Taxing and Patrolling... is it worth it?

[Squirrelloid]

I'm not talking about killing off the entire population. I'm talking about how long it takes to break even on cumulative income (after which time just letting it grow was the better option).

I noted that population does decrease with 20% tax and G3 in a 5k pop province. This is relevant if you plan on bloodhunting in the future, because 5k is the magic number below which you get reduced slave income.

Also, numbers are for CBM, as i used +9% income from growth scales.

Anyway, the whole point is that patrol and tax is advantageous over some timeframe. if the game goes longer, it would have been worthwhile to just let the province grow. (Of course, your income is also more front-loaded, which has its own advantages that you have to weigh).

[iRFNA]

The manual says that overtaxing kills 0.1% of the population per 3% tax and increases unrest by 1 per 5% tax. So no matter the province size, 18% tax is going to kill more than 3G can replenish, and that isn't even considering the pop loss from patrolling down the unrest. Did the % pop kill get removed, cause otherwise it seems iffy to do this for more than a few turns, regardless of scales.

[Mardagg]

I have a lot of experience with LA Ulm regarding this.
In all my SP and MP games with LA ULm with Growth 3 I basically ended up blood hunting all 4.5-8k pop provinces and overtaxing all 8k+ provinces with 120%(for like 8k pop) and up to 140-150% for like 15k+ pop.I used overtaxing right from the start of the game.
Some things are worth mentioning here:

-Patrolling does not always reduce unrest to zero for a turn
-Patrolling does cost upkeep and "free" troops,which can be difficult to have while e.g. waging a war

-you catch a lot of scouts/spies this way and the patrollers in addition to PD can make the difference vs raiders.

It certainly is a very strong tactic imo if you have lot of upkeep-free spawn troops that are decent patrollers like e.g. LA Ulm(the wolves are great for this).
It does give you a huge income advantage for the crucial Early game which is much more important imo,than having more income late game.

[Squirrelloid]

Originally Posted by iRFNA

The manual says that overtaxing kills 0.1% of the population per 3% tax and increases unrest by 1 per 5% tax. So no matter the province size, 18% tax is going to kill more than 3G can replenish, and that isn't even considering the pop loss from patrolling down the unrest. Did the % pop kill get removed, cause otherwise it seems iffy to do this for more than a few turns, regardless of scales.

I would take anything the manual says with a large dose of salt until tested. That said, I haven't actually taxed long term because of the free troop requirement, so i can neither confirm nor deny that overtaxing actively kills population or at what rate it does so. The type of analysis I did is the type you'd want to do, so long as you could account for all the factors, whatever they may be.

[iRFNA]

I did test it, a province at 120% tax with 3 growth holds its population steady. I didn't patrol down the unrest, so it was just the death from the taxes. Might want to redo your spreadsheet if you're making your predictions based only on the death from patrolling down unrest, as this makes a rather large difference, especially for heavily populated provinces.

Wolfram Alpha has a use! (oh god, edit, it mangles the url when the input is in it)
Input this crude little thing, but it'll do the trick: f(t+1)=(f(t)*c)-b,f(0)=x

Just use the recurrence relation equation at the bottom for any time t to predict the pop with growth/death rate c and constant amount of deaths b starting with initial pop x. Grab the summation or integral from 0 to maxt - 1 to get total income over that time. And the common growth formula for a prov would be the simple e^kt, or initial pop * e^ln(growth/death)t

I might whip something up in maple, but this seems sufficient...

[TheDemon]

The population killed from having a tax rate above 100% is far FAR more significant than the population killed by patrolling. I tested this extensively for my Bogarus guide on the wiki. After testing, the manual formulae for both items are correct.

I then spreadsheeted the tax formula. Conditions:
Patrol down all unrest
No other income percentage bonuses
Growth income % = 2% (no CBM)
Starting Population 30000:

At Growth 0, Growth 3, and Death 3, the last turn the income for 150% tax is greater than the income for 100% tax is turn 20, 19 and 21 respectively.
At Growth 0, the last turn the total income for 150% tax is greater than the total for 100% tax is turn 42.
At Growth 3, the last turn the total income for 150% tax is greater than the total for 100% tax is turn 39.
At Death 3, the last turn the total income for 150% tax is greater than the total for 100% tax is turn 45.

Starting Population 5000:
At Growth 0, Growth 3, and Death 3, the last turn the income for 150% tax is greater than the income for 100% tax is turn 10, 10 and 11 respectively.
At Growth 0, the last turn the total income for 150% tax is greater than the total for 100% tax is turn 21.
At Growth 3, the last turn the total income for 150% tax is greater than the total for 100% tax is turn 20.
At Death 3, the last turn the total income for 150% tax is greater than the total for 100% tax is turn 22.


Spreadsheet attached, sorry I have no idea how the conditional formatting will show up in the old excel file (xls) but the new ones can't be attached. The spreadsheet lets you tweak with all kinds of income percentages and bonuses so its quite a powerful tool.

[Kobal2]

Uh ? How come Growth 0 is more overtax profitable than Growth 3 ?

[Squirrelloid]

The Demon: that's turns until the turn income is higher without overtaxing, yes? What about cumulative income? How long until the *total* income collected in the province is higher if you just let it go? (I'd check myself, but strangely enough i don't have excel on this computer - maybe i'll look tonight)

[Kobal2]

He listed both, greater income and greater total income.

[DeadlyShoe]

Uh ? How come Growth 0 is more overtax profitable than Growth 3 ?

It's only relative profitability. Growth will always be more profitable in the absolute sense. But like I was saying earlier, growth isnt any sort of 'counter' for overtax losses.