Battle System

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

There is a battle calc. for the mods. Too bad the public can't use it.

Napísal Mr_Own_U, 31.01.2014 at 17:36

There is a battle calc. for the mods. Too bad the public can't use it.

Really?
The reason why I wanted to know this info is to make one in a batch file lol.

Napísal Guest, 31.01.2014 at 17:38

Napísal Mr_Own_U, 31.01.2014 at 17:36

There is a battle calc. for the mods. Too bad the public can't use it.

Really?
The reason why I wanted to know this info is to make one in a batch file lol.

This was used for catching a hacker.. Would really be cool if we could use this.

Napísal Mr_Own_U, 31.01.2014 at 17:39

Napísal Guest, 31.01.2014 at 17:38

Napísal Mr_Own_U, 31.01.2014 at 17:36

There is a battle calc. for the mods. Too bad the public can't use it.

Really?
The reason why I wanted to know this info is to make one in a batch file lol.

img

This was used for catching a hacker.. Would really be cool if we could use this.

Where did you get that from?

Napísal Guest, 31.01.2014 at 17:45

Napísal Mr_Own_U, 31.01.2014 at 17:39

Napísal Guest, 31.01.2014 at 17:38

Napísal Mr_Own_U, 31.01.2014 at 17:36

There is a battle calc. for the mods. Too bad the public can't use it.

Really?
The reason why I wanted to know this info is to make one in a batch file lol.

img

This was used for catching a hacker.. Would really be cool if we could use this.

Where did you get that from?

A mods SS when he helped me figure out something.

Calculator would only be useful for determining what attacks are 100% winnable. But it's pretty obvious to determine that when you judge the amount of troops you attack with compared to the amount defending.

Other than that it will only show you your chances of winning which is just as useful as looking at the odds the game gives you. Also, the calculator would only work right if you knew your opponents strategy.

Napísal Fockmeeard, 31.01.2014 at 17:47

Calculator would only be useful for determining what attacks are 100% winnable. But it's pretty obvious to determine that when you judge the amount of troops you attack with compared to the amount defending.

Other than that it will only show you your chances of winning which is just as useful as looking at the odds the game gives you. Also, the calculator would only work right if you knew your opponents strategy.

A calculator would be useful so I can know chances, seems useful to me. And by "odds", you mean the att/def thing that shows up when hover on a stack? That is not useful at ALL. It just gives the att/def stats from default units. Not counting HP, crits and strat stats. (I think they fixed it and now it shows strat based strats, but still)

Napísal Guest, 31.01.2014 at 17:18

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

id like to know this too.

also why is the battle calc not made available to the public? seems pointless to have it exclusively a mod feature when the community could make use of it

Napísal Permamuted, 31.01.2014 at 17:56

Napísal Guest, 31.01.2014 at 17:18

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

id like to know this too.

also why is the battle calc not made available to the public? seems pointless to have it exclusively a mod feature when the community could make use of it

It seems like a program made on Visual Basic. I bet admins or Meester made it and give it to mods. There was a hacker (Logic) having insane unit stats, he was mixing boosts. For example, marines with GW cost and MOS attack combined with IF's HP boost, I think they made this tool just for this guy, I'm pretty sure no one ever was suspicious of hacking before.

Moderators have no such calculator. I just want to make that clear to everyone before this escalates.

Napísal Spart, 31.01.2014 at 21:28

Moderators have no such calculator. I just want to make that clear to everyone before this escalates.

Guess I was misinformed! Sorry Alex.

Napísal Mr_Own_U, 31.01.2014 at 21:34

Napísal Spart, 31.01.2014 at 21:28

Moderators have no such calculator. I just want to make that clear to everyone before this escalates.

Guess I was misinformed! Sorry Alex.

Why would Fart admit they have a calculator, it's a conspiracy!

Napísal 4Chan, 01.02.2014 at 01:53

Napísal Mr_Own_U, 31.01.2014 at 21:34

Napísal Spart, 31.01.2014 at 21:28

Moderators have no such calculator. I just want to make that clear to everyone before this escalates.

Guess I was misinformed! Sorry Alex.

Why would Fart admit they have a calculator, it's a conspiracy!

Spart isn't a liar.

Napísal Mr_Own_U, 01.02.2014 at 04:10

Napísal 4Chan, 01.02.2014 at 01:53

Napísal Mr_Own_U, 31.01.2014 at 21:34

Napísal Spart, 31.01.2014 at 21:28

Moderators have no such calculator. I just want to make that clear to everyone before this escalates.

Guess I was misinformed! Sorry Alex.

Why would Fart admit they have a calculator, it's a conspiracy!

Spart isn't a liar.

Spart?

Actually, a 'calculator', running a number of iterations, could definitely give you the PROBABILITY of one set of units against another set of units. From probability, one can calculate odds, of course.

And this would be very useful. 'Certainty' (five nines/99.999%) is a lot more expensive than 'probably' (>.5). Knowing that if I send 5 units to attack a city, I have an 80% chance but that I would need to send 8 units to have a 99.999% chance of taking the same city might change the way I deploy forces.

I think most players want to know how many units would be required to have a (60~90%) chance. Of course they would rage on losing a battle they had a 90% chance of winning ....

The 'easy' way to write such an app would not be to exhaust the Markov chains of 100s of units vs. 100s of units (actually, probably impossible), instead, it would simulate a given battle many many many times, giving result(s) which would be 'practically indistinguishable' from the exhaustive analysis. Clearly the battle calculator screenshot shown uses the 'Monte Carlo' vs. exhaustive approach (simulator; repeat etc.)
It should be fairly straightforward to create an app which would allow the user to specify x(1,2,3) units vs. y(1,2,3) and present the top z most probable outcomes. I'd be happy to confuse someone with the pseudocode if they're interested.
---
Related: I am working on an algorithm to ascertain the overall battle effectiveness of each type of unit, and will submit to the wolves that you all are soon.

Napísal Fockmeeard, 31.01.2014 at 17:47

Calculator would only be useful for determining what attacks are 100% winnable. But it's pretty obvious to determine that when you judge the amount of troops you attack with compared to the amount defending.

Other than that it will only show you your chances of winning which is just as useful as looking at the odds the game gives you. Also, the calculator would only work right if you knew your opponents strategy.

Yes, crit of 5 means a 5% chance of a critical hit.
Therefore the 'average' damage of a conventional infantry defending in a city/line is 4.2 includig crit.
(Damage of 1-7, median damage of 4, 5% chance of crit, crit damage same as that being rolled).

Napísal Guest, 31.01.2014 at 17:18

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

Things to remember:
- One player's good luck is another player's bad luck.
- Everyone has an expectation of what the result should be of a battle. When it exceeds their expectation, it is considered good luck, when it falls short, bad luck.
- Player expectation has only some degree of connection to the statistical mean.
- The actual result of a battle, while obviously mathematically possible, may be no where near the statistically likely/expected/average result.

There are at least 3 reasons why big stacks 'seem' luckier than the same forces spread out. Part is perception, the other part is that epic successes and failures actually cannot manifest without big stacks.

1. Perception: You pay a lot more attention to big stack battles than small battle, all other things being equal. 100 units vs. 100 units is only marginally more likely to produce the statistically-most-likely result than 10v10.
100,000,000 units vs. 100,000,000 units are almost certainly to produce the mathematically expected outcome.

2. Perception: Even though the battle mechanics and likely outcomes are *knowable* by anyone who wants to take the time, the mathematically expected outcomes are *unknown* at the time of battle (few people really have the information), but people have non-rational expectations of what the outcome should be, and the actual outcome is quickly assessed (if at all) by the player, and quickly classified as rage, joy or meh.
And then forgotten.

3. Reality: A unit's 'luck' cannot be properly expressed unless it battles many units.
Consider: A defending infantry can do up to 7 damage to an attacking tank. The tank can do up to 8 damage to the infantry. Both units have 7 HP.
The defending infantry can one-hit the attacking tank 1/7th of the time, and the tank does minimum damage (1 HP) to the defending infantry 1/8 of the time.
(1/7*1/8) is about 2%. So about 2% of the time, the infantry kills the tank, one hit, and takes 1 HP damage from the tank, leaving 6 HP.
- The *probability* of our Hero Infantry defeating 7 tanks before dying is about 0.0000000000006
- The *odds* of our Hero Infantry defeating 7 tanks are about 6 in Ten Trillion (if I counted correctly).
- The likelihood of one defending infantry defeating 3 tanks is about 1 in 10,000.

Napísal Guest, 31.01.2014 at 17:18

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

Napísal zombieyeti, 01.02.2014 at 06:21

Things to remember:
- One player's good luck is another player's bad luck.
- Everyone has an expectation of what the result should be of a battle. When it exceeds their expectation, it is considered good luck, when it falls short, bad luck.
- Player expectation has only some degree of connection to the statistical mean.
- The actual result of a battle, while obviously mathematically possible, may be no where near the statistically likely/expected/average result.

There are at least 3 reasons why big stacks 'seem' luckier than the same forces spread out. Part is perception, the other part is that epic successes and failures actually cannot manifest without big stacks.

1. Perception: You pay a lot more attention to big stack battles than small battle, all other things being equal. 100 units vs. 100 units is only marginally more likely to produce the statistically-most-likely result than 10v10.
100,000,000 units vs. 100,000,000 units are almost certainly to produce the mathematically expected outcome.

2. Perception: Even though the battle mechanics and likely outcomes are *knowable* by anyone who wants to take the time, the mathematically expected outcomes are *unknown* at the time of battle (few people really have the information), but people have non-rational expectations of what the outcome should be, and the actual outcome is quickly assessed (if at all) by the player, and quickly classified as rage, joy or meh.
And then forgotten.

3. Reality: A unit's 'luck' cannot be properly expressed unless it battles many units.
Consider: A defending infantry can do up to 7 damage to an attacking tank. The tank can do up to 8 damage to the infantry. Both units have 7 HP.
The defending infantry can one-hit the attacking tank 1/7th of the time, and the tank does minimum damage (1 HP) to the defending infantry 1/8 of the time.
(1/7*1/8) is about 2%. So about 2% of the time, the infantry kills the tank, one hit, and takes 1 HP damage from the tank, leaving 6 HP.
- The *probability* of our Hero Infantry defeating 7 tanks before dying is about 0.0000000000006
- The *odds* of our Hero Infantry defeating 7 tanks are about 6 in Ten Trillion (if I counted correctly).
- The likelihood of one defending infantry defeating 3 tanks is about 1 in 10,000.

Napísal Guest, 31.01.2014 at 17:18

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

Yes like you said, it's such a small chance but I doubt it is just "luck", this happens a lot.

I suspect most players (including myself), when playing, really have no deep understanding of how high the variability is when attacking/defending. The *information* is available, most just don't internalize it. A tank [Max Damage 8) attacking an infantry in a city does an average of 4.725 damage. The defending infantry does an average of 4.2 damage. The tank really has only a 12.5% advantage over the infantry.

On a 1v1 basis, a defending milltia with a max defense of 4 takes out a tank with max attack of 8 only about 6% of the time, yet it is unlikely for an attacking tank to take out more than 3 militia in a particular battle ... which sounds insanely counterintuitive but that's where minimum damage and HP come into play. The militia will always do 1 damage per skirmish round, and has as many HP as the tank. With a median damage of 2.625 each defense, against a tank's median attack of 4.725, each militia does about 5.25 damage to each tank before dying.
If every skirmish in a battle between a militia and a tank was 'average':
T1 kills M1, but has only 1.75 HP remaining.
M2 kills T1, has 2.275 HP remaining.
T2 kills M2, has 4.375 HP remaining.
T2 and M3 kill each other.

T3 and M4 face each other, and T1 kills M1, but has only 1.75 HP remaining ...

So if every battle were 'average' it takes 2 tanks to kill 3 militia: no bargain on a cost basis.

Napísal Guest, 01.02.2014 at 11:38

Napísal zombieyeti, 01.02.2014 at 06:21

Things to remember:
- One player's good luck is another player's bad luck.
- Everyone has an expectation of what the result should be of a battle. When it exceeds their expectation, it is considered good luck, when it falls short, bad luck.
- Player expectation has only some degree of connection to the statistical mean.
- The actual result of a battle, while obviously mathematically possible, may be no where near the statistically likely/expected/average result.

There are at least 3 reasons why big stacks 'seem' luckier than the same forces spread out. Part is perception, the other part is that epic successes and failures actually cannot manifest without big stacks.

1. Perception: You pay a lot more attention to big stack battles than small battle, all other things being equal. 100 units vs. 100 units is only marginally more likely to produce the statistically-most-likely result than 10v10.
100,000,000 units vs. 100,000,000 units are almost certainly to produce the mathematically expected outcome.

2. Perception: Even though the battle mechanics and likely outcomes are *knowable* by anyone who wants to take the time, the mathematically expected outcomes are *unknown* at the time of battle (few people really have the information), but people have non-rational expectations of what the outcome should be, and the actual outcome is quickly assessed (if at all) by the player, and quickly classified as rage, joy or meh.
And then forgotten.

3. Reality: A unit's 'luck' cannot be properly expressed unless it battles many units.
Consider: A defending infantry can do up to 7 damage to an attacking tank. The tank can do up to 8 damage to the infantry. Both units have 7 HP.
The defending infantry can one-hit the attacking tank 1/7th of the time, and the tank does minimum damage (1 HP) to the defending infantry 1/8 of the time.
(1/7*1/8) is about 2%. So about 2% of the time, the infantry kills the tank, one hit, and takes 1 HP damage from the tank, leaving 6 HP.
- The *probability* of our Hero Infantry defeating 7 tanks before dying is about 0.0000000000006
- The *odds* of our Hero Infantry defeating 7 tanks are about 6 in Ten Trillion (if I counted correctly).
- The likelihood of one defending infantry defeating 3 tanks is about 1 in 10,000.

Napísal Guest, 31.01.2014 at 17:18

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

Yes like you said, it's such a small chance but I doubt it is just "luck", this happens a lot.

Napísal zombieyeti, 01.02.2014 at 13:40

I suspect most players (including myself), when playing, really have no deep understanding of how high the variability is when attacking/defending. The *information* is available, most just don't internalize it. A tank [Max Damage 8) attacking an infantry in a city does an average of 4.725 damage. The defending infantry does an average of 4.2 damage. The tank really has only a 12.5% advantage over the infantry.

On a 1v1 basis, a defending milltia with a max defense of 4 takes out a tank with max attack of 8 only about 6% of the time, yet it is unlikely for an attacking tank to take out more than 3 militia in a particular battle ... which sounds insanely counterintuitive but that's where minimum damage and HP come into play. The militia will always do 1 damage per skirmish round, and has as many HP as the tank. With a median damage of 2.625 each defense, against a tank's median attack of 4.725, each militia does about 5.25 damage to each tank before dying.
If every skirmish in a battle between a militia and a tank was 'average':
T1 kills M1, but has only 1.75 HP remaining.
M2 kills T1, has 2.275 HP remaining.
T2 kills M2, has 4.375 HP remaining.
T2 and M3 kill each other.

T3 and M4 face each other, and T1 kills M1, but has only 1.75 HP remaining ...

So if every battle were 'average' it takes 2 tanks to kill 3 militia: no bargain on a cost basis.

Napísal Guest, 01.02.2014 at 11:38

Napísal zombieyeti, 01.02.2014 at 06:21

Things to remember:
- One player's good luck is another player's bad luck.
- Everyone has an expectation of what the result should be of a battle. When it exceeds their expectation, it is considered good luck, when it falls short, bad luck.
- Player expectation has only some degree of connection to the statistical mean.
- The actual result of a battle, while obviously mathematically possible, may be no where near the statistically likely/expected/average result.

There are at least 3 reasons why big stacks 'seem' luckier than the same forces spread out. Part is perception, the other part is that epic successes and failures actually cannot manifest without big stacks.

1. Perception: You pay a lot more attention to big stack battles than small battle, all other things being equal. 100 units vs. 100 units is only marginally more likely to produce the statistically-most-likely result than 10v10.
100,000,000 units vs. 100,000,000 units are almost certainly to produce the mathematically expected outcome.

2. Perception: Even though the battle mechanics and likely outcomes are *knowable* by anyone who wants to take the time, the mathematically expected outcomes are *unknown* at the time of battle (few people really have the information), but people have non-rational expectations of what the outcome should be, and the actual outcome is quickly assessed (if at all) by the player, and quickly classified as rage, joy or meh.
And then forgotten.

3. Reality: A unit's 'luck' cannot be properly expressed unless it battles many units.
Consider: A defending infantry can do up to 7 damage to an attacking tank. The tank can do up to 8 damage to the infantry. Both units have 7 HP.
The defending infantry can one-hit the attacking tank 1/7th of the time, and the tank does minimum damage (1 HP) to the defending infantry 1/8 of the time.
(1/7*1/8) is about 2%. So about 2% of the time, the infantry kills the tank, one hit, and takes 1 HP damage from the tank, leaving 6 HP.
- The *probability* of our Hero Infantry defeating 7 tanks before dying is about 0.0000000000006
- The *odds* of our Hero Infantry defeating 7 tanks are about 6 in Ten Trillion (if I counted correctly).
- The likelihood of one defending infantry defeating 3 tanks is about 1 in 10,000.

Napísal Guest, 31.01.2014 at 17:18

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

Yes like you said, it's such a small chance but I doubt it is just "luck", this happens a lot.

Hmm no you can't calculate "average"; I mean, rolls vary a lot.
Battles work like this:
Max damage points/roll = Attack / Defence.
A random number between 1 and Att/Def is chosen and dealt as damage to the other unit. This step is done by both parts, at same time, meaning EVERY unit does damage, though the HP is restored when a battle finishes.

I will make calcs with the tool I am going to make, based on 1000 (or more) battles.

For brevity I used 'average' in most cases. A mean, meadian and mode are all averages.
I think I'm pretty aware of battle mechanics (see my examples, but invite correction) but am only as good as my sources. I don't know if the roll is of the form INT(RND*7)+1 or (RND*7)+1, so I took a stab in the void. The practical results are the same.

I do believe the mean damage for a unit with a min damage of 1, max damage of 8, critical chance of 5% as being 4.725.
Would you be so kind as to confirm?

My reasoning:
The minimum damage is 1.
The maximum damage is 8. The mean (average) of the damage space (1+2...7+8)/8 = 4.5
The critical chance is 5%. 95% of the time, no additional damage is accrued. 5% of the time, the damage rolled is applied. As the average is 4.5, 4.5 * 1.05 = 4.725. Or, 4.5+(4.5*.05).

[Edit] I looked at the simulator screenshot again. Of course it calculates the average Attack and Defense.
___
If you're looking to calculate probability, and derive the odds, and then apply these in a time-limited (quick) game, you'll definitely need to look at 'average' results tailored to your risk tolerance.

Napísal Guest, 01.02.2014 at 14:11

Napísal zombieyeti, 01.02.2014 at 13:40

I suspect most players (including myself), when playing, really have no deep understanding of how high the variability is when attacking/defending. The *information* is available, most just don't internalize it. A tank [Max Damage 8) attacking an infantry in a city does an average of 4.725 damage. The defending infantry does an average of 4.2 damage. The tank really has only a 12.5% advantage over the infantry.

On a 1v1 basis, a defending milltia with a max defense of 4 takes out a tank with max attack of 8 only about 6% of the time, yet it is unlikely for an attacking tank to take out more than 3 militia in a particular battle ... which sounds insanely counterintuitive but that's where minimum damage and HP come into play. The militia will always do 1 damage per skirmish round, and has as many HP as the tank. With a median damage of 2.625 each defense, against a tank's median attack of 4.725, each militia does about 5.25 damage to each tank before dying.
If every skirmish in a battle between a militia and a tank was 'average':
T1 kills M1, but has only 1.75 HP remaining.
M2 kills T1, has 2.275 HP remaining.
T2 kills M2, has 4.375 HP remaining.
T2 and M3 kill each other.

T3 and M4 face each other, and T1 kills M1, but has only 1.75 HP remaining ...

So if every battle were 'average' it takes 2 tanks to kill 3 militia: no bargain on a cost basis.

Napísal Guest, 01.02.2014 at 11:38

Napísal zombieyeti, 01.02.2014 at 06:21

Things to remember:
- One player's good luck is another player's bad luck.
- Everyone has an expectation of what the result should be of a battle. When it exceeds their expectation, it is considered good luck, when it falls short, bad luck.
- Player expectation has only some degree of connection to the statistical mean.
- The actual result of a battle, while obviously mathematically possible, may be no where near the statistically likely/expected/average result.

There are at least 3 reasons why big stacks 'seem' luckier than the same forces spread out. Part is perception, the other part is that epic successes and failures actually cannot manifest without big stacks.

1. Perception: You pay a lot more attention to big stack battles than small battle, all other things being equal. 100 units vs. 100 units is only marginally more likely to produce the statistically-most-likely result than 10v10.
100,000,000 units vs. 100,000,000 units are almost certainly to produce the mathematically expected outcome.

2. Perception: Even though the battle mechanics and likely outcomes are *knowable* by anyone who wants to take the time, the mathematically expected outcomes are *unknown* at the time of battle (few people really have the information), but people have non-rational expectations of what the outcome should be, and the actual outcome is quickly assessed (if at all) by the player, and quickly classified as rage, joy or meh.
And then forgotten.

3. Reality: A unit's 'luck' cannot be properly expressed unless it battles many units.
Consider: A defending infantry can do up to 7 damage to an attacking tank. The tank can do up to 8 damage to the infantry. Both units have 7 HP.
The defending infantry can one-hit the attacking tank 1/7th of the time, and the tank does minimum damage (1 HP) to the defending infantry 1/8 of the time.
(1/7*1/8) is about 2%. So about 2% of the time, the infantry kills the tank, one hit, and takes 1 HP damage from the tank, leaving 6 HP.
- The *probability* of our Hero Infantry defeating 7 tanks before dying is about 0.0000000000006
- The *odds* of our Hero Infantry defeating 7 tanks are about 6 in Ten Trillion (if I counted correctly).
- The likelihood of one defending infantry defeating 3 tanks is about 1 in 10,000.

Napísal Guest, 31.01.2014 at 17:18

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

Yes like you said, it's such a small chance but I doubt it is just "luck", this happens a lot.

Hmm no you can't calculate "average"; I mean, rolls vary a lot.
Battles work like this:
Max damage points/roll = Attack / Defence.
A random number between 1 and Att/Def is chosen and dealt as damage to the other unit. This step is done by both parts, at same time, meaning EVERY unit does damage, though the HP is restored when a battle finishes.

I will make calcs with the tool I am going to make, based on 1000 (or more) battles.

Napísal zombieyeti, 01.02.2014 at 14:45

For brevity I used 'average' in most cases. A mean, meadian and mode are all averages.
I think I'm pretty aware of battle mechanics (see my examples, but invite correction) but am only as good as my sources. I don't know if the roll is of the form INT(RND*7)+1 or(RND*7)+1, so I took a stab in the void.

I do believe the mean damage for a unit with a min damage of 1, max damage of 8, critical chance of 5% as being 4.725.
Would you be so kind as to confirm?

My reasoning:
The minimum damage is 1.
The maximum damage is 8. The mean (average) of the damage space (1+2...7+8)/8 = 4.5
The critical chance is 5%. 95% of the time, no additional damage is accrued. 5% of the time, the damage rolled is applied. As the averageand median is 4.5, 4.5 * 1.05 = 4.725. Or, 4.5+(4.5*.05)

___
If you're looking to calculate probability, and derive the odds, and then apply these in a time-limited (quick) game, you'll definitely need to look at 'average' results tailored to your risk tolerance.

Napísal Guest, 01.02.2014 at 14:11

Napísal zombieyeti, 01.02.2014 at 13:40

I suspect most players (including myself), when playing, really have no deep understanding of how high the variability is when attacking/defending. The *information* is available, most just don't internalize it. A tank [Max Damage 8) attacking an infantry in a city does an average of 4.725 damage. The defending infantry does an average of 4.2 damage. The tank really has only a 12.5% advantage over the infantry.

On a 1v1 basis, a defending milltia with a max defense of 4 takes out a tank with max attack of 8 only about 6% of the time, yet it is unlikely for an attacking tank to take out more than 3 militia in a particular battle ... which sounds insanely counterintuitive but that's where minimum damage and HP come into play. The militia will always do 1 damage per skirmish round, and has as many HP as the tank. With a median damage of 2.625 each defense, against a tank's median attack of 4.725, each militia does about 5.25 damage to each tank before dying.
If every skirmish in a battle between a militia and a tank was 'average':
T1 kills M1, but has only 1.75 HP remaining.
M2 kills T1, has 2.275 HP remaining.
T2 kills M2, has 4.375 HP remaining.
T2 and M3 kill each other.

T3 and M4 face each other, and T1 kills M1, but has only 1.75 HP remaining ...

So if every battle were 'average' it takes 2 tanks to kill 3 militia: no bargain on a cost basis.

Napísal Guest, 01.02.2014 at 11:38

Napísal zombieyeti, 01.02.2014 at 06:21

Things to remember:
- One player's good luck is another player's bad luck.
- Everyone has an expectation of what the result should be of a battle. When it exceeds their expectation, it is considered good luck, when it falls short, bad luck.
- Player expectation has only some degree of connection to the statistical mean.
- The actual result of a battle, while obviously mathematically possible, may be no where near the statistically likely/expected/average result.

There are at least 3 reasons why big stacks 'seem' luckier than the same forces spread out. Part is perception, the other part is that epic successes and failures actually cannot manifest without big stacks.

1. Perception: You pay a lot more attention to big stack battles than small battle, all other things being equal. 100 units vs. 100 units is only marginally more likely to produce the statistically-most-likely result than 10v10.
100,000,000 units vs. 100,000,000 units are almost certainly to produce the mathematically expected outcome.

2. Perception: Even though the battle mechanics and likely outcomes are *knowable* by anyone who wants to take the time, the mathematically expected outcomes are *unknown* at the time of battle (few people really have the information), but people have non-rational expectations of what the outcome should be, and the actual outcome is quickly assessed (if at all) by the player, and quickly classified as rage, joy or meh.
And then forgotten.

3. Reality: A unit's 'luck' cannot be properly expressed unless it battles many units.
Consider: A defending infantry can do up to 7 damage to an attacking tank. The tank can do up to 8 damage to the infantry. Both units have 7 HP.
The defending infantry can one-hit the attacking tank 1/7th of the time, and the tank does minimum damage (1 HP) to the defending infantry 1/8 of the time.
(1/7*1/8) is about 2%. So about 2% of the time, the infantry kills the tank, one hit, and takes 1 HP damage from the tank, leaving 6 HP.
- The *probability* of our Hero Infantry defeating 7 tanks before dying is about 0.0000000000006
- The *odds* of our Hero Infantry defeating 7 tanks are about 6 in Ten Trillion (if I counted correctly).
- The likelihood of one defending infantry defeating 3 tanks is about 1 in 10,000.

Napísal Guest, 31.01.2014 at 17:18

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

Yes like you said, it's such a small chance but I doubt it is just "luck", this happens a lot.

Hmm no you can't calculate "average"; I mean, rolls vary a lot.
Battles work like this:
Max damage points/roll = Attack / Defence.
A random number between 1 and Att/Def is chosen and dealt as damage to the other unit. This step is done by both parts, at same time, meaning EVERY unit does damage, though the HP is restored when a battle finishes.

I will make calcs with the tool I am going to make, based on 1000 (or more) battles.

Yeah, if you make thousands of that, the average would be close to what you said. But rolls are pretty "wide", from 1 to 8 for example. In small/normal stack battles, it depends on luck.
If you wanna know if 2 tanks beat 3 militia, then I suggest doing this battle and then see the results. Don't use average damage.
Btw, crits do a normal roll + full roll. For example, a tank does a critical hit, doing 5 as a roll and 8 extra for being a crit. Total 13.

Alex, I was trying to HELP you, not ARGUE with you!
You put up a post asking for Help. I am trying to help, and I also share an interest in the battle mechanics. I am working on a similar project.

"Yeah, if you make thousands of that, the average would be close to what you said. But rolls are pretty "wide", from 1 to 8 for example. In small/normal stack battles, it depends on luck." - Please look at the simulator. It determines averages, for a reason.
I can quickly think of three legitimate ways to forecast outcomes of battles:
1. Use the millions of battles already fought and determine the outcomes and distill the averages. We do not have access to the data.
2. Simulate battles, determine outcomes, and distill the averages. You're working on this.
3. Exhaust the Markov Chains (ugh) and determine the probability of a given outcome (I already tried, no no no, maybe a better maths guy could find a shortcut).

"If you wanna know if 2 tanks beat 3 militia, then I suggest doing this battle and then see the results. Don't use average damage."
This was an example. Remember how you observed much 'luck'? This was an example of a statistically expected outcome which would surprise many players. It would take many many many battles and recording the results. It would probably take less time for me to relearn programming and implement a Monte-Carlo-style simulator like you are.

"Btw, crits do a normal roll + full roll. For example, a tank does a critical hit, doing 5 as a roll and 8 extra for being a crit. Total 13."
Thank you! I was wrong and will correct the quoted post. The previous ones will remain so I may wallow in my ignorance.
Much appreciated.

Napísal Guest, 01.02.2014 at 14:53

Napísal zombieyeti, 01.02.2014 at 14:45

[EDITED with AlexMeza's correction to Critical Damage]

For brevity I used 'average' in most cases. A mean, meadian and mode are all averages.
I think I'm pretty aware of battle mechanics (see my examples, but invite correction) but am only as good as my sources. I don't know if the roll is of the form INT(RND*7)+1 or(RND*7)+1, so I took a stab in the void.

I do believe the mean damage for a unit with a min damage of 1, max damage of 8, critical chance of 5% as being 4.9.
Would you be so kind as to confirm?

My reasoning:
The minimum damage is 1.
The maximum damage is 8. The mean (average) of the damage space (1+2...7+8)/8 = 4.5
The critical chance is 5%. 95% of the time, no additional damage is accrued. 5% of the time, the Max damage is applied to the roll. As the average is 4.5, the critical 'chance' is 5%, and the Max Damage is 8, the Average Damage is .4 (8 * 5%) + 4.5.
___
If you're looking to calculate probability, and derive the odds, and then apply these in a time-limited (quick) game, you'll definitely need to look at 'average' results tailored to your risk tolerance.

Napísal Guest, 01.02.2014 at 14:11

Napísal zombieyeti, 01.02.2014 at 13:40

I suspect most players (including myself), when playing, really have no deep understanding of how high the variability is when attacking/defending. The *information* is available, most just don't internalize it. A tank [Max Damage 8) attacking an infantry in a city does an average of 4.725 damage. The defending infantry does an average of 4.2 damage. The tank really has only a 12.5% advantage over the infantry.

On a 1v1 basis, a defending milltia with a max defense of 4 takes out a tank with max attack of 8 only about 6% of the time, yet it is unlikely for an attacking tank to take out more than 3 militia in a particular battle ... which sounds insanely counterintuitive but that's where minimum damage and HP come into play. The militia will always do 1 damage per skirmish round, and has as many HP as the tank. With a median damage of 2.625 each defense, against a tank's median attack of 4.725, each militia does about 5.25 damage to each tank before dying.
If every skirmish in a battle between a militia and a tank was 'average':
T1 kills M1, but has only 1.75 HP remaining.
M2 kills T1, has 2.275 HP remaining.
T2 kills M2, has 4.375 HP remaining.
T2 and M3 kill each other.

T3 and M4 face each other, and T1 kills M1, but has only 1.75 HP remaining ...

So if every battle were 'average' it takes 2 tanks to kill 3 militia: no bargain on a cost basis.

Napísal Guest, 01.02.2014 at 11:38

Napísal zombieyeti, 01.02.2014 at 06:21

Things to remember:
- One player's good luck is another player's bad luck.
- Everyone has an expectation of what the result should be of a battle. When it exceeds their expectation, it is considered good luck, when it falls short, bad luck.
- Player expectation has only some degree of connection to the statistical mean.
- The actual result of a battle, while obviously mathematically possible, may be no where near the statistically likely/expected/average result.

There are at least 3 reasons why big stacks 'seem' luckier than the same forces spread out. Part is perception, the other part is that epic successes and failures actually cannot manifest without big stacks.

1. Perception: You pay a lot more attention to big stack battles than small battle, all other things being equal. 100 units vs. 100 units is only marginally more likely to produce the statistically-most-likely result than 10v10.
100,000,000 units vs. 100,000,000 units are almost certainly to produce the mathematically expected outcome.

2. Perception: Even though the battle mechanics and likely outcomes are *knowable* by anyone who wants to take the time, the mathematically expected outcomes are *unknown* at the time of battle (few people really have the information), but people have non-rational expectations of what the outcome should be, and the actual outcome is quickly assessed (if at all) by the player, and quickly classified as rage, joy or meh.
And then forgotten.

3. Reality: A unit's 'luck' cannot be properly expressed unless it battles many units.
Consider: A defending infantry can do up to 7 damage to an attacking tank. The tank can do up to 8 damage to the infantry. Both units have 7 HP.
The defending infantry can one-hit the attacking tank 1/7th of the time, and the tank does minimum damage (1 HP) to the defending infantry 1/8 of the time.
(1/7*1/8) is about 2%. So about 2% of the time, the infantry kills the tank, one hit, and takes 1 HP damage from the tank, leaving 6 HP.
- The *probability* of our Hero Infantry defeating 7 tanks before dying is about 0.0000000000006
- The *odds* of our Hero Infantry defeating 7 tanks are about 6 in Ten Trillion (if I counted correctly).
- The likelihood of one defending infantry defeating 3 tanks is about 1 in 10,000.

Napísal Guest, 31.01.2014 at 17:18

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

Yes like you said, it's such a small chance but I doubt it is just "luck", this happens a lot.

Hmm no you can't calculate "average"; I mean, rolls vary a lot.
Battles work like this:
Max damage points/roll = Attack / Defence.
A random number between 1 and Att/Def is chosen and dealt as damage to the other unit. This step is done by both parts, at same time, meaning EVERY unit does damage, though the HP is restored when a battle finishes.

I will make calcs with the tool I am going to make, based on 1000 (or more) battles.

Yeah, if you make thousands of that, the average would be close to what you said. But rolls are pretty "wide", from 1 to 8 for example. In small/normal stack battles, it depends on luck.
If you wanna know if 2 tanks beat 3 militia, then I suggest doing this battle and then see the results. Don't use average damage.
Btw, crits do a normal roll + full roll. For example, a tank does a critical hit, doing 5 as a roll and 8 extra for being a crit. Total 13.

Napísal zombieyeti, 01.02.2014 at 15:34

Alex, I was trying to HELP you, not ARGUE with you!
You put up a post asking for Help. I am trying to help, and I also share an interest in the battle mechanics. I am working on a similar project.

"Yeah, if you make thousands of that, the average would be close to what you said. But rolls are pretty "wide", from 1 to 8 for example. In small/normal stack battles, it depends on luck." - Please look at the simulator. It determines averages, for a reason.
I can think of three legitimate ways to forecast outcomes of battles:
1. Use the millions of battles already fought and determine the outcomes and distill the averages.
2. Simulate battles, determine outcomes, and distill the averages.
3. Exhaust the Markov Chains (ugh) and determine the probability of a given outcome (I already tried, no no no).

"If you wanna know if 2 tanks beat 3 militia, then I suggest doing this battle and then see the results. Don't use average damage."
This was an example. Remember how you observed much 'luck'? This was an example of a statistically expected outcome which would surprise many players.

"Btw, crits do a normal roll + full roll. For example, a tank does a critical hit, doing 5 as a roll and 8 extra for being a crit. Total 13."
I will review my sources and make an adjustment if necessary. THANK YOU!!!!

Napísal Guest, 01.02.2014 at 14:53

Napísal zombieyeti, 01.02.2014 at 14:45

For brevity I used 'average' in most cases. A mean, meadian and mode are all averages.
I think I'm pretty aware of battle mechanics (see my examples, but invite correction) but am only as good as my sources. I don't know if the roll is of the form INT(RND*7)+1 or(RND*7)+1, so I took a stab in the void.

I do believe the mean damage for a unit with a min damage of 1, max damage of 8, critical chance of 5% as being 4.725.
Would you be so kind as to confirm?

My reasoning:
The minimum damage is 1.
The maximum damage is 8. The mean (average) of the damage space (1+2...7+8)/8 = 4.5
The critical chance is 5%. 95% of the time, no additional damage is accrued. 5% of the time, the damage rolled is applied. As the averageand median is 4.5, 4.5 * 1.05 = 4.725. Or, 4.5+(4.5*.05)

___
If you're looking to calculate probability, and derive the odds, and then apply these in a time-limited (quick) game, you'll definitely need to look at 'average' results tailored to your risk tolerance.

Napísal Guest, 01.02.2014 at 14:11

Napísal zombieyeti, 01.02.2014 at 13:40

I suspect most players (including myself), when playing, really have no deep understanding of how high the variability is when attacking/defending. The *information* is available, most just don't internalize it. A tank [Max Damage 8) attacking an infantry in a city does an average of 4.725 damage. The defending infantry does an average of 4.2 damage. The tank really has only a 12.5% advantage over the infantry.

On a 1v1 basis, a defending milltia with a max defense of 4 takes out a tank with max attack of 8 only about 6% of the time, yet it is unlikely for an attacking tank to take out more than 3 militia in a particular battle ... which sounds insanely counterintuitive but that's where minimum damage and HP come into play. The militia will always do 1 damage per skirmish round, and has as many HP as the tank. With a median damage of 2.625 each defense, against a tank's median attack of 4.725, each militia does about 5.25 damage to each tank before dying.
If every skirmish in a battle between a militia and a tank was 'average':
T1 kills M1, but has only 1.75 HP remaining.
M2 kills T1, has 2.275 HP remaining.
T2 kills M2, has 4.375 HP remaining.
T2 and M3 kill each other.

T3 and M4 face each other, and T1 kills M1, but has only 1.75 HP remaining ...

So if every battle were 'average' it takes 2 tanks to kill 3 militia: no bargain on a cost basis.

Napísal Guest, 01.02.2014 at 11:38

Napísal zombieyeti, 01.02.2014 at 06:21

Things to remember:
- One player's good luck is another player's bad luck.
- Everyone has an expectation of what the result should be of a battle. When it exceeds their expectation, it is considered good luck, when it falls short, bad luck.
- Player expectation has only some degree of connection to the statistical mean.
- The actual result of a battle, while obviously mathematically possible, may be no where near the statistically likely/expected/average result.

There are at least 3 reasons why big stacks 'seem' luckier than the same forces spread out. Part is perception, the other part is that epic successes and failures actually cannot manifest without big stacks.

1. Perception: You pay a lot more attention to big stack battles than small battle, all other things being equal. 100 units vs. 100 units is only marginally more likely to produce the statistically-most-likely result than 10v10.
100,000,000 units vs. 100,000,000 units are almost certainly to produce the mathematically expected outcome.

2. Perception: Even though the battle mechanics and likely outcomes are *knowable* by anyone who wants to take the time, the mathematically expected outcomes are *unknown* at the time of battle (few people really have the information), but people have non-rational expectations of what the outcome should be, and the actual outcome is quickly assessed (if at all) by the player, and quickly classified as rage, joy or meh.
And then forgotten.

3. Reality: A unit's 'luck' cannot be properly expressed unless it battles many units.
Consider: A defending infantry can do up to 7 damage to an attacking tank. The tank can do up to 8 damage to the infantry. Both units have 7 HP.
The defending infantry can one-hit the attacking tank 1/7th of the time, and the tank does minimum damage (1 HP) to the defending infantry 1/8 of the time.
(1/7*1/8) is about 2%. So about 2% of the time, the infantry kills the tank, one hit, and takes 1 HP damage from the tank, leaving 6 HP.
- The *probability* of our Hero Infantry defeating 7 tanks before dying is about 0.0000000000006
- The *odds* of our Hero Infantry defeating 7 tanks are about 6 in Ten Trillion (if I counted correctly).
- The likelihood of one defending infantry defeating 3 tanks is about 1 in 10,000.

Napísal Guest, 31.01.2014 at 17:18

How do they exactly work?
From what I saw, this is it:

Battle mechanics
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneosly, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.

So, for example, 1 Tank (9 HP) attacks 1 Infantry (8 HP) and 1 Militia (7 HP). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 5 HP left and Infantry 2 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 1 damage, but survives to fight another day. After the battle all HP is restored for surving units.

Critical hits
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.

I do understand how battles work but what's the exact formula to calculate them?
And about critical hits, I guess each critical point gives a 1% chance of doing a critical hit of CurrentRoll + Att/Def?

And one more thing; big stacks are clearly much stronger/luckier than regular-sized stacks. Why is this?

Yes like you said, it's such a small chance but I doubt it is just "luck", this happens a lot.

Hmm no you can't calculate "average"; I mean, rolls vary a lot.
Battles work like this:
Max damage points/roll = Attack / Defence.
A random number between 1 and Att/Def is chosen and dealt as damage to the other unit. This step is done by both parts, at same time, meaning EVERY unit does damage, though the HP is restored when a battle finishes.

I will make calcs with the tool I am going to make, based on 1000 (or more) battles.

Yeah, if you make thousands of that, the average would be close to what you said. But rolls are pretty "wide", from 1 to 8 for example. In small/normal stack battles, it depends on luck.
If you wanna know if 2 tanks beat 3 militia, then I suggest doing this battle and then see the results. Don't use average damage.
Btw, crits do a normal roll + full roll. For example, a tank does a critical hit, doing 5 as a roll and 8 extra for being a crit. Total 13.

Sorry <3
I found out how battles work, thanks everyone. I had to ask tophats.
Please ~lock.

Question answered. Moved to questions and locked.