Taxing and Patrolling... is it worth it?
 

What is everyone's feeling on raising taxes while, at the same time, having your units patrol to keep down unrest? Is it a good short term strategy for certain situations, a good long term strategy for certain situations, or neither of the above?

Re: Taxing and Patrolling... is it worth it?
 

I use it as a short term strategy.
It's good for early wars when you find yourself short in cash, sacrificing a few thousand people to taxing/paroling is very much worth it if it gives you a military advantage and the ability to rush someone, or defend against an onslaught.
If you take good scales and growth for example you can gain a substantial lead in gold for early wars and not even lose much population.

Re: Taxing and Patrolling... is it worth it?
 

Most people do it on turn one.
Some nations are exceptionally good at it (Caelum with their flyers!)

It can be a good idea to do it in provinces fixed income through gold mine, they'll have high income even when its population 0.

Re: Taxing and Patrolling... is it worth it?
 

Who mines the gold??

Re: Taxing and Patrolling... is it worth it?
 

I think they fish for it.

Re: Taxing and Patrolling... is it worth it?
 

Yes, I have been experimenting with LA Man, combining Judges (patrol bonus of 20), Growth-3, Order-3, and fortresses to great effect. All those multipliers add up to a lot of extra gold.

Think of it this way, if your troops are not currently invading territory, then they cost upkeep with no immediate benefit. Having them patrol is a no brainer, and overtaxing at 120% will only due minimal population damage, which Growth-3 seems to largely mitigate. Obviously, you miss out on the longterm growth benefits, but without running the numbers it would a lot of turns to make up an extra 20% income from a province with a growth rate of 1.006%.

Obviously, anything less than Growth-3 makes this highly questionable.

Re: Taxing and Patrolling... is it worth it?
 

Sometimes being a god is useful.

Re: Taxing and Patrolling... is it worth it?
 

I often heavily overtax for the first 5-10 turns. One game I overtax-killed 5,000 of my capital population. It does give you enough burst gold to get extra forts up, or buy extremely expensive starting units like Mammoths. So often its worth it, even if your capital isnt worth as much in the long haul.

Re: Taxing and Patrolling... is it worth it?
 

Depends on initial population.

So, iirc, 10% taxation generates 2 unrest per turn and patrolling away 1 unrest kills 10 population. If i'm misremembering numbers, the below is wrong, but its not that hard to calculate with a spreadsheet.

Assuming only G3 scales, a province that starts with 10k population will, in cumulative income, do better with taxing and patrolling until a whopping 93 turns have passed. (Of course, this assumes you have nothing better to do with the troops patrolling as I'm not counting their upkeep against them here.)

A 5k pop province, however, will net lose population in this situation, and will only be better in terms of income for 45 turns.

So, barring better uses for troops, patrolling is certainly better for 10k pop provinces for most games (since by the time G3 breaks even, the game is basically over.

Re: Taxing and Patrolling... is it worth it?
 

Those numbers must be off in some way, I would have taken 40 turns at 160% tax to kill 5k peeps.

I think Growth really is irrelevant to overtaxing, because it doesnt actually mitigate the population kill; you're still losing just as much tax in the long term. The notion that you can have a stable income is a mirage since those 120 scale points were supposed to give you an increasing income that you are now missing out on.

Re: Taxing and Patrolling... is it worth it?
 

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).

Re: Taxing and Patrolling... is it worth it?
 

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.

Re: Taxing and Patrolling... is it worth it?
 

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.

Re: Taxing and Patrolling... is it worth it?
 

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.

Re: Taxing and Patrolling... is it worth it?
 

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...

Re: Taxing and Patrolling... is it worth it?
 

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.

Re: Taxing and Patrolling... is it worth it?
 

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

Re: Taxing and Patrolling... is it worth it?
 

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)

Re: Taxing and Patrolling... is it worth it?
 

He listed both, greater income and greater total income.

Re: Taxing and Patrolling... is it worth it?
 

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.

Re: Taxing and Patrolling... is it worth it?
 

Exactly. I didn't set my spreadsheet up to do comparisons because I was looking for the breakeven point. If you copy the whole thing to a new sheet, I'm sure you can set up a comparison column.


I mentioned both.

For 30k pop:
This is per turn income.


Total income = cumulative income

Re: Taxing and Patrolling... is it worth it?
 

sorry, was reading too fast apparently. Now that i've gotten a chance to look at your spreadsheet it was more obvious. =P

Re: Taxing and Patrolling... is it worth it?
 

I get that, but it's still quite counter-intuitive that the scales which make population re-grow actually end up making a net loss faster than the scales that kill pop even faster.

Re: Taxing and Patrolling... is it worth it?
 

Net loss? Wow, I think you are interpreting it a bit wrong. It makes the overtaxing tactic less effective quicker. Because if you didn't overtax the pop that doesn't disappear would also grow quicker and raise your income quicker.

Say at turn 40 without growth the 100% cumulative income is 3000gold. But with growth 3 it is 4000k. Of course the point where the overtax would give less than these values comes earlier when the end number is higher.

Re: Taxing and Patrolling... is it worth it?
 

That's what I said, yes. Overtaxing starts making a net loss earlier with G3 than with G0, compared to 100% taxes with the same scales.

I realize the total income made during those 20ish turns will have been higher with G3 than G0 or D3. However, it is still very puzzling to me that G3 makes overtaxing less (relatively) effective, when you'd expect the pop regrowth would mitigate the pop loss from overtaxing and thus keep the overtaxing gravy train going a bit longer.

Re: Taxing and Patrolling... is it worth it?
 

Then I would advice you never to get stock options or other financial stuff IRL. At least not without proper guidance. :)

Re: Taxing and Patrolling... is it worth it?
 

In slightly more intuitive terms:

Both the 100% and the 150% sides of the equation had their income grown by Growth. I am ignoring the 6% income bonus, I am talking about only population growth. BUT, despite Growth the 150% side of the equation is losing population overall. Growth is a percentage; since the 150% loses population every turn, the gains from Growth are less every turn in absolute terms. By contrast, the 100% side gains population every turn, so it grows faster every turn in absolute terms.

Growth causes both incomes to grow, but the 100% side grows faster than the 150% side. Every turn the 150% slows as it bleeds population and the 100% speeds up as it gains population. That gap means the 100% side catches up to the 150% side earlier.

Just to put forth an example, with no Growth, the 100% side and the 150% side both hit 300 gpt at turn 20. With Growth 3, the 100% side and the 150% side both hit 355 gpt at turn 19. It's earlier, but both sides of the equation are making more gold in absolute terms.

Re: Taxing and Patrolling... is it worth it?
 

Ok, I understand now. Yeah, that makes sense. Thanks for taking the time to explain.

@Soyweiser : Tell me about it. This is why I can't have nice things :)

Re: Taxing and Patrolling... is it worth it?
 

Ah, don't worry. The whole system is biased for the ultra rich. The more disposable income you have the easier it is to get richer. (The last 20 years the gap between rich and poor has increased! Go conservatives).

Re: Taxing and Patrolling... is it worth it?
 

guys,its nice to know some precise numbers now,but you are missing lots of things that are important to sucessfully use this strat.

1. only big population provinces should be overtaxed at 150,because only there the shortterm net money for early/midgame outweighs the longterm loss of population in my experience.This is common sense after a while if you try and test a lot with this strat.
Those provinces keep losing pop and therefore they are basically taxed 140,130,120,110 until they are taxed 100 and keep getting population again with grotwh 3.
This means you got only some provs starting with tax 150,some with 140,some with 130 and most with 120/110 and all the low pop provinces arent overtaxed at all.

2.sometimes the patrollers dont make all unrest go away,thus it makes no sense to overtax the province that turn because you would only get like 1-5 gold more,meaning that growth 3 is a good way to regain at least some pop that turn.

3. overtaxing makes a lot of sense for blood hunt nations,since they often lose a lot of money blood hunting all those 4.5k to 8k pop provinces.Growth 3 offsets the population loss of blood hunt/
low tax combo and nearly offsets the loss of blood hunt/patrol combos.

4.You need the same number of patrollers to fight the unrest regardless of the province being 8k pop or 30k pop.That means your per number patroller that is sitting in the province every turn is effectively worth much more "gold" in big provinces.This is especially important to consider when you start with the strat at early game,where you normally only get a few new patrollers every turn...thats why you start and should concentrate your efforts on the biggest provinces.

All in all,this strat is relying on micromanaging your provinces every turn.

Re: Taxing and Patrolling... is it worth it?
 

You're looking at this backwards... look at it from a long term vs. short term perspective.

The purpose of overtaxing is to improve your short term at the expense of the long term. With a growth scale, your overtaxing is hurting a really good long term, so the short term gain comes at a high long term cost and hits breakeven quickly. With a death scale, your long term sucks anyway, so you're sacrificing little for what you gain, so breakeven occurs later.

Re: Taxing and Patrolling... is it worth it?
 

To take the extreme example, with LA Ermor's death dominion you want to overtax everywhere. The peasants are all going to die anyway, get some money out of them while you can.

Re: Taxing and Patrolling... is it worth it?
 

it really isnt that simple.
The main purpose of overtaxing is to improve your short term income while still in Early game/early midgame.This is where any income advantage pays out fast on multiple levels.
(Think about it: how much could you do with 500 gold extra on turn 12,compared to 500 extra on turn 70? )

Since it is impossible to overtax many/all provinces that early,due to lack of patrollers for one of the many reasons,your whole example growth/death scale is basically nothing but theory since for most provinces the growth scale still has a big longterm gain.
In other words: you boost your early game start while still remaining competetive for the late game.

Another purpose of overtaxing could be in late game,when you know the final war starts soon and thus you dont have to worry about longterm pop loss.Taking a death scale here makes even less sense though,since you would have suffered already a lot until you get to the endgame.

Re: Taxing and Patrolling... is it worth it?
 

Ermor: yes,good example where overtaxing always makes sense.Can be a bit annoying though,if you are unlucky and your chaff troops cant deal with the unrest,since you only got very few turns to squeeze out the money.

@Krpeters
one more thing:
Growth positively affects your provinces before you switch them to overtax,which may take quite some time.Likewise Death negatively affects them.

(The Death scale+overtax rush idea is a fail,since,again,it is impossible to get enough patrollers going early on,while expanding at the same time.)