I ask because I built my first one in my only orc province and my corruption didn't fall at all. I have a couple centaur provinces but eh rest are are humans(albeit a lot of barbarians and nomads)

Ok thanks, I will try my highest pop centaur province next.

Math of corruption: http://www.gog.com/forum/eador_series/corruption_bankrupted_me/post2

As you can see, you can hit the roof with LordCorruption variable and have corruption at 60 + 6*difficulty even when all your provinces have "-100% corruption" building.

Also, corruption is a multiplier to your expenses, so you can see increased corruption after building deputy's house - typical turn is "hire guard", "build deputy's house".

Can be:
before
Total expenses 400
Corruption 50% (200)
Total -600

After deputy's house
Total expenses 420
Corruption 49% (206)

Ok so what would you recommend?

Well, there are 2 approaches:
1. Munchkin:

Corruption from race.var
Goblins 20
Dwarves 15
Humans 10
Halflings 10
Lizardmen 9
Elves 5
Orcs 8
Centaurs 0

Bigger number - higher corruption. Deputy's house is almost useless in centaur provinces (though can help against hidden dens and lairs), useless against corruption in fully explored and cleared from thieves centaur province. Usable for increased gold income anyway.

So, prioritize goblins, then conquered brigand's outlaws lands, if you don't have time/patience to fully explore them and clear all lairs of bandits. Lair is always generated here, so human province with one lair would be comparable to goblins. Then dwarves.

Then choose unexplored provinces by weight of thieves guild (can be generated more than once in one province. Actually, once I had demesne with 3 of them. 0 gold income was really unfriendly.)
Plains: 6
Forest: 5
Hills: 4
Swamp: 3

2. Feng shui
Just build them clockwise/counterclockwise around demesne.

Ok thanks I will try that next average or larger shard.

It helps to have a development plan: if you know you're going to want a stable (for the movement increase) and a mine/mill/sawmill/etc (for income) in a province then that only leaves room for one other building. A deputy's house is great for dealing with corruption, but you might also want to put an outpost, arena, secret monastery, etc in that province, which doesn't leave room for one.

In this case, depending on the map layout, you might be able to shift the stable or the misc building to a neighboring province that has additional building space (swamps don't have income buildings, for example, so they're good spots to drop random special structures), to ensure that you have a slot open in each for the eventual deputy's house (and/or unexpected special structures that might become available). Provinces with low corruption races are also better candidates for going without one, but this may also require that you plan your other structures (especially your stable-highways) ahead of time.

This is wrong.
You should build it in 100% of your provinces (except centaurs which have no corruption).
Here is a list of the races and their corruption:
http://translate.google.com/translate?act=url&depth=1&hl=en&ie=UTF8&prev=_t&rurl=translate.google.com&sl=ru&tl=en&u=http://eador.com/en/page3.html

Corruption is a global effect, the income of the province is completely and utterly irrelevant. Corruption takes a chunk out of your gross (not net profit, gross income) overall worldwide income. Here is how it works:
%Corruption = (LordCorruption +sum(Province corruption))/10 + 2*difficulty - 18.

Each province has its own corruption score (race + modifiers), the corruption of ALL your provinces is SUMMED (rather than averaged; so more provinces = more corruption).

For example, if you have 50 human provinces, your lord corruption is 100, and your difficulty is lowest.
%corruption = (100 + 50*10)/10 + 2*1 - 18 = 44%
At 106 human provinces your corruption would be 100% and you get no money at all.
In late game, every province you conquer results in a reduction to your overall income due to corruption increase.

Corruption is a retarded mechanic and the absolute worst enemy of any late game world. The solutions are to minimize the provinces you conquer, build a deputy house in every possible province, and always choose corruption reducing stuff in random events. The pittance you get from the event is not worth the amount you lose to corruption. (ex: when traders come offering bribes, taking bribes gives money but raises corruption; when catching a corrupt official, do a show trial or execution).

This is wrong.
There is cap on max corruption, double expenses at last difficulty, 66% at novice. So what? Just don't hire 100 gold/turn guards in each province and you would be fine. After hitting corruption cap each new province would add only income if you wouldn't put guard here. And even if you do, just hire something cheap, like secret agents. 2 gold/turn, with 100% corruption - 4 gold/turn. Even swamp province(with arena) would give you profit.
(usually I use siege engineers - 12 gold/turn, enough punch to stop inquisition and don't need crystals)

More provinces - more chances for events which can increase income. I had provinces with 200+ gold/turn in long games.

PS: there is potential bug with diplomacy. When you join province with negotiation, AI can calculate cost of the guards up to 200+ gold/turn. THIS would hurt you even without corruption(usually when defenders have Hydra or something similar). Sometimes I get 3 nomads with 25 gold/turn and so on.

If you don't mind can you discuss which 'normal' guards do you usually use?

My favorite is centaurs but it's not always possible to ally with centaurs and can only be placed in plains/forest. Most of the others [that I have tried] tend to simply be a good source of experience for enemy heroes!

Monsters guard packs a punch but is really expensive at 45 upkeep. However it at least manages to kill enough of the invading heroes' army that my heroes can then finish the job easily.

I am not sure what you saying Which is insanely high. Fair enough,
But I DID get to the point where every province I conquered lowered my total income. Which is why you should keep your lord corruption value low.
By keeping it low and lowering/eliminating province corruption with buildings, you can eliminate corruption

Max corruption on Overlord is 96%, in short - doubles expenses. I don't mind if someone corrects me. I wouldn't negate my lack of practice in English:(

So your corruption was lower than cap. You could continue to conquer provinces, hit cap and then see growth of your income.
When you have really high expenses, ask yourself - "do I really need all these T1 veterans with medals?", check provinces with allied/bought guards for expensive ones.


As for guards - in sandbox PVE I use golems on demesne for income, watchmen at the start, siege engineers for somewhat useful provinces, high tier guards from scrolls on strategical resources. For defense against AI before closing him in demesne I use only forts with 1 slinger.