A Mathematical Analysis of the Egyptian Settlement

[Muhabir]

Hello folks, I am Muhabir from the East Nagach server. I’ve been playing FoE for about a year now but haven’t really been active on the forums. However the – relatively – new settlement appeared to be quite a mathematical curiosity from a few points and over the course of the last couple of weeks I’ve done some basic analysis of the battles, goods produced, time limits and so on which I decided would better serve the community out here in the open instead of being forgotten in one of my workdesk’s many drawers. So, let’s get started shall we?

The basic formula for success in the Egyptian Settlement consists of gathering coins, training Egyptian units, fighting battles with Egyptian units, getting loot from those battles, using the loot to produce goods, unlocking buildings with those goods and completing quests until you’re done. We will now take a look at each of those steps.

DEBEN COINS, UNITS & BATTLES

While there is much to be said about the way Egyptian battles work, the general overabundance of randomness and data to be plotted in the system (Each battle has 210 tiles, 16 units of 5 types, a changing initiative order based on the unit types and numbers and so on…) makes a rigorous analysis of the battles themselves nigh-impossible. We can, however, make some general deductions based on a basic set of data available to us:

1) We want to win all three battles offered to us every day in the settlement;

2) Each unit has 10 hit points and “winning” a battle consists of killing the enemy off by reducing all enemy units’ hit points to 0 before the enemy can do the same to you;

3) Therefore, the ultimate goal in any battle is causing as much disparity in terms of damage as possible;

5) There are 5 types of units in the Egyptian settlement:

a) Khopesh Fighters – Light Units, counter fast & heavy, ATTACK 100 / DEFENCE 100 / RANGE 1 / SPEED 8, get +30 DEFENCE per adjacent Khopesh Fighter

b) Mounted Camel Archers – Ranged Units, counter light & artillery, ATTACK 90 / DEFENCE 110 / RANGE 4 / SPEED 8, can retaliate against any attack made from within their attack range

c) Nubian Archers – Artillery Units, counter light & heavy, ATTACK 100 / DEFENCE 100 / RANGE 6 / SPEED 6, can hide in bushes

d) War Chariots – Fast Units, counter ranged & artillery, ATTACK 100 / DEFENCE 90 / RANGE 3 / SPEED 10, get +30 ATTACK boost when attacking adjacent enemies

e) War Elephants – Artillery Units, counter fast & ranged, ATTACK 80 / DEFENCE 120 / RANGE 1 / SPEED 10, have a 20% chance of doubling damage when attacking

4) Units may attack other units within range (this range is 1, or adjacent tiles for Khopesh Fighters and Elephants), and may or may not receive retaliation damage depending on the type of the attacked unit;

5) If a unit is dead already by the time its turn comes around, it can’t deal damage;

6) If a unit is alive but there are no enemy units within its movement + attack range, it can’t deal damage;

7) Therefore, the key to increasing the damage disparity lies in concentrating your fire to kill the enemy units as quickly as possible and staying out of the range of enemy units which are left alive;

8) Since there are no attack boosts in the settlement, the only advantages we as the player can have are

a) A numerical superiority – The enemy armies almost never have the full 8 units, meaning bringing 8 units to a battle will automatically confer an advantage on the player

b) A terrain / positioning superiority – Meaning we fight in terrain that is favourable to us and/or unfavourable to the enemy, however it is impossible to manipulate the terrain of the battlefield and therefore this type of superiority is impossible to generalize on – If you get a good set of tiles, good for you. You just can’t depend on it

c) A tactical superiority in unit types, meaning our 8 units are the best counters to the enemy units, which will be the gist of our strategy here

Now, as we have previously established, Khopesh Fighters and Elephants have a range of 1. These two units are therefore extremely easy to pick off if your own units have a longer range than their movement range. They are also both countered by Nubian Archers which can move and attack targets 9 tiles away in a single turn, whereas Khopesh Fighters only have a combined movement and attack range of 5, and elephants 6 (Do note that tiles take 2 – 4 movement points to cross, meaning a unit’s “speed” is halved or cut to a third in the battle screen). Coupled with the Archers’ attack bonuses, they can take out melee units in 2, or at most 3 hits. In other words, Nubian archers can kill elephants and/or Khopesh Fighters without taking any damage barring some extraordinary circumstances. Meaning these units are questionable choices at best, especially since we only have limited Deben coins and space to dedicate to military units.

That’s two unit types down already. Let’s look at the others.

Chariots, Camels, and Nubian Archers are all ranged units, although the chariots have a marked disadvantage when firing from range due to their special ability. However, the AI seems to only use this ability sporadically and thus enemy chariots are weaker than they seem. The question is, just how weak are they?

As I have unfortunately finished all 3 of today’s battles, I am currently unable to provide numerical data on the damage – defence ratios of chariots. But based on experience, I can say that Camels and Nubian Archers can take out chariots with relatively minor losses because Chariots don’t retaliate against damage from ranged attacks meaning you can stay out of their range, let them move, and pick them off with your ranged troops before they can cause any significant damage. But howso?

Chariots have a range of 3 tiles and a speed of 10 tiles per turn. Meaning their effective reach is at most 8 tiles, since even plains tiles cost 2 movement points to cross. Meanwhile, Camels have a range of 4 + 8 movement, making their reach 8 tiles as well. As a result, if you stay out of the chariots’ range, let them make their move, and then move closer to attack you can easily pick them off.

Nubian Archers are even better choices here, since their range of 6 + 6 movement gives them an effective reach of 9 tiles, meaning on a completely flat map chariots can’t even reach your archers before they find a storm of arrows coming their way.

The exact damage statistics for these two scenarios are unfortunately unavailable to me right now (which is kind of ironic, not having enough mathematical data in a post about mathematical analysis) but chariots in general are outclassed rather easily by Nubian Archers & Camels, which incidentally are the two most versatile Egyptian units. As for why, that’s our next point.


Camel Archers have the “Contact!” ability, which allows them to retaliate against any attack made from within their attack range. This retaliation attack, from experience, tends to be a 1 – 4 points attack against fellow camels and more against Khopesh Fighters and Archers. Elephants are harder to take down, but as we’ve seen before, they can be massacred at will by Nubian Archers and the Camels outrange them nonetheless, allowing correctly-positioned Camels to make a free shot without getting hit by the elephant before the elephant can even move.

And then we have Chariots, but here the Camels also have a couple advantages. One, they match or outrange chariots and thus can also take a free shot at them before the chariot can attack. Two, because chariots have a shorter range than Camels, they will retaliate against all chariot attacks. Effectively, camels get 2 shots for each one the chariot takes at them. Furthermore, due to a quirk of the FoE Combat system, ranged units deal less damage if they are not at full health, so a camel archer that damages a chariot actually lessens the damage output of the chariot, and the advantage becomes slightly more than 2 shots per shot received. While by no means a no-questions-asked counter to chariots, camels still hold an edge over them in one-to-one combat. Consequentially, camels are an effective counter against all units except for other camels.


This brings us to our final unit, the Nubian Archer which – as we have already seen – can also take out Elephants, Khopesh Fighters, and Chariots with relative ease by outranging them and not even allowing them to attack. (This is actually true, I’ve had fights where my 8 Nubian Archers faced 3 elephants + 4 Khopesh fighters or a similar setup and managed to win without taking any damage whatsoever.) As for other Archers and Camels, there are a couple caveats and tactics you can use.

As is obvious to anyone who has ever engaged in FoE combat, dead units don’t shoot back. Therefore, shooting first, killing off some enemy units, and preventing the enemy from attacking on its turn can significantly reduce the enemy’s damage capacity. The archers, which outrange any unit other than other archers, are perfect for this strategy and can take out elephants, khopesh fighters, and chariots without breaking a sweat using it.

But camels are sneaky little fiends who can almost match the archers’ range and they come with an attack bonus against the archers. Here, we will use two basic facts to neuter the Camels’ natural advantages:

1) Archers can hide in bushes. If the archer is hiding, only adjacent units can attack it. This brings the camels’ effective range down a notch, but unless the archer has another bush tile within 2 tiles’ range the camel will catch up the next turn anyhow.

2) Archers outrange camels, and as a result, camels can’t use their Contact! ability against attacks made from 5 or 6 tiles away. HOWEVER this also works – somewhat counterintuitively – in reverse and camels can and will retaliate against attacks made from hiding archers within a 4-tile range of the targeted camel.

These two facts, along with the camels’ attack and defence bonuses vs. archers, cut both ways: We can use them to our advantage when attacking enemy camels with our archers AND we can use them when attacking enemy archers with our camels.

As a natural result of all aforementioned points, a combined arms strategy involving varying numbers of Nubian Archers and Mounted Camel Archers becomes obvious:

1) Nubian Archers can take out Khopesh fighters & Elephants with ease.

2) Camels can take out Chariots without receiving significant damage in return, Archers can also assist by hiding in strategically-placed bushes and taking pot shots at enemy chariots.

3) When attacking enemy Camels, Nubian Archers can stay out of their range and weaken them to the point that a single attack (or an attack + retaliation when the enemy camel shoots back next turn) from a friendly Camel can take them out.

4) When attacking enemy Nubian Archers, Camels can rush into a 4-tile range of the enemy archers, weaken them via retaliation and take them out in melee the next turn.

There are a couple more fine points to Egyptian combat that are readily available, mainly that it is imperative to not move much during the first combat turn or two; let the enemy come to you and try to isolate their faster units, and take those units out before the rest of the enemy army attacks – effectively dividing the enemy army into “waves” but these are much more intuitively acquired via trial-and-error. Fight a few battles for yourself and you’ll start using them.



Now, since we know that our armies will consist entirely of Nubian Archers and Camels, we can start calculating some costs. Do note that other army setups might be better for specific instances, but the Archer – Camel combo is the best all-rounder.

For further refutation of other army setups, I am now going to refer to two extremely important bottlenecks in the Egyptian Settlement: Time & Space



As Loot is absolutely required to succeed in the settlement without using obscene amounts of diamonds, our main bottleneck in Egypt is how much we can fight. The answer is simple: 3 times per 24 hours. This means everything operates on the basic time unit of one day.

Chariots and elephants may be better alternatives to archers and/or camels, especially in fights with plenty of enemy camels because they are just a nuisance to counter effectively even with the abovementioned strategies. However, they take 8 hours each to train. You will only ever be able to replace 3 chariots or elephants per day per building if you lose your precious units. What’s more, these blokes cost 350 Deben Coins per unit whereas our Archers & Camels only cost 200 Deben. Adding the fact that chariots & elephants only unlock once you have progressed a bit in the settlement, we see why they are poor alternatives: To get them, you need to be able to complete the 3 fights and if you can complete them without using chariots or elephants, why not keep completing them without maintaining these expensive units?

Khopesh Fighters, meanwhile, do cost the same as Archers & Camels and get obscene bonuses versus heavy & fast units. Nonetheless, elephants are trivial to take out using massed archers and as we’ve seen before, chariots are manageable using camels and/or archers. If you happen to get some bizarre combination of elephants & chariots, Khopesh Fighters might actually be useful. Otherwise they’ll be massacred. If you happen to have an extra 9 tiles + 8 tiles for the population needed + a couple roads + some spare Deben lying around, you could as well maintain a Training Camp for them. But in the same space you can build one more goods building or an extra Archery Range or Camel Stables instead, which are all more versatile choices.

Now, let’s talk about money. Unlike the Vikings & Japanese settlements, in Egypt there is very little use for coin. This is in fact perfectly historically accurate as Egyptian labourers were usually paid in beer, barley and other subsistence goods instead of coin. If you are decent at combat, your coin budget might be tight without using any diplomacy buildings. Having just one or two divine statues will literally leave you with thousands of spare deben if you play the combat game right.

 

[Muhabir]

And so, I present you with the first of our many calculations:

*Sighs in relief as the combat section is already 5 times as long as I intended it to be*

Since Nubian Archers are a bit more useful against certain enemy types when massed (i.e. You will rarely need 8 Camels but you might sometimes need 8 Archers) and also because you already receive 5 unattached Camels from the get-go, you might find it prudent to keep a full 8-troop-stack of them in reserve. This means we are going to build 2 Archery Ranges and 1 Camel Stable.

The buildings themselves don’t cost any coin. Opening slots, however, does. To unlock the third and fourth slots in the archery ranges we will need 1350 (650 + 700) Deben each, 2700 in total. Since we only have 1 Camel Stables, having an extra camel in reserve might come in handy and we will unlock all 3 unlockable slots for 650 + 700 + 750 = 2100 Deben. Meaning 4800 Deben spent.

This gives us 13 troop slots to play with. With each troop costing 200 Deben to train, that makes for 2600 Deben.

In total, we will need 2600 + 4800 = 7400 Deben for our initial troop production needs. Luckily, we already start with 9000 Deben coins in stock, leaving us with 1600 Deben or the equivalent of 8 road tiles from Day 1 of our Egyptian venture.

Now, thankfully we have those 5 camels that we got from Quest #3, so the total cost of our camel stable – 3100 Deben – can be spread over the first few days if we’re short of coin.



So, how many coins do we get per day after that?

The embassy itself gives 600, and that will be our base minimum. But the houses also generate a little bit: The initial Simple Clay Hut model, for example, produces 29 Deben per 4 Hours. This can amount to as much coin as 174 per day if you are a mindless zombie who wakes up at 4 a.m. to collect a miniscule amount of coin, or as little as the base 29 Deben if you just collect once per day and then forget about the settlement. On average, this guide will assume 3 collections per day, giving us a sweet sweet 87 Deben daily. Now, our two Archery Ranges and Camel Stables don’t run themselves and need 121 Egyptian workers to be built. That number being exactly 1 worker more than the output of 5 Simple Clay Huts, we come to two shocking conclusions:

1) Whoever designed this settlement has learned a thing or two from the playbook of Honourable Marquis de Sade about inflicting extreme pain upon unfortunate human beings

And

2) The 6 Huts we need to build will give us a healthy 522 additional Deben per day, if they are connected via roads, bringing our daily total to 1122 Deben.

But wait a second… Our Cultural Goods Buildings required population as well! In fact, the two nigh-initial choices – Grain Farm and Pottery – both require 48 Workers each, or 2 Simple Clay Huts. We can therefore think of goods buildings as producing coins – 174 Coins per day, in fact – as a secondary good as well. In the next couple of chapters of this guide we will illustrate how 3 or 4 goods buildings per day is a reasonable goal from day #2 onwards, so we can assume an extra 522 or 696 Deben per day as well, for a grand total of… 1818 Deben

That is either 9 new streets per day or the ability to replace 9 units losses without any additional coin producers. And in a perfect world with spherical cows and no air resistance, that would be a boatload of coin. Unfortunately I’m not a physicist and this world is not perfect. As an unfortunate side effect, not all of your houses will be connected to the embassy. In my current settlement, only 7 of 14 Huts actually produce coin. Half of your houses being connected is a decent fare, but more is always welcome.

With these quirks in mind, let’s take a look at a few different scenarios and compare their coin income:

First, the everyman scenario: You collect your houses 3 times per day and have 7 houses connected to the embassy. This nets you 87 Coins per house per day and 609 extra coins, for a total coin budget of 1109 per day – You can train 5 new units or build 5 more streets and have some left over which is more than reasonable.

If you have a bit more time, you could collect 4 or 5 times per day and get 116 or 145 Deben per house per day instead, bringing your grand total to 1312 or 1515 Coins per day. If you can connect more houses, that number increases rather quickly: At the far edge of the spectrum, the Absolute Maximum coins you can get is achieved at 14 houses, 6 collections, and 3036 Coins daily, although it would probably not be worthwhile seeing as how coins are mostly abundant.

If you slack off a little, your coin production could drop down to 1006 coins at 2 collections per day, 774 coins if you only have 3 connected houses or even the lonely 600 coins from the embassy if you aren’t collecting from houses at all. And should you ever need more coins, it’s as easy as replacing a goods building with a divine statue for an extra 428 coins per day at minimum using the 24-hour option.

In short, as long as you lose less than 5 units per day, your coin budget should be stable – if relatively tight – in the early game.

And what happens when you unlock Multi-Story Clay Houses? That’s the tricky bit. You see, the multi-story houses produce an average of 146 Deben if you collect them twice – once in the morning & once in the evening – but they also have twice as many residents as the Simple Clay Hut, and are therefore worth 2 Huts each. But two huts would produce 174 Deben per day – meaning the Multi-Story Houses actually produce less coins on a per-capita basis than their predecessors. How come?

Here, the magic of population efficiency comes into the picture. Each Multi-Story House holds the same population as 2 Simple Huts in 1.5 Simple Hut’s worth of space. Meaning the 14 Simple Huts you had previously can now be replaced with 7 Multi-Story Houses and you get 14 squares of free space by making the switch. This is easily enough to hold an additional Multi-Story House and a Divine Statue, increasing your Deben income by 428 per day.

Accordingly, let us assume you can collect 2 times a day from 4 Multi-Story Clay Houses and Once a Day from the Divine Statue. This gives us a total coin production of…

600 (Embassy) + 174 x 4 = 696 (Houses) + 428 = 1724 Deben Coins per day

In other words, as soon as you unlock the houses you will need to kill off 8 units per day before your coin needs catch up with your production. That is no easy feat to say the least.

Now, let’s speak of streets. We could tweak some values and make some calculations and find the most space-efficient layout for any given combination of impediments… But there is a much simple alternative: Experimentation!

In my current Egyptian settlement, I have 7 simple huts, 4 goods buildings, 2 archery ranges and 1 camel stable connected to my embassy using only 19 road tiles. As you might remember from above, our initial budget allowed for 8 road tiles using leftover Deben. If needed, you can postpone unlocking the last slot in your Camel Barn for a few days, saving 950 coins or almost 5 additional road tiles, for a total of 13 roads. Even in a rather space-inefficient setup, we only need to come up with 6 additional road tiles or a bit more than one day’s coin income for the whole settlement – and won’t need to add anything else until we have unlocked the Flower Farm. Not exactly elementary, but not difficult to achieve with a bit of clever thinking either.

And thus, we have shown that Deben Coins are hardly a limiting factor at the beginning of the settlement and are a mere afterthought once you have unlocked the second housing type available – which can be done in the third day or so by using the strategies provided in this analysis. With that out of the way, let us now take a look into the easier, more constrained calculations on loot and cultural goods.

 

[Muhabir]

LOOT & GOODS

The Egyptian Settlement has one trait in common with the other two cultures: There is an upper limit to the number of cultural goods you will need to produce to complete the settlement, assuming you have pissed off some deity and do not hit any 4X bonuses at all. The unique – and dare I say, elegant – feature of Egypt that sets it apart from its siblings, however, is the presence of a Time Bottleneck in the form of Loot.

As stated before, we gain loot by fighting battles and there are only 3 battles available per day. This puts a hard limit – although not nearly as hard a limit a one would assume, as we will see in a moment – on the number of days you can finish the settlement in without using diamonds. Let’s go to the drawing board:

From experimentation, we know that the easy battle produces between 250 – 350 Loot, the medium 300 – 400, and the hard battle gives 400 – 500 Loot.

This amounts to between 950 – 1250 Loot per day assuming one completes all three battles, with an average sitting at 300 (Easy) + 350 (Medium) + 450 (Hard) = 1100 Loot per day.

Now, this is where the aforementioned elegance comes in. You see, players have a chance of getting 4 times the normal amount of loot when winning a battle. The equivalent in the Vikings or Japanese settlements would have been the game handing you a third of your daily coin production for free. The system, being based on pure luck, is utter madness and yet it is elegant when it comes to analysing the processes.

For our first settlement the chance of hitting a 4x is 5%. Assuming we finish all three battles and have precisely average loot income (1100 Loot per day) This would mean we get an average one instance of 4x per 20 combats (i.e. per week, give or take) and receive 1100 extra Loot from it. The calculation is as follows:

An average fight provides [300 (Easy) + 350 (Medium) + 450 (Hard) = 1100] / 3 Loot,

The average 4x bonus (Actually only 3x, since you’d get the 1x naturally from the fight anyhow) would therefore also give 3 x (1100 / 3) = 1100 Loot.

Since we expect to gain it once per twenty fights, this would mean each fight is worth 55 Loot more than the sticker amount.

Adjusting our previous calculations:

We should get 355 (Easy) + 405 (Medium) + 505 (Hard) = 1265 Loot per day on average

Now, the key word here is “should”. Unfortunately, due to the way 4x works, you could get it on 3 consecutive fights and receive 1200 (Easy) + 1400 (Medium) + 1800 (Hard) = 4400 Loot in a single day or you might not hit it at all throughout your full Egyptian run.

Now, these values are averages obviously, so what happens if we skew away from the average?

Assuming we get the lower bounds in all battles, our daily Loot income is:

250 (Easy) + 300 (Medium) + 400 (Hard) = 950 Loot

And if we manage to hit the upper bounds, that would grant us:

350 (Easy) + 400 (Medium) + 500 (Hard) = 1250 Loot

All at once. But we can go further, say we hit 4x bonuses on all 3 battles when the battles themselves would give us the maximum amount of loot. That means a whopping

1250 x 4 = 5000 Loot in a single day.

For the readers’ convenience, I have provided below the average loot calculations for each iteration of the Egyptian settlement. Assuming everything goes as expected and you get the average number of 4x’s and the average amount of loot, the total you will receive per day is:

1100 + 165 = 1265 Loot in Settlement #1 @5% 4x Chance

1100 + 231 = 1331 Loot in Settlement #2 @7% 4x Chance

1100 + 297 = 1397 Loot in Settlement #3 @9% 4x Chance

1100 + 363 = 1463 Loot in Settlement #4 @11% 4x Chance

1100 + 429 = 1529 Loot in Settlement #5 @13% 4x Chance

1100 + 495 = 1595 Loot in Settlement #6 @15% 4x Chance

1100 + 561 = 1661 Loot in Settlement #7 @17% 4x Chance

1100 + 627 = 1727 Loot in Settlement #8 @19% 4x Chance

1100 + 693 = 1793 Loot in Settlement #9 @21% 4x Chance

1100 + 759 = 1859 Loot in Settlement #10 @23% 4x Chance

1100 + 825 = 1925 Loot in Settlement #11 and beyond @25% 4x Chance

As it can obviously be observed, the chance of getting 4x loot increases significantly (By 52% to be exact) between the first and last settlements. Now, the maximum loot gainable in any one day stays the same – 5000 Loot is still the upper limit because that particular instance makes the 4x chance itself irrelevant, but the loot average actually increases quite favourably compared to the decrease observed in the time limit for getting the golden settlement rewards: Where the average loot gained has increased by 52% from 1265 to 1925, the time limit has gone down by 50% from 28 Days to 14 Days. Judging from this, one might assume the settlement’s difficulty stays more or less the same. But that would be a rather significant error, as collecting the loot is only part of the problem. For the other part, we have goods. But before proceeding to that section, let’s take a look at the distribution of Loot instead of mere minimums, maximums and averages:

Calculating a true distribution of possible amounts of loot gained might be impossible in practice since – as far as I am aware – we do not have access to InnoGames’ internal data or code, and have no way of calculating such useful statistics as standard deviation, median, mode, 25th percentiles and so on… But we can analyse two possible distributions as a mental exercise:

Assuming the distribution is flat i.e. consistently getting the maximum 1250 loot per day is as likely as getting the minimum 950 or the average 1100; a player at the 90th percentile of the Loot Curve would gain 1220 Loot per day. Not a bad haul, since we’re speaking of averages. This would also mean that one percent of all players would get 1247 Loot or more per day on average. Conversely, 10th percentile would be 980 Loot and there would be quite a few somebodies with an average of 950 Loot per day in their hands. While not impossible, I find the possibility of a flat distribution highly unlikely, especially considering how actual battles with the minimum and maximum loot amounts appear to be almost non-existent if some data from the Beta servers are to be believed. Still, pending more data, my guess is as good as any.

Assuming a more-or-less regular bell curve (Like the IQ curve) distribution however, we *could* get a 90th percentile sitting at a mere 1160 Loot on average and one percent of players would get something in the 1190 – 1220 range. Only 430 players per MILLION would get 1250 Loot. At the other edge of the spectrum, the 10th and 1st percentiles would be 1040 and 980 – 1010 respectively.

The table I have provided above could be extended to include these percentiles and their respective Loot per day hauls, but for now the following should suffice:

1st Percentile Loot + 4x:

980 + 147 (49 per fight) = 1127 Loot in Settlement #1 @5% 4x Chance

980 + 735 (245 per fight) = 1715 Loot in Settlement #11 @25% 4x Chance



10th Percentile Loot + 4x:

1040 + 156 (52 per fight) = 1196 Loot in Settlement #1 @5% 4x Chance

1040 + 780 (260 per fight) = 1820 Loot in Settlement #11 @25% 4x Chance



50th Percentile Loot + 4x [Same as average from above]:

1100 + 165 (55 per fight) = 1265 Loot in Settlement #1 @5% 4x Chance

1100 + 825 (275 per fight) = 1925 Loot in Settlement #11 and beyond @25% 4x Chance



90th Percentile Loot + 4x:

1160 + 174 (61 per fight) = 1334 Loot in Settlement #1 @5% 4x Chance

1160 + 870 (270 per fight) = 2030 Loot in Settlement #11 and beyond @25% 4x Chance

99th Percentile Loot + 4x:

1220 + 183 (61 per fight) = 1403 Loot in Settlement #1 @5% 4x Chance

1220 + 915 (305 per fight) = 2135 Loot in Settlement #11 and beyond @25% 4x Chance

 

[Muhabir]

Now, as I was saying, getting the loot in is only part of the problem. Since we don’t actually use loot to complete the settlement – we use goods instead – the real bottleneck calculations come in the form of goods produced per building per day. But first, how many goods do we really need to complete Egypt?

It’s a rather straightforward calculation:

All buildings taken together require 1549 cultural goods of various types. Then, the final quest requires 30 of each cultural good – 120 goods in total. We will also need to account for settlement expansions but unlike the previous two settlements Egypt also doesn’t require as many goods to be spent here. For now, I will note the number of expansion goods as 24 and we’ll talk about the how’s and why’s really soon. Finally, we actually receive 25 barley from an early quest, so that’s -25.

In total: 1549 (Unlocks) + 120 (Quest) + 24 (Expansions) – 25 (Barley from quest) = 1668 Goods needed

And here we see the elegance of Egypt once more: You only need to spend 1668 goods, you don’t need to produce 1668 goods. The difference is non-trivial. Since goods buildings also have a chance to provide 4x goods, we only need to calculate how many times our buildings will produce goods to provide us with the magic 1668. In other words, we can formulate 1668 as:

1668 = x Goods produced + 3xy Goods bonus

The term “y” here being a placeholder for the 4x chance.

For our first settlement, the 4x chance on goods is 5% or 1/20. In turn the equation becomes:

1668 = x Goods produced + 3x/20 Goods bonus

= 20x/20 Goods produced + 3x/20 Goods bonus

= 23x/20 Goods produced

multiplying both sides by 20/23, we get:

1668x20/23 = x Goods produced

33360/23 = x Goods produced

1450.434782 = x Goods produced

Thus, we don’t need to produce 1668 goods to complete the settlement. We only need to produce 1451 or so, and we’ll get the rest for free from the 4x bonus. You might want to play safe here and accept a good round 1500 as your target, but as the settlement progresses you can infer the actual number you need from the goods you have and the goods you need to finish the settlement. For the rest of the guide, we’ll stick with the slightly more ambitious 1460 instead.

Here, again, hard minimums and maximums come into play. If we get absolutely no 4x hits at all (NUTS), we will be forced to produce all 1668 goods manually. If all our productions are 4x hits (Also NUTS), we will only need to produce 1668/4 = 417 goods. Since the second number is largely theoretical and almost impossible to come by in practice, we will ignore it for the time being.



It is now established that on average we will need to produce 1460 goods to finish our first Egyptian settlement, though that number could be as large as 1668. Since each good produced costs us 10 Loot, that means we will need between 14600 and 16680 Loot in total to wrap things up. We also receive 300 Loot from Quest #4, and modifying for this, our final numbers become 14300 and 16380.

As we had demonstrated above, our average Loot income for Settlement #1 is 1265 Loot per day. Dividing our total required loot by this number, we see that it will take between 12 and 13 (Actually 11.3 and 12.9 but battles refresh every 24 hours, so we always round this particular calculation up) days to accumulate the needed Loot in Settlement #1. Considering how the Golden Time Reward gives us 24 days to work with, my reaction to this was *EXCLAMATIONS REDACTED SO AS TO ENSURE A FAMLIY-FRIENDLY FORUM ENVIRONMENT*.

But again, there’s always great value in caution. What if we wanted to make sure we will get that Golden Time Reward, no matter what? Assuming we get no 4x bonuses at all, not on Loot, not on Goods, not at all, and that we will always get the minimum loot possible from all battles, we are looking at 16380 Loot needed and an income of 950 Loot per day. This corresponds to 17.2, or rounded up 18 days required to muster all that loot. Meaning even if you are totally, absolutely, 1 in a billion odds unlucky you will still be able to complete settlements #1 through #8 on time to get the Golden Reward. For once, InnoGames seems to have eliminated the dependence on luck in a cultural settlement. /Respekt

And here is a table of average Loot needed, average Loot per day, and number of days per settlement:

14300 / 1265 = 12 (11.30) Days in Settlement #1 @5% 4x Chance (20/23 or 100/115 Loot Modifier)

13550 / 1331 = 11 (10.17) Days in Settlement #2 @7% 4x Chance (100/121 Loot Modifier)

12900 / 1397 = 10 (9.23) Days in Settlement #3 @9% 4x Chance (100/127 Loot Modifier)

12320 / 1463 = 9 (8.41) Days in Settlement #4 @11% 4x Chance (100/133 Loot Modifier)

11790 / 1529 = 8 (7.70) Days in Settlement #5 @13% 4x Chance (100/139 Loot Modifier)

11380 / 1595 = 8 (7.08) Days in Settlement #6 @15% 4x Chance (20/29 or 100/145 Loot Modifier)

10850 / 1661 = 7 (6.53) Days in Settlement #7 @17% 4x Chance (100/151 Loot Modifier)

10440 / 1727 = 7 (6.04) Days in Settlement #8 @19% 4x Chance (100/157 Loot Modifier)

10050 / 1793 = 6 (5.60) Days in Settlement #9 @21% 4x Chance (100/163 Loot Modifier)

9700 / 1859 = 6 (5.21) Days in Settlement #10 @23% 4x Chance (100/169 Loot Modifier)

9360 / 1925 = 5 (4.86) Days in Settlement #11 etc. @25% 4x Chance (20/35 or 100/175 Loot Modifier)

Do note that all required loot numbers are rounded up to the nearest multiple of 10 (For example 11784 becomes 11790 and so on).

As readily apparent from this table, if your particular settlement instance stays anywhere near average values, Egypt takes nowhere near the advertised 14- 28 Days to complete on Gold – assuming you can complete all 3 battles each day of course.

Here we will add another simple factor to the calculations: Goods produced per building per day. As you can’t actually produce goods in bulk directly from loot, you need a set number of buildings to turn your hard-earned loot into various cultural goods. The number necessary depends on your loot income per day. We can assume, as a baseline, that each goods building can produce 25 goods per day via 8 + 8 + 4 productions. But this could be as few as 20 or as many as 30 goods instead. Assuming 25 goods per day, or rather 250 Loot consumed; we see that for our first settlement we need

1265 / 250 = 5 (Actually 5.06 but we round down for this particular calculation)

goods buildings up and running to catch up with the speed of loot accumulation.

This number becomes 6 in Settlement #5 and 7 in Settlement #9 and beyond.

However, it isn’t actually possible to have 3 military buildings and 5 goods buildings running simultaneously from day 1. Again, we will have a couple crucial efficiency ratios to work from here. For starters, the 2 initial goods buildings – Barley Field and Pottery – each take 12 spaces themselves. If we’re using Simple Clay Huts the 48 population we need for each goods building will take a further 8 spaces, giving us a total footprint of 20 spaces per goods building. For the two advanced goods buildings – Flower Farm and Place of Prayer – this number becomes 15 for the building itself and 1-and-a-half clay hut (6 spaces), or 21 squares per building. With Multi-Story Clay Houses the calculations become a bit weirder but potteries and barley fields have a rough footprint of 18 squares while flower farms and places of prayer take somewhere between 19 and 20.

Still, these numbers are meaningless in and of themselves if we don’t know how many squares we actually have to work with. And the answer to that particular question is… Well, it depends. Each expansion in the settlement grid has 16 squares, and we begin with 8 such expansions cleared. Minus the 48 squares for the Embassy, initially the settlement provides us with 80 squares to play with. Enough for exactly 4 goods buildings – minus the roads, without which they won’t actually be operational. Oopsie…

In other words, we will need to unlock more expansions soon to reach our target. But each expansion after the initial 8 has a 1x2 or 2x1 impediment on it, meaning each further expansion provides 14 squares instead of the advertised 16. However, and this is a big however, some quests provide us with an impediment removal item: A not-so-shiny pickaxe (The shiny ones are sold for diamonds instead). We get a total of 6 such items: One almost immediately, one around the time Multi-Story Clay Houses are unlocked, one after unlocking flower farms, one after unlocking elephant stables, one after unlocking processions, and one near the very tail end of the settlement. For all intents and purposes, the last two are irrelevant and the third-to-last is of marginal utility at best. So we will have around 6 additional tiles to work with thanks to these.

Now, the question turns to “How many expansions do I want to unlock and when?” which is possibly the single trickiest calculation in this thread. First, let’s take a look at one particular rush strategy that is rather easy to execute:

The prudent readers amongst you would’ve noticed how we received 25 Barley from an early quest and that reduced the total goods required. But that 25 Barley has a much more crucial role: It serves as a springboard to unlock the Pottery. Howso? Simple. Unlike all further building unlocks, the first two Egyptian buildings require a set amount of a single good to unlock: 44 Barley. And you get 25 Barley from a quest, meaning you only need to produce 20 Barley on your own and will have 1 Barley to spare, giving you an extra expansion from the get-go. With 2 Barley Farms this will take 8 Hours to complete – or even 4 Hours if you are lucky and hit a 4x. So, the initial settlement setup would have:

2 Barley Farms @ 12 squares each = 24 squares

4 Simple Clay Huts @ 4 sq. ea. = 16 squares

We are only using half of our 80 squares allowance. Let’s add a couple military buildings:

2 Archery Ranges @ 10 sq. ea. = 20 squares

4 Simple Clay Huts @ 4 sq. ea. = 16 squares

In total, this setup would take 76 Squares, which is probably impossible since you’d need to connect 4 buildings using only 4 squares of road. But we can delay the second the Archery range by 4 hours, unlock a new expansion and voila, we get 14 additional squares. (16 if you are willing to use the pickaxe immediately). Meaning, this setup is definitely viable for the first 8 hours. And now we have access to the Pottery!

According to the expansion cost tables on the FoE Wiki, our first expansion bought using Barleys cost us 1 Barley. The next 4 expansions will cost 1 Pottery each so we can just add them to the mix without any reservations. And that’s where things start to get complicated. Until now, us buying new expansions didn’t further increase the cost of future expansions. But the 6th expansion costs 5 Pottery instead of the previous 1 Barley/Pottery expansions, whereas it would still cost only 1 Cultural Good if bought with Flowers or Sacrificial Offerings. By buying this expansion, we are actively costing ourselves more cultural goods than we need. Since the Loot we can gather per day is the real bottleneck and we have a set amount of Loot we need to complete the settlement, being able to run more goods buildings than the number we initially calculated doesn’t help us complete the settlement faster. Counter-intuitive? Hell yeah.

As a result, the question becomes less “Will this expansion give me more goods than it costs?” and more “Do I already have the optimal number of goods buildings?” when determining whether to buy an expansion or not. Luckily, we can – at least in theory – determine the answer by using more maths! Yay!

At this point, the expansions we have already unlocked provide us with a grand total of 152 Squares of space to work with. The only goods buildings we have unlocked are the Barley Farm and Pottery, each with a total footprint of 20 squares including the required population. Meanwhile, our military complexes will require:

2 Nubian Archery Ranges @ 10 sq. ea. = 20 Squares

1 Camel Barn = 12 Squares

6 Simple Clay Huts @ 4 sq. ea. = 24 Squares

Total = 56 Squares

As demonstrated beforehand, we require 5 goods buildings to churn through our entire expected Loot Production, meaning a grand total of:

56 (Military) + 5 x 20 = 100 (Goods) = 156 Squares

are needed – 4 more than what we have right now. However, adding one more expansion for 5 Pottery give us 10 squares to spare. Probably not enough for all the roads we will need. Luckily, we have another trick up our sleeve: Multi-Story Clay Houses. We need a total of 50 additional Pottery and Barley to unlock them. Assuming we now have 4 Goods Buildings set up instead of the planned 5, this will take us 12 Hours without any 4x events – although you will probably have had one at this point.

To recount our progress so far:

1 Hour to build the Barley Farms

8 Hours to unlock Pottery

1 Hour to build the Potteries

4 Hours for Pottery production #1 – We will have 1 Pottery Left

1 Hour to build more Potteries / Barley Farms (Depending on goods needed to unlock Multi-Story Houses)

12 Hours to gather the goods – We now have 61 goods

Total: 27 Hours + A few minutes, so let’s be generous and assume 28 Hours

In short, we are expected to unlock Multi-Story Houses just over a day after the settlement has begun. In fact, the times fit rather neatly with a regular working day as well. The first 5 steps take 15 hours plus some spare time which you can fit to your day and you can just set the buildings to an 8-hour overnight production for the last step, wake up and gather them, and set an additional 4/8 hour production.

Multi-Story Houses change the space dynamics of the settlement a fair bit. To recalculate, we will need:

121 (Military Buildings) + 240 (Goods Buildings) = 361 Population

for our “ideal” setup. This maps to 7 Multi-Story Houses (357 pop) plus 1 Simple Hut (24 pop) and will take 46 Squares. Since the recalculation changes the footprints of all other buildings, our new space requirements will be:

46 Squares (Pop Buildings)

32 Squares (Military Buildings)

60 Squares (Goods Buildings)

Total: 138 Squares needed

Meanwhile, we have 168 Squares available from the initial 80, 6 expansions at 14 each and 4 from pickaxes (You’ll get another one after unlocking Multi-Story Houses). 30 Squares available for all our road needs and a few dead spaces here and there? Reasonable. If you get terrible impediments and can’t fit the buildings around, unlocking a 7th expansion for 12 Pottery may also be considered.

And so, we’ve come full-circle back to our initial goods calculation: We have used exactly 10 goods so far to unlock expansions and all parameters are tight but manageable. What happens when we unlock Flower Farms?

For starters, we get 2 or 3 new expansions and 1 additional pickaxe, for a total of 30 – 44 additional squares. Even in a theoretical worst-case scenario where we need an entire boatload of flowers for the next few steps and decide to add a 6th goods building to cover our goods deficit from day #1 (We ran only 2/4 goods buildings for a fair amount of time, remember?), this would translate to:

121 (Military) + 216 (Goods) = 337 Population Needed (7 Multi-Stories)

42 Squares (Pop Buildings)

32 Squares (Military Buildings)

90 Squares (Goods Buildings)

Total: 164 Squares Needed (minus roads)

Meanwhile we have between 198 and 212 squares available, and if you can’t connect this setup using a whopping 48 road squares, something is seriously wrong with your impediment setup.

Assuming we will unlock a further 3 expansions using Sacrificial Offerings once they become available, we have spent a grand total of 24 Cultural Goods on buying expansions and can run at least 9, possibly as many as 12 goods buildings concurrently. With our “optimal” 6-building layout, it would take 12 days to churn out enough goods for completing Egypt since each goods building is assumed to produce 25 goods + whatever 4x you get per day. With 12 concurrent buildings, it would take less than 5 days. But of course, you won’t be able to maintain such a gargantuan industrial complex for the whole duration of the settlement.

It should be noted that as with all other things settlement-related, your mileage may vary. There are expansions where instead of the theoretical 14 tiles, you’ll only be able to make use of 10 or even 8 tiles effectively. While such situations may increase the number of expansions you’ll need, the last 5 – 6 expansions aren’t being properly utilized under our current calculations anyhow and being forced to unlock them earlier than theorized would at most cost you another 100 or so cultural goods, or just one more day of looting. This might bring the total time needed to finish the settlement up to 14 or 15 days under the ideal circumstances detailed above, for the first settlement where the Golden Time Reward is… 28 Days. In other words, even if everything goes awry and you just happen to forget the settlement for a week or so in the middle… You’ll be fine. So long as you fight and win all 3 battles every day. Which is, admittedly, not an easy feat for some more casual FoE players. Fear not though! In the next section we will take a brief look at less-than-optimal fighting setups where we forego fighting the hard battles. But before that, here’s a fun calculation and a couple finer points for the settlement’s endgame:

Let’s assume you have hacked the FoE servers and somehow managed to alter the settlement code to make all your battles give the maximum amount of loot with a 4x bonus, and all your productions to have a 4x bonus as well. How long would it take to complete the settlement?

Well… As we have calculated previously, you will need to produce 417 goods, although that becomes 420 since you can only produce in multiples of 5. This means we will need 4200 Loot. As you can produce 5000 Loot per day at maximum, you can gather the needed loot in… Around 30 minutes. With 9 goods buildings producing simultaneously, it will take you around 2 days to finish cycling through all that Loot (Assuming 25 goods produced per day per building, with the remaining 4 hours used to construct / demolish buildings and gather diplomacy). And then you will hit a couple roadblocks:

ONE: Quest #20

TWO: Quest #23

The first is a quest to gather 300 Loot. The problem? It comes at the very tail end of the settlement, when you have probably gathered all the Loot you might need anyhow and are waiting for your goods buildings to catch up (Since they tend to “lag behind” Loot production by a day or two). In fact, if you know for certain that you won’t need more loot, you may even have destroyed your entire military complex. That’s why it’s important to preserve the unattached troops you were given in Quest #3. 300 Loot is at most one medium or two easy battles. With 5 Khopesh Fighters and 5 Camels, you should be able to defeat that day’s first two battles or the easy battles of two consecutive days without any significant problems. This will allow you to save some space where you might be able to fit an extra cultural building or two.

The second problem requires you to collect 30.000 Deben Coins. While this is kind of annoying, it actually solves what was very much a real problem in the Japanese and Viking settlements: You unlocked the last couple of buildings and had no real use for them because they took 4 hours to build and by the time they were built the settlement was completed anyhow. Not so in Egypt. Pyramids are actually useful since a single Pyramid produces as many Deben Coins as 11 Water Gardens in a third of the space. Pyramids even outproduce processions by around 150%, though Processions only take 1 Hour to build compared to 4 Hours for the Pyramids. While it is possible to prebuild Processions the day before your last in the settlement, set them to 24-hour productions and only collect them once you are at the final quest, this may or may not be practical. Instead, if you go for Pyramids:

Each Pyramid takes 36 squares, plus around 16 squares of population – assuming you’re using Luxury Estates which are the most efficient population building – and you will need 52 squares per Pyramid. Our settlement will have around 288 squares to play with at this point, meaning we can fit 5 Pyramids in theory. In practice however, the huge 6x6 footprint of the Pyramid makes it almost impossible to fit more than 4, even if you have destroyed literally everything else. The good news is, even with 4 Pyramids it will only take you 32 hours at most (4 for building Luxury Estates, 4 for building Pyramids, 24 hours to produce the Deben) to collect the needed coins and wrap your settlement up. If you opt for the 8-hour production instead, it will only take 24 hours. The 4-hours option is done in 20 hours, the 1-hour option in 16 hours, the 15-minute option in 13-and-a-half and for the botnets amongst us, running all 5-minute productions in the Pyramids would take you a mere 4-and-a-half hours plus 8 hours’ construction time for a total of 12-and-a-half-hours for your settlement to be done. Another option might be to use Processions and Multi-Story Clay Houses, which will require 144 spaces for the processions and a further 120 spaces for the houses to feed them, in total 264 spaces. On the flip side, this setup will only take 2 hours to be ready but will produce 10.000 Deben less than the Pyramids using the 24-hour option. All in all, the Pyramids appear to be slightly more efficient but as always, this is not a definitive finding and some situations may require you to be “creative” with your Deben productions.



Taking these numbers into account, I would predict that it would take a further 2 or 3 days to finish the settlement once you have all the loot you need. Applying this “lag” to the table we had produced, we get an average of:

14 - 15 Days to finish Settlement #1

13 - 14 Days to finish Settlement #2

12 - 13 Days to finish Settlement #3

11 - 12 Days to finish Settlement #4

10 - 11 Days to finish Settlement #5

10 - 11 Days to finish Settlement #6

9 - 10 Days to finish Settlement #7

9 - 10 Days to finish Settlement #8

8 - 9 Days to finish Settlement #9

8 - 9 Days to finish Settlement #10

7 - 8 Days to finish Settlement #11 and beyond

Which conforms with my – albeit limited – experimentation so far. In fact, the first 3 – 4 settlements might even take a day or two less than indicated.

It is thus demonstrated that in contrast to the initial expectations set forth by the 28-Day Gold Timer on Settlement #1, Egypt does not take significantly more time than the previous settlements to complete, although it could be argued that it takes significantly more effort. In fact, completing the entire Egyptian Questline may take only 3 months or so with some luck and optimal play, and 4 months otherwise.

 

[Muhabir]

EGYPT WITHOUT THE HARD BATTLES

With these two warnings, our mathematical analysis of the Egyptian Settlement has come to an end for the most part. As you may have noticed though, the entire premise of our analyses depended on a player’s ability to fight and win the hard fights every day in each iteration of the settlement. It is readily apparent that not all players share this level of fighting expertise or enthusiasm. For this bonus section, we will take a look at three additional playstyles:

1) A player who completes all easy and medium battles everyday

2) A player who completes all easy battles every day, and medium battles half the time

3) A player who completes only the easy battles

Do note that Loot per battle calculations from the 4x bonus will differ somewhat from those established previously. This is because not fighting the hard battles skews the distribution somewhat.

But beforehand, let’s make another brief calculation. We know that the time to get the Golden Rewards Chest varies from 28 Days for Settlement #1 to only 14 Days for Settlements #11 and beyond. Given this knowledge, assuming 3 days of lag after enough loot has been gathered and average loot and 4x chances, what is the minimum effort a player can put in before they struggle to achieve the Golden chest?

For settlement #1, this means gathering the needed Loot in 25 days. At 14300 Loot needed, this gives us… Only 572 Loot needed per day.

Each Easy battle on average provides 345 Loot once 4x chances are taken into account. This leaves 227 Loot per day to be gained from the Medium Battle. Since each Medium Battle provides around 402.5 Loot, our player would need to win the medium battles 57% of the time (actually 56.3975%) to ensure they can beat the average and receive the golden time chest.

For Settlement #10, the last needed for a max level Bathhouse, the time limit is 15 Days, 10 Hours, 27 Minutes, 19 Seconds. Assuming a round 15 days, this requires the loot to be gathered in 12 days, for a total of 810 Loot needed per day. Easy battles provide an average of 507 Loot per battle, leaving 303 Loot from Medium Battles, which grant 591.5 Loot on average. Our player will therefore need to win the Medium Battles 52% of the time (actually 51.2256%) and some luck on their side to get the Gold Reward. As seen previously, the 4x Chance – Time Limit balance tends to favour the player slightly more in further settlements, but not in any way that can be depended upon.

In short, try to complete your Medium battles a bit more than half the time and collect your goods on time and you should receive the Golden Time Reward.

With that being said, let’s take a look at the scenarios we established above:

1) A player who completes all easy and medium battles everyday

For Settlement #1, this player will receive an average of 345 Loot from easy battles and 402.5 Loot from medium battles, for a total of 747.5 Loot per day. It will take them 20 Days on average to gather the needed loot and 23 Days or so to finish the settlement – enough to receive the Golden Time Reward by a large margin. If they receive no 4x bonuses at all and receive only the minimum loot possible, it will take them 26 Days to gather the needed loot and 29 Days to finish the settlement – skirting with the silver reward.

The average completion table is as follows (NOTE: ADD 2 – 3 DAYS TO THE GIVEN NUMBERS TO ACCOUNT FOR LAG AND COMPLETING THE LAST QUEST):

14300 / 747.5 = 20 (19.13) Days in Settlement #1 @5% 4x Chance (20/23 or 100/115 Loot Modifier)

13550 / 786.5 = 18 (17.22) Days in Settlement #2 @7% 4x Chance (100/121 Loot Modifier)

12900 / 825.5 = 16 (15.62) Days in Settlement #3 @9% 4x Chance (100/127 Loot Modifier)

12320 / 864.5 = 15 (14.25) Days in Settlement #4 @11% 4x Chance (100/133 Loot Modifier)

11790 / 903.5 = 14 (13.04) Days in Settlement #5 @13% 4x Chance (100/139 Loot Modifier)

11380 / 942.5 = 13 (12.07) Days in Settlement #6 @15% 4x Chance (20/29 or 100/145 Loot Modifier)

10850 / 981.5 = 12 (11.05) Days in Settlement #7 @17% 4x Chance (100/151 Loot Modifier)

10440 / 1020.5 = 11 (10.23) Days in Settlement #8 @19% 4x Chance (100/157 Loot Modifier)

10050 / 1059.5 = 10 (9.48) Days in Settlement #9 @21% 4x Chance (100/163 Loot Modifier)

9700 / 1098.5 = 9 (8.83) Days in Settlement #10 @23% 4x Chance (100/169 Loot Modifier)

9360 / 1137.5 = 9 (8.22) Days in Settlement #11 etc. @25% 4x Chance (4/7 or 100/175 Loot Modifier)

As readily apparent from the above table, this player is usually well within the time limit needed to get the Golden Time Reward, demonstrating that – barring some bizarre statistical occurrence – merely completing the Easy and Medium battles every day is enough to finish the Egyptian Settlement on time without much of a hassle.



2) A player who completes all easy battles every day, and medium battles half the time

This is where things get tricky. As demonstrated above, on average it is necessary to complete the Medium Battles slightly more often than half the time to be eligible for the Golden Time Rewards. This player completes the Medium battles exactly half the time and will need to have a slight bit of luck on their side to get those Golden Time Rewards.

Here is their average completion table (NOTE: ADD 2 – 3 DAYS TO THE GIVEN NUMBERS TO ACCOUNT FOR LAG AND COMPLETING THE LAST QUEST):

14300 / 546.25= 27 (26.17) Days in Settlement #1 @5% 4x Chance (20/23 or 100/115 Loot Modifier)

13550 / 574.75 = 24 (23.57) Days in Settlement #2 @7% 4x Chance (100/121 Loot Modifier)

12900 / 603.25 = 22 (21.38) Days in Settlement #3 @9% 4x Chance (100/127 Loot Modifier)

12320 / 631.75 = 20 (19.50) Days in Settlement #4 @11% 4x Chance (100/133 Loot Modifier)

11790 / 660.25 = 18 (17.85) Days in Settlement #5 @13% 4x Chance (100/139 Loot Modifier)

11380 / 688.75 = 17 (16.52) Days in Settlement #6 @15% 4x Chance (20/29 or 100/145 Loot Modifier)

10850 / 717.25 = 16 (15.12) Days in Settlement #7 @17% 4x Chance (100/151 Loot Modifier)

10440 / 745.75 = 14 (13.99) Days in Settlement #8 @19% 4x Chance (100/157 Loot Modifier)

10050 / 774.25 = 13 (12.98) Days in Settlement #9 @21% 4x Chance (100/163 Loot Modifier)

9700 / 802.75 = 13 (12.08) Days in Settlement #10 @23% 4x Chance (100/169 Loot Modifier)

9360 / 831.25 = 12 (11.26) Days in Settlement #11 etc. @25% 4x Chance (4/7 or 100/175 Loot Modifier)

The table reinforces our conclusions, though calculating the “downtime” after all loot is gathered as 3 days may have made this option appear slightly worse than it really is when it comes to receiving the gold reward. Either way, it appears that even completing the medium battles only half the time would present a solid shot at getting Gold in every settlement.

3) A player who completes only the easy battles

Not much to be said about this sort of player. They aren’t really invested in the game; they might log in once a day and autobattle the easy option using 8 Nubian Archers. On the flip side, their Deben Coin expenditures will likely be non-existent.

Unfortunately, no Time Rewards for them with an average completion table like this (NOTE: ADD 2 – 3 DAYS TO THE GIVEN NUMBERS TO ACCOUNT FOR LAG AND COMPLETING THE LAST QUEST):

14300 / 345 = 42 (41.44) Days in Settlement #1 @5% 4x Chance (20/23 or 100/115 Loot Modifier)

13550 / 363 = 38 (37.19) Days in Settlement #2 @7% 4x Chance (100/121 Loot Modifier)

12900 / 381 = 34 (33.85) Days in Settlement #3 @9% 4x Chance (100/127 Loot Modifier)

12320 / 399 = 31 (30.87) Days in Settlement #4 @11% 4x Chance (100/133 Loot Modifier)

11790 / 417 = 29 (28.27) Days in Settlement #5 @13% 4x Chance (100/139 Loot Modifier)

11380 / 435 = 27 (26.16) Days in Settlement #6 @15% 4x Chance (20/29 or 100/145 Loot Modifier)

10850 / 453 = 24 (23.95) Days in Settlement #7 @17% 4x Chance (100/151 Loot Modifier)

10440 / 471 = 23 (22.16) Days in Settlement #8 @19% 4x Chance (100/157 Loot Modifier)

10050 / 489 = 21 (20.55) Days in Settlement #9 @21% 4x Chance (100/163 Loot Modifier)

9700 / 507 = 20 (19.13) Days in Settlement #10 @23% 4x Chance (100/169 Loot Modifier)

9360 / 525 = 18 (17.82) Days in Settlement #11 etc. @25% 4x Chance (4/7 or 100/175 Loot Modifier)

Strangely enough, however, it appears they will receive 8 Bronze Time Rewards over the course of their Egyptian Campaign – enough to build One Obelisk. Not too bad so far as consolation prizes go…



CONCLUSIONS

In all, it appears as though InnoGames has finally done something to be applauded with the Egyptian Settlement: They’ve given players who are more invested in the game a clear advantage over casual players, while also leaving open the possibility of completing the minigame “as it was meant to” for most of the playerbase. Ironically, Egypt might be the most luck-dependent of all settlements and the one that receives the largest boost from skilled play at the same time.

The delicate numerical balance I have discovered in certain parts of the settlement also makes me believe that despite a mixed response as best, the Egyptian Cultural Settlement has received extensive balancing and playtesting before being released – even on Beta, since as far as I know there haven’t been any major changes to the settlement during Beta testing. While this balancing may have been intended to put players on the edge and get them to spend more diamonds, I will still give unto Caesar what is Caesar’s and congratulate the developers at InnoGames for their execution of what could as well have been the core of an entirely new game under different circumstances. Furthermore, settlements actually have one of the more reasonable price-performance ratios when it comes to diamonds. Spending 50 diamonds here and there for an impediment removal actually makes financial sense, but is strictly unnecessary based on available data.

Unfortunately, fighting in the settlement quickly gets stale and the main settlement reward is lacklustre at best. The time rewards on the other hand provide the best FP/space ratio of any readily-available building: You can get the equivalent of a Lvl. 2 Shrine of Knowledge in a mere 2 weeks – even less with some luck. Taken to the max level, they also provide a respectable 6% defence boost to your attacking army – a newly added boost that is otherwise only available from event to event in the form of Sentinel Outposts.

As to the methodology used in this analysis, there isn’t much to be said. While I have assumed optimal play in quite a few places, that kind of is the point of this entire endeavour: To figure out how Egypt can be completed optimally, tweak the numbers until that optimal point is reached, and then extrapolate to less optimal playstyles based on that. The calculations may have been complicated by my occasional decision to round the raw data and use the results produced: Had I been working on an actual engineering project I would’ve been fired already. Fortunately, a couple percentile differences here and there don’t impact the overall picture all that much. If any mathematical or methodological errors are found in my work, I do implore the discoverers of such errors to contact me at their leisure to ensure the existence of an impartial and accurate source for any and all FoE enthusiasts.

Light & Liberty!

-Muhabir

 

[DeletedUser118252]

Wow, that took me undergraduate degrees in Statistical Analysis and Science of Luck to understand, and 1¼ cups of coffee per section to read, resulting in 0.45 headaches per bolded phrase. So remember to add the amount of time it takes to get up from the computer, go to the kitchen and brew some java into your final calculations (if you have 25% Luck, there will be some Advil in the bathroom cabinet).
Amazing Analysis, Muhabir! Thanks. As a bottom-dwelling mudsucker picking off the easy fights (and losing some of them), I wish I'd seen this post a month ago. In that case I would have had fingernails remaining.

 

[Goremise]

What staying inside all day does:

(also nice write-up, so much information to process)

 

[Galladhorn]

I have stopped playing settlements.
– The reason is displayed wonderfully by Muhabirs incredible analysys

 

[Deleted User - 12275984]

I have stopped playing settlements.
– The reason is displayed wonderfully by Muhabirs incredible analysys

Do you want me to give you my analysis?

 

[WinnerGR]

Thanks for writing this up xD

 

[Zeratul 2.0]

Can I ask a question before reading the post in its entirety given its extreme length?

Question:

Is the hard battle on Day #1 meant to be lost? (when only unattached, seemingly weak units are available)

Spoiler: Battle #1 (Easy) without Losing Units

Battle #1 (Easy) without Losing Units

Spoiler: Battle #2 (Medium) without Losing Units

Battle #2 (Medium) without Losing Units

Spoiler: Battle #3 (Hard) Looking Impossible

Battle #3 (Hard) Looking Impossible

Note: I've put all numbers in bold to match the theme, in other words, I'm also mathematical (numerical)

 

[Zeratul 2.0]

Never mind.

Stay tuned for the glorious final battle report! (a.k.a. for the answering of one's own question)

 

[LastWarrior]

no point trying the third battle until your archers are up and elephants will sort anything later on

 

[Muhabir]

Can I ask a question before reading the post in its entirety given its extreme length?

Question:

Is the hard battle on Day #1 meant to be lost? (when only unattached, seemingly weak units are available)

Spoiler: Battle #1 (Easy) without Losing Units

Battle #1 (Easy) without Losing Units
View attachment 21369

Spoiler: Battle #2 (Medium) without Losing Units

Battle #2 (Medium) without Losing Units
View attachment 21370

Spoiler: Battle #3 (Hard) Looking Impossible

Battle #3 (Hard) Looking Impossible
View attachment 21371

Note: I've put all numbers in bold to match the theme, in other words, I'm also mathematical (numerical)

Well, it's been a while since I last ran the Egyptian settlement. But..
1) You don't need to win the hard fight every day, only every other day, meaning you can easily afford to lose the first day's hard battle.
2) Depending on when you started the settlement, you should be able to get a few more Nubians / Camels out from your barracks before taking this one on. I would assume a 4 Nubian - 4 Camel build would be sufficient. Take out the chariots early on and use the Nubians to snipe the enemy camels from afar.

EDIT: lol, it's been so long I forgot my own data. You only need to win medium difficulty battles half the time, you don't need to win a single hard battle at all to finish Egypt on time.