User:Erdtirdmans

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.

Builds

Halfling Sage Attacker\Thief

Protection

Homes: 24%

Farms: 10%

Banks: 22%

Armouries: 22%

Guilds: 16%

Towers: 6%

Peace

Homes: 23%

Farms: 5%

Banks: 16%

Guilds: 18%

Towers: 3%

Libraries: 15%

Schools or Armouries: 20%

War

The assumption here is that I have 1000 acres. It will scale to roughly the same numbers for acreages above that, provided I grow at whatever rate will maintain my sciences.

Buildings

Homes: 23% - +1,840 maximum population, +83.73% birth rate

Farms: 5% - Produce 4,137 bushels (5,171 with FL)

Training Grounds: 20% - +28.37% offense bonus

Barracks: 8% - 13.05% attack time redux

Guilds: 10% - Training about 2.36 wizards per hour

Towers: 3% - Produce 426 runes per hour

Thieves' Dens: 16% - +47.66% effectiveness, -63.54% losses

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

Sciences

125 bpa: 25.5% Income

125 bpa: 18.2% Building Effectiveness

125 bpa: 11.9% Population Limits

75 bpa: 113% Food Production

75 bpa: 19.8% Gains in Combat

100 bpa: 97.9% Thievery Effectiveness

50 bpa: 69.2% Magic Effectiveness & Rune Production

Roughly 9k runes per day required for MPx2, MSx2, FL, QF, IAx2, and WS

487.296 runes per tower per real day

176.2362 bushels per farm per real hour

Population and Army

30033 peasants

-7738 for 100% rBE

22295 idle peasants

-1000 wizards (1 rWPA, 1.7 mWPA)

-5000 Thieves (5 rTPA, 9.9 mTPA OoW, 14.6 mTPA in war)

16,295 elites & specialists (16.3 TrPA)

@ 75% Elites (12.2 ePA, 4.1 dSPA):

73,326 rOffense, 94129 mOffense (73 and 94 OPA respectively)

81,475 rDefense (81 DPA)

71% draft target

Income

21,850gc mIncome, 524,400 income per RL day

8,148 wages at 100% efficiency, 6,926 when IA is active (estimated 9 hours) = 184,554 wages paid per RL day

9,100 gold for active sciences, 152,880 per RL day

186,966gc free income per RL day during war

Avian Sage Heavy Attacker

Peace

Homes: 25%

Farms: 6%

Banks: 15%

Guilds: 15%

Towers: 6%

Libraries: 15%

Schools\Armouries: 18%

War

Homes: 25%

Farms: 6%

Training Grounds: 21%

Guard Stations: 15%

Guilds: 12%

Towers: 6%

Libraries: 15%

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 60 DPA is respectable, with 70 or so being regarded as high. As for OPA, the sky's the limit. Obviously, you'll need >60 to hit most people your size, though playing the role of retaliator is feasible - for hybrids especially.

Thieves wreak havoc by causing direct destruction to their opponent. 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. Anything below a 5 mTPA will prevent you from doing much more than intel gathering and robbery, with 10 mTPA on the high-end for those looking to run Nightstrikes and Wizard Assassinations.

Mages don't have quite the power they once had in Utopia. Despite this, key spells like Meteor Showers and Chastity can be devastating when run consecutively or across entire kingdoms. A coordinated guild of mages can essentially turn a war into a war of attrition, forcing their opponents to endure starvation and little to no income. The combination of direct damage from thieves and withering by mages can keep a player out of war altogether as he or she tries to keep his or her province together. 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. 3 mWPA will get you in on the action for Greeds, Pitfalls, Chastity, and Fireballs, with 5 or 6 mWPA giving you the power of non-stop Meteor Showers.

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. Due to the mechanical limitations of the game, Attacker-Mages probably have the short straw right now.

Races and Personalities

Without getting into full-fledged theorycrafting, here's how the races and personalities of Utopia break down:

Humans are a powerful attacking force, boasting 8-offense elites and 6-point defensive specialists. Though they have high training costs, a racial bonus of 25% income enables them to maintain a strong army with relative ease. Though hybridizing with thieves is possible, it is unpopular due to the lack of direct bonuses for thievery gains or cost reduction. Paired with Sage, a Human becomes an economic powerhouse, allowing huge armies that can double-tap with defense to spare.

Orcs are meant to be pack hunters, as the lone Orc can be retalled and ambushed with devastating effect. However, with +50% gains, a roller coaster ride of back-and-forth attacking will normally end with the Orc on top, especially considering that even a small number of Hospitals will enable the Orc to gain more specialist (or in their case elite) training credits than they'll suffer in casualties. A kingdom with a handful of Orcs will have a far easier time winning wars thanks to the power of 150% gains. Oddly, Orcs have the most diverse choices when it comes to a good personality pairing, with Warrior, Sage, Shepherd, and Tactician all viable (ordered from best to worst).

Race and Personality combos Per acreages Buildings

War

Max gains Starvation strategies Peasant killing Troop killing\economic domination

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

Confusing Calculations

Ambush

When you are attacked, you have the opportunity to Ambush your attacker before his army makes it back home, provided the attacker didn't use War Spoils or Anonymity. You can only Ambush the most recent attack on you, and you can only Ambush an 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.

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 and the OFFENSIVE STRENGTH of the offensive specialists, plus 1 point for every soldier. Multiple this value by 0.8. This is the total defensive strength of this army during an ambush - there are no modifiers to factor in, no horses, and no mercenaries.

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.

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