Latest revision as of 04:43, 18 November 2010

This is my user page, where I will dump links to articles I'm tinkering with and little bits of math that I am working on (despite my inability to comprehend their significance). Also, I might just dump my strats here since I won't be posting my province and KD #s anywhere.

Please put any feedback on my discussion page. I'm trying to keep this thing organized as I fill it up with bits and bobbles.

Builds

Human Sage Heavy Attacker

War Build

Homes: 24%

Farms: 5%

Banks: 17%

Training Grounds: 15%

Guilds: 7%

Towers: 2%

Watchtowers: 10%

Libraries: 20%

Population

30 PPA

9 dPA

8.5 ePA

1 rWPA

2 rTPA

9.5 pPA

65% draft target

Sciences

150 Alch

150 Tools

150 Housing

100 Food

50 War

125 Crime

75 Channelling

800 bpa

Old Builds

Age 47 (Justice): Halfling Sage Attacker\Thief

Protection Build

Homes: 24%

Farms: 10%

Banks: 22%

Armouries: 22%

Guilds: 16%

Towers: 6%

Peace Build

Homes: 23%

Farms: 5%

Banks: 17%

Guilds: 18%

Towers: 2%

Libraries: 15%

Schools or Armouries: 20%

War Build

Homes: 23% - +1.84 ppa, +75.6% birth rate

Farms: 5% - Produces 7.869 mod bushels per acre, 9.836 w/ FL

Training Grounds: 18% - +23.6% offense bonus

Forts: 12% - +16.9% defense bonus

Guilds: 10%

Towers: 2%

Thieves' Dens: 15% - +40.81% effectiveness, -54.42% losses

Libraries: 15% - +25.5% science effects (not affected by BE)

Sciences

180 bpa (ratio 15): 30.6% Income

180 bpa (ratio 15): 21.9% Building Effectiveness

180 bpa (ratio 15): 14.2% Population Limits

72 bpa (ratio 6): 110.7% Food Production

84 bpa (ratio 7): 20.9% Gains in Combat

108 bpa (ratio 9): 101.7% Thievery Effectiveness

96 bpa (ratio 8): 95.9% Magic Effectiveness & Rune Production

Population and Army

Per acreages, etc. are given for War build except when noted otherwise.

30.7 peasants per acre

-9 for 106.7% rBE

21.7 idle peasants

-1 rWPA (2 mWPA)

-3 rTPA (OoW: 6 Esp mTPA, 8.5 Sab mTPA, 8.5 Esp mTPA, 11.9 Sab mTPA)

17.7 troops

10 ePA (73.9 mOPA, 103.2 mDPA @ 100% elites)

7.7 dsPA (45 mDPA @ 0% elites)

67.4% draft rate

Weighted Average Cost of Army per Acre

A possibly useful formula for attackers, this seeks to demonstrate the economic viability of running a predetermined OPA and a predetermined DPA through the most population-efficient means. It does not take in to consideration variables beyond troop stats and cost. Also, it doesn't account for DPA w/ 50% or 75% of your elites out, which could hurt your ability to hybridize.

Detailed Explanation

In order to evaluate the economic viability of race's armies, we'll need a goal for them to reach. For attackers, this is obviously a goal Offense per Acre and Defense per Acre. They will be noted in our formula as gOPA and gDPA. Let's get specific so it is easier to discuss and go with 90 OPA and 70 DPA - fair raw numbers for a heavy attacker. Let's assume we're Avians too so that we can give concrete examples alongside the arcane symbols.

In the interest of population - the most important resource of all - we'll be using as many elites as possible. Since no race has a primarily defensive elite, we'll be getting all of our offense from elites and adding defensive specialists to bolster what's left. This means we can already get our first derived variable - Elites per acre (ePA)!

ePA = gOPA / eO

ePA = 90 / 8 = 11.25

(eO is Elite Offense, the offensive strength of the race's elites)

Now, we can do the same for our gDPA. However, we have to account for the defense provided by the number of elites we've just determined we'll need. So, we'll subtract out the elite defense to find the gap between our current and our goal defense and use specialists to fill it in. In terms of Defensive Specialists per Acre (dSPA), it will go like this:

dSPA = [gDPA - (eD * ePA) ] / dSD

dSPA = [70 - (3 * 11.25)] / 5 = 7.25

(eD is Elite Defense, the defensive strength of the race's elites. dSD is Defensive Specialist Defense, the defensive strength of the race's defensive specialists because remember Humans have a +1 to this)

Now that we know how many Elites and Defensive Specialists we'll need to train per acre, it's simple addition to figure out our Army size per Acre (APA). For our Avian, this is 18.5. Furthermore, we know how much of our army is divided between elites and specialists - simply divide elites per acre by army per acre and likewise for specialists. Combine this with the fact that the costs for these things are preset by the game, and we have all the components for a Weighted Average Cost per Troop!

For the math illiterate: let's say you're throwing a party and need to buy beer. You buy a case of one beer for $22 and a case of another for $25. You'd get the average cost per case by simply adding them together and dividing by the number of cases, right? So it's $23.50 per case. Let's say you bought 3 cases of the cheaper beer. What's the average now? If you simply add them together and divide like you normally would, you'll be wrong because the two items cost different amounts. 3 out of 4 (75%, or .75) of the cases were $22 while only the 1 out of 4 (.25) was $25. So, you'd do the math as .75*22 + .25*25 which equals $22.75 per case of beer. The same logic applies with what we're doing now.

So, to find the Weighted Average Cost Per Troop, we'd do this:

[(ePA / APA) * cE] + [(dSPA / APA) * cdS]

(cE is the cost to train an elite while cdS is the cost to train a defensive specialist)

But wait! We know that APA is Army per Acre, or (ePA + dSPA), so we could expand it to this:

[(ePA / [ePA + dSPA]) * cE] + [(dSPA / [ePA + dSPA]) * cdS]

For our Avian that would be

[(11.25 / [11.25 + 7.25]) * 800] + [(7.25 / [11.25 + 7.25]) * 350]

[(11.25/18.5)*800] + [(7.25/18.5)*350]

(.6081*800) + (.3919*350)

486.48 + 137.17

624

So, now that we know how much is costs us on average to train a troop, we can compare the costs of maintaining attacker-level OPA and DPAs between races, right? Wait! Different races will need a different APA, so we'll need to account for that by multiplying that WACT by APA. For our Avian, this is 11,537gc.

The Formula

Above, we realized that we could break APA down into known terms. Say you wanted to start this formula from scratch with no intermediate steps? It would look like this (abbreviations are explained in the above section):

[([(gOPA / eO) / ([gOPA / eO] + [(gDPA - [eD * ePA] ) / dSD] )] * cE) + ([([(gDPA - [eD * ePA] ) / dSD]) / ([gOPA / eO] + [[(gDPA - [eD * ePA] ) / dSD]])] * cdS)] * [(gOPA / eO) + ([(gDPA - [eD * ePA] ) / dSD])]

It's absolutely mad, isn't it? If you rerun these numbers in a future age, I recommend including the intermediate steps in a spreadsheet program so you don't have tons of errors. For now, I've done the math for you below.

Age 47 (Justice) Numbers

For Age 47 with 90 OPA and 60 DPA (note the 10 less DPA from above), the following information applies. I have included in parenthesis things that may affect the overall economic viability of attacker strats with this race, whether directly through an income bonus or reduction in other costs, or indirectly by allowing you more acres than otherwise that you could use for Banks, Libraries, etc. I am not including things such as Townwatch that have a largely detrimental effect to match their benefit nor Spell success bonuses which may allow you to marginalize your already marginal number of Guilds and Towers.

Avian:      10,838gc   16.5 APA    (Attack time redux)
Dark Elf:    9,750gc   15 APA      (No rune cost, Invisibility, Tree of Gold w/ +efficacy)
Dwarf:      10,886gc   14.57 APA   (Free construction, +30% BE)
Elf:        10,886gc   14.57 APA   (Clear Sight, Fountain of Knowledge)
Gnome:       7,200gc   18 APA      (Halved thief cost)
Halfling:    8,250gc   15 APA      (Sabotage gains, Stealth recovery)
Human:      10,531gc   15.63 APA   (Income bonus)
Orc:        12,000gc   20 APA      (Elite credit training)

Mistake to be Corrected

If you allow dSPA to fall below 0 in your calculations, you'll end up with skewed numbers. I may at some point take the time to clarify this in the above formulas, but I'm a very busy (Re: lazy) man. The Age 47 numbers ARE corrected, though

General Tips and Strategy

Province Development

Roles

A player's role is the first and foremost thing they should decide. This is the end goal that guides all your strategic decisions from what race to pick to what buildings to build. So, are you an Attacker, a Thief, a Mage, or a hybrid of two of these? A kingdom needs some of each of these roles to survive and at war, how a kingdom plays its strengths and feints its weaknesses will determine a win or a loss. If you can't decide what role you want to play, try asking your monarch what the kingdom needs.

Attackers take the forefront in today's Utopia, as every race has been granted powerful offensive elites. Who wins a war is determined by the exchange of acres so ultimately, it's the attackers who decide the outcome. Being an attacker means you'll need to focus on your OPA and DPA. Currently 40 DPA with elites out is a bare minimum (except for Orcs), with 55 or so often being the tipping point for whether or not you'll get retalled. As for OPA, the sky's the limit, with 60 mOPA being an acceptable low-end for hybrids.

Thieves wreak havoc by focusing immediate destruction to their opponent's resources. Coordinated thievery can decimate armies, scourge civilians, and deplete resources to 0. However, because thieves can only damage their opponents in short bursts as their stealth allows, it will take a small group of thieves or a combination of roles to truly bring a province to its knees. For this reason, Thieves are often paired with Mages in war strategies or used to run chained ops against a target to open them up for the attackers. A minimum of 3 mTPA will allow you to get involved in robberies, with 6 mTPA opening up the potential for Nightstrikes and Wizard Assassinations.

Mages focus more on damage over time. A coordinated guild of mages can essentially turn a war into a war of attrition, forcing their opponents to endure starvation, no peasant growth, and little to no income. In essence, a coordinated group of mages is like a dragon on crack, causing millions of gold of damage and stopping all progress. Thus, the more protracted a war is, the more useful your mages become. The combination of direct damage from a Thief and withering by a Mage can keep a player out of war altogether as he or she tries to simply stay afloat. 3 mWPA will get you in on the action for Greeds, Storms, and other easier spells with 6+ mWPA giving you the power to hit with Meteor Showers and Tornadoes.

Hybrids are for more experienced players who can minimax their way into two roles. Attacker-Thieves, Attacker-Mages, and Thief-Mages are all viable and all quite powerful. With stealth and mana as delimiters, a Super Thief or Super Mage would be a wasted strat, as their hybridized attacker counterparts can accomplish the same number of ops while also being able to attack.

So, which role is for you? The devastating Heavy Attacker? The feared Thief-Mage? The cunning Attacker-Thief? Or perhaps the slow but steady Attacker-Mage?

Races and Personalities

Before we get into the race-personality combinations that suit each role, we need to highlight the fact that the personalities in Utopia are woefully imbalanced. This is largely due to the Sage personality, which for even a moderately skilled player can achieve the same benefits as other personalities and then some.

Consider Merchant, which gets a +25% income bonus. As a Sage, you are earning more science points AND getting a flat +25% bonus to those sciences, which - on the low end - would lead to another 10% income over what you'd achieve as a non-Sage. As a result, Merchant is only really getting a small income boost compared to Sage, while Sage is also getting a +30% Science Effectiveness to Housing (max pop), Tools (BE), Food (food production), War (gains), Crime (TPA), and Channeling (WPA and rune production). As such, Merchant becomes a highly situational personality choice, benefiting only a Human player (because of stacked bonuses) who seeks to intentionally tank their economy in favor of extremely high troop counts. In the end, that same player would probably have an overall healthier province from choosing Sage, and so it's highly inadvisable to choose Merchant for any reason. By this same logic, Artisan is useless as well.

Rather than run down the races and describe what each is good at, instead let's look at the race-personality choices relative to the worthwhile roles.

Heavy Attacker

Any race can play this role, though Gnomes, Halfling, Elves, and Dark Elves are better suited to hybrid roles. Good combinations follow:

Human: Shepherd, Sage, Warrior

Dwarf: Shepherd, Sage, Warrior

Avian: Shepherd, Sage, Warrior, Tactician

Orc: Shepherd, Sage, Warrior, Tactician

Attacker-Thief

Orcs and Elves are terrible at this, and some other races are not best-suited for this role. Good combinations follow:

Dwarf:

Gnome:

Halfling:

Race and Personality combos Per acreages Buildings

War & Peace

Max gains Starvation strategies Peasant killing Troop killing\economic domination

Tips for peace... Wages at 50% Bumping up guilds dropping science and drafts for the day when you change over your build Reservist + Patriotism Not wasting thieves banks, armouries, or schools?

Tools

Utopiapimp

Using Pimp Getting on Pimp Selecting targets Using the front page to post intel Including attack data Ghost data Submonarchs

UTools

Gains column Ambush calculator Using the Foremen

How do I calculate...

Intel

The intelligence provided by an SoT is vital. It only costs 1% stealth, is incredibly easy to succeed on even when the enemies' TPA is much higher than yours, and gives you nearly everything you need to know about a province. However, there's a small random factor at play (for everyone but Gnomes). The reliability of an SoT depends on how many thieves you send. If you send a simple majority of your thieves (50% + 1), you'll reduce this randomness to ~3%. Using Angel, if you copy the target's kingdom page before getting the SoM, you can actually get estimations of the target's Thieves and Wizards too.

When someone attacks, you need to get an SoM. Again, they're easy enough and the intel they provide is awesome in the right hands. They're deceptive though, because the only thing in an SoM that is PERFECTLY ACCURATE is the figures for the Army Out columns. This is accurate regardless of the number of thieves you send, so just send 10.

So, for the most accurate intel possible:

Total troops (from SoT) - Total troops sent out (SoM) = Total troops left at home * DME (SoT)

Ambush

When you are attacked, you have the opportunity to Ambush your attacker's army before it makes it back home (except when he used War Spoils or Anonymity). You can only Ambush the most recent attack on you, and you can only Ambush a specific army once. If you succeed, you will devastate his troops with casualties and earn back half the acres he took from you. To perform an Ambush, follow these simple steps:

1. Get an SoM (remember, all you need to know is how many troops the person sent)

2. For the army that most recently attacked you (check the acres they're returning with if it's unclear), add the DEFENSIVE STRENGTH of the elites, the OFFENSIVE STRENGTH of the offensive specialists, and 1 point for every soldier. Multiple this value by 0.8 (because armies being Ambushed are not ready for it, they fight at 80% strength). This is the total defensive strength of this army during an ambush - there are no modifiers to factor in, no horses, and no mercenaries (the mercs have already quit).

3. Send about 5% more RAW offense than the number found in 2. Again, there are no modifiers here, so don't waste any extra generals on an Ambush, and don't expect your Training Grounds to mean anything here. HOWEVER, your horses DO matter.

Want to make this easier? Use UTools and, from the SoM of your target, click the "Ambush Calculator" button.