
I also tried rounding to full digits, doesn't do the trick either.

Another province with the same scales has 9080 pop, basic income 90,8, actual income 101.
So actual scale effect for this province is roughly 11% (101/90,8=1,112).
Am I missing something?

[shatner]

I agree, it's puzzling. The only formula I've gotten to work so far was
1) Round income down to nearest 10: 52.6 becomes 50
2) Sequentially multiply by negative modifiers first: ((50 * .95) * .96) = 45.6
3) Sequentially multiply by positive modifiers: ((45.6 * 1.06) * 1.18) = 57.03648
4) Round result down: 57

And that's just me throwing those numbers into the formula-blender and taking whatever output looks right. I'll need more data points to test this or any other formula before I can be confident we've reverse-engineered the solution.

Also, are you sure the base income for that province is population/100? I ask because if the base number weren't 52.6 than it'd explain the difficulty we're having.