Civ 3 math problems

[ZergMazter]

I don't know if it's just the way my brain works, but after hearing my story I'd like to know if anyone else has the same issues.

We take math through our lives as a kid and through high school. In high school I took a decent amount of algebra, but nothing so advanced. I kept thinking I was being prepared for real life situations, until reality hit me hard. I'm unable to use any form of algebra for real life situations such as calculating stuff in civilization 3, and end up using 3rd-6th grade math (+-x/%) that might or might not work.

I mean on paper it's all good, but I cannot independently go on my way and assemble a solvable expression that I could then solve. It just didn't come naturally to me. I knew how to solve a predetermined expression, but I could not take a real problem, and build an expression myself, because even though I knew the rules I actually did not understand algebra as a language.

It's kinda like saying a phrase in a foreign language, and you are sure what it means as a whole, but not knowing what each individual word means making you unable to use those words independently to build new phrases. I feel exactly the same way, and it's a very frustrating thing.

I know most of the rules after I practice a little, but I can't use them in a creative way to solve real math problems on civ 3!

I was on another thread and someone had come up with this expression to calculate an anti-aircraft probability of shooting down a plane 1 - (D / (D+A))^min(N,4).

But how?!?! I can finally solve it now after I got some help, but change it a bit and instead of trying to find how probable is it to shut down a plane with an AA, tell me to find whats the probability an aircraft will intercept another aircraft. I know the game mechanics, I know how the math plays on paper with the previous problem, but I'm unable to adapt it to a new problem, rendering all my math knowledge useless.

Is it because I lack practice due to not being a programmer, or is it really because some people actually understand math as a language beyond whats on paper, and that's why they are programmers?

I have a feeling I'm just comparing myself to the wrong crowd. Some people on this forum must be exceptional, because no one I know is able to perform math at such a level as it is done on this forum. It's not just knowing, but applying it too, and for the most part I can't even solve a problem until after I've done some research to refresh my mind and then ask questions.

Lets face it this is simple math and I know this, but it stops being simple when you are able to actually use it and apply it for different situations. That is a skill in itself and it means you understand it as you would a language.

I should mention I do this as a hobby only. I just wanna play my civ 3 mod in an efficient way. I've had no need after high school to use anything other than addition, subtraction, very minor multiplication, and rarely dividing in my every day life. I make a living as an artist. I'm a musician/producer, and a self taught sound engineer, and the only conscious math I do is at the gym counting reps and sets

Am I alone in my struggle, or are there others who suffer my same fate with math?

 

[walletta]

I am with you Zerg. The math goes over my head. I play the game by feel based on experience. If my elite ancient cavalry loses to a regular spearman in an unwalled town I am mildly peeved, without actually knowing what the odds were or how they are worked out (at least I understand that calculation when I see it - your example is totally incomprehensible). If I may add a question of my own to yours, are there any of these formulas that we need to know?

 

[justanick]

If you intend to comprehend the game you need to understand them. But if you are fine with lacking the finer understanding of the math at work you can play at least at the lower settings and have fun. Although i have trouble understanding how missing the fun part is fun.

 

[ZergMazter]

If you intend to comprehend the game you need to understand them. But if you are fine with lacking the finer understanding of the math at work you can play at least at the lower settings and have fun. Although i have trouble understanding how missing the fun part is fun.

Well at least for the AA I could have lived without it being accurate, but now I know how to be accurate. The rate at which the normal game shut planes down was too low for me, so I increased all AA points to taste to the point that I think about it twice before sending a very expensive plane to bombard an aegis cruiser without using math.

I currently don't know of anything else I might need to use more math. I use simple percentage equations to calculate my combat even if its not dead accurate it feels about right. I liked most of the combat values from the original game so basically I kept the same ratio of OvsD, but made the numbers bigger.

For example:

Lets say a tank has 3 parts combat points total. Lets say 1/3 was spent in defensive points, and 2/3 on offensive points. I would still keep the ratio 1/3 D and 2/3 O, turn it to percentage to understand it better, and increase their numbers. They will still be proportionate to what it use to be, but bigger. If it felt wrong I adjusted it till it felt right in my tests.

For rate of fire, and bombard I never really liked the randomness of the normal game. A RoF of 3 would mostly yield 1-2 attacks very often, so I changed it without really looking at the math. I just adjusted it to taste while testing the rate in test scenarios. Some units have a guaranteed set of RoF because of my values, and some are more random but not so random like vanilla. I did it also because I wanted some specialized units like cruise missiles that would hit hard no matter what (mostly a Rof of 3-4 consistently)

I'm more comfortable when I play knowing what I can count with, whether it is a guaranteed RoF of 3, or a high chance of being intercepted, so I didnt bother much about the math there.

Lets just say I'm not a friend of randomness lol. If you ever played world of warcraft you'll know what I mean. I depised how my attacks would not crit when i needed them to crit, and always aimed at maximizing consistency.

While not accurate I have a general idea of how combat is supposed to feel, so I go by that. An example of my philosophy goes like this:

-If a unit is offensive go 10/1
-If a unit is defensive go 1/10
-If a unit is versatile go 5/5

It goes the same for all my units, then I go in and fill in the blanks to give the units a bit more variation instead of a plain 10/1, 1/10:

-Modern Tank 10/4
-Mech Infantr 4/10
-Tow infantry 5/5 + bomb+RoF

If the AI build priority goes crazy I'll adjust until it works.

So far this feels about right to me

 

[walletta]

If you intend to comprehend the game you need to understand them. But if you are fine with lacking the finer understanding of the math at work you can play at least at the lower settings and have fun. Although i have trouble understanding how missing the fun part is fun.

Depends on your idea of fun I guess. Whatever, I made Deity with no math so it can be done!

 

[Buttercup]

I'm not a fan of random either, as many on the board will testify. The way I see it is:

If you have an attacker with 10/1 attacking a defender with 1/10, then the only random you need mathematically is a 50% chance of who wins each hit point - and this would be the most random possible encounter in the game. So the only math you'd need would be a 2 sided dice per round (or, coin flip) for both players.

If you have an attacker with 10/1 attacking a defender with 1/5, then the attacker should have a 2 to 1 advantage, so the dice should just be changed to reflect that, the attacker uses a 10 sided dice and the defender uses a 5 sided dice.

What I find annoying about Civ 3's mathematics (if the formulas quoted on the forums are even 100% correct), is that it's vastly over complicated for no other reason than being vastly over complicated. Games like this evolved from dice games and replacing the dice with something more complicated is alienation for the sake of alienation.

There would also be no harm in removing the random altogether from a gameplay perspective, so that if a 10/1 attacked a 1/5 then you could be guaranteed a win but always with 50% of your health gone. It really doesn't change the game that much, it actually makes it more tactical because you can accurately, very accurately, manage your empire. It doesn't matter about realism because games are not about realism, they're about enjoyable gameplay. Also, massively convoluted RNG still produces a simple long-term average that is the same as if you made each individual fight static in result, convoluted RNG just punishes smaller stacks via wider result ranges.

While it might be 'fun' to have the odd unpredictable result, it can never be more fun than having an easily understandable and simple system. The difference being that if you understand why you lose then you can accept it, but if you lose to RNG then you have no choice but to feel 'unlucky', which is a completely different emotional response. An understandable loss is more in keeping with a game designed to test your number crunching skills than an unlucky loss which is more akin to games like casino games. We're not betting for money here, we're just trying to play a management game.

So with dice you can add some low level random to spice things up that tiny little bit, provide that glimmer of hope in very close encounters if you want random, but having diabolically complex equations that are hidden behind a sound effect and animation alone is just silly and does more damage than good. And it's the ridiculously complex which causes Tanks to explode attacking Spearmen.

Let's say the spearman is well defended and we have 16/8 attacking 1/4. Even with dice the Tank should have a 4x advantage each roll, so the tank rolls a 16 sided dice and the spearman a 4 sided dice. However, the Tank has a defence value above 1, so now we have to find a way to make the Tank's defence stat relevant, to which it seems logical that the Spearman's victory only applies one eighth of the normal damage. With a really simple system like this you now have complexity in simplicity while making close battles still interesting but no longer will a tank lose to a spearman - because the Spearman, even with an extra 100% defence, would have to beat a 16 sided dice with a 4 sided dice between 8 and 40 times to defend against a tank, leaving only the red-lined Tank as even statistically remotely possible - and, as a bonus, if a Spearman ever did defend even a regular Tank then that would at least be an interesting screenshot rather than a facepalm meme.

So, from my point of view, the over-complication is more like someone trying to hide a lack of actual game-making skill, like a salesman spewing jargon, rather than something to take genuine interest in or aspire to.

 

[Lanzelot]

@ZergMazter: Don't be too intimidated by the formulas. The guys who discovered them, had one (or several) of the below advantages:

• Acces to the source code of the game, so they could simply copy the formula from the code itself (Firaxis programmers and/or their buddies, who in the old days posted here or over on Apolyton.)
• Knowledge of the .sav file format, so they could read certain values from the auto-save files. (This is how CivAssistII and other tools work).
• Lot's of time to conduct 10.000s of test runs and then reverse-engineer the formula from the test-data.

These formulas (whether it be the flip risk, the probability for shooting down a plane or the corruption-percentage of a certain town on a certain tile of the map) cannot be deduced by just playing the game or reading the manual... (If that consoles you...)

@Buttercup: I think with the combat system in Civ5 they went a big step into the direction you are describing. There is still a little bit of randomness, but not so much that it annoys you or makes you feel unlucky. You know pretty well in advance, what to expect from each single battle. Let me give an example:

Each unit has 100 hit points and a "strength" value (which gets modified by terrain, fortification bonus, unit promotions etc.). The relative strength of the two combatant's "strength" values determines how much damage each unit will take in the fight. For example, if your unit attacks an enemy unit of same strength, the defender being un-fortified and on grassland, then each unit will take between 28 and 38 hitpoints damage. So "on average" both units will take 33 HP damage. (The game calculates and displays this average value for you, if you activate your unit and move the mouse over the unit you are planning to attack.) So you know in advance that no matter how unlucky the dice-roll is for you, you will inflict a guaranteed minimum damage of 28 HP on your enemy, while your own unit will not be suffering more than 38 HP damage at most.

This is quite an improvement over the Civ3 combat system, where in a battle between two 4/4 units any outcome between "I win with 4/4 left" and "he wins with 4/4 left" is possible, isn't it?

And even better: the minimum guaranteed damage can be bigger than 100. So if for example a modern armor with strength 100 attacks a spearman with strength 11, the "window" of the inflicted hitpoint damage may be "127 - 147" (meaning the spearman is dead 100% guaranteed), while the "window" of suffered damage would be "1-3" (meaning just a few scratches on your armor). So these ridiculous outcomes that may happen in Civ3 are impossible in Civ5.
(Note: the numbers given in the example above are not the "correct" ones, just some plausible ones close to what I remember from the game so as to give you the idea.)

Also the feature that you don't need to do the number crunching yourself, but the game already displays the average damage for both sides, when you mouse-hoover over the target unit, is very nice. Then you can decide in an instant, whether you want to risk the attack or better retreat and wait for more reinforcements in order to get a "sure kill".

Of course the above is a bit simplified. There are also "bombard" values for artillery type units, ship units and planes, and "strength" values for ship-vs-ship or plane-vs-plane battles, etc. But it's not "over-complicated" -- rather quite well thought-out.

(There are, however, other aspects of the game, which are not as well thought-out -- but hey, that's Firaxis... we are used to it, aren't we... )

 

[Buttercup]

What we need is Civ 3 with: a Civ 5 combat (but allowing stacks) mod, a Civ 4 corruption and pollution mod and a Civ 2 tech speed mod

 

[walletta]

Gotta say I don't mind the Civ 3 random element. It makes the game, err .. realistic. I once had a curragh that circumnavigated the globe despite being set upon by more powerful vessels along the way. What might be nice would be if an individual's prolonged success in combat was 'remembered' by the game and resulted in that unit becoming more likely to produce a GL. Then the randomness would seem more meaningful.

 

[walletta]

Also the feature that you don't need to do the number crunching yourself, but the game already displays the average damage for both sides, when you mouse-hoover over the target unit, is very nice. Then you can decide in an instant, whether you want to risk the attack or better retreat and wait for more reinforcements in order to get a "sure kill".

Wait. What?

 

[Lord AJ]

You don't really have to do all the math. I just remember and make a mental note when I see a formula that what is the most important/influential/significant factor in that formula and while playing I keep that in mind. Sometimes, saying the formula tells me what I had been doing wrong all this while and I make it a point to correct it when I play. There's really no need to calculate everything. For me, I'd rather say that attacking an unfortified spearman on a size one town with a cavalry or tank is likely to end in a success for me so I'll do it rather than calculate exactly how likely is my success.

 

[Lord AJ]

Gotta say I don't mind the Civ 3 random element. It makes the game, err .. realistic.

Seconded. Without the randomness, the game just won't be as enjoyable. I agree it's frustrating losing armies to flips or losing elites to much weaker units but this same randomness helps cavs defeat stacks of rifles at the higher levels or a spearman to defend a border town for a couple of turns until reinforcements arrive. Also, knowing how a battle would end will simply make things too easy. You could, theoretically, finish a game without a single casualty. Is that an enjoyable idea. No, methinks.

 

[ZergMazter]

Seconded. Without the randomness, the game just won't be as enjoyable. I agree it's frustrating losing armies to flips or losing elites to much weaker units but this same randomness helps cavs defeat stacks of rifles at the higher levels or a spearman to defend a border town for a couple of turns until reinforcements arrive. Also, knowing how a battle would end will simply make things too easy. You could, theoretically, finish a game without a single casualty. Is that an enjoyable idea. No, methinks.

I think not being random is more realistic. Reason:

-Just an example-

A tank takes a defensive spot on a hill, and some poor bastard attacks. Even though the attacking unit is the attacker, a tank from a hill will see the enemy first, therefore it will attack first even though it's 'defending', and realistically speaking the 'defending' tank would fire first since it has the advantage in a real situation.

Randomness will not let that happen. A tank with the strategic advantage will have a good chance to lose against an even power unit, just because the numbers say so, instead of having an almost guaranteed chance of wining since it will basically be an ambush on the attacker.

Randomness in the game is like gambling. You will win some and lose some even if you have an incredible strategic location. Taking randomness away makes controlling specific locations a real tactical advantage.

An example of real tactical advantage without randomness would be:

-X2 tanks (10/2/1)
-A hill with a 1000% defensive bonus

On normal terrain the attacker will almost certainly win, because it ambushed(or whatever you wanna call it) it's opponent.

On a hill the attacker will almost certainly lose because, even though it is the attacker, the tank on top of the hill will see it coming and open fire first.

Though the game mechanics don't work like this, by using the hill example it would simulate this and the outcome will be the same both in game and real life. That's what I call realistic. This also makes tactical positions much more valuable and a whole lot of fun since this is one of the few things the AI does well. It knows what terrain gives the best defensive bonuses and prefer to end a turn there.

Anyway back to topic, randomness just feels like a gamble each turn to me and very unrealistic for the reasons I mentioned. Units that shouldnt die easily end up dying anyways. Why would the undamaged unit on the best strategic location die on the very first engagement? Not cool and I dont like it lol.

 

[Lord AJ]

Sure the randomness takes the realism away but why have realism when it may tilt the game unrealistically into one direction.
Continuing your example...
If that tank (or a German Panzer) stays on that Hill and attacks a town (which will have no walls since it's a town) and every turn it kills as many units as it's movement points are without taking a scratch on its armor unless the town has a Fighter jet stationed there. This would continue until that city has been captured. Rinse and Repeat.
Conversely, you can exhaust all of your army attacking a city that's built on a hill but you'll never be able to attack since the defenders spot you first and finish you before you can attack. This city will be completely immune to invasions until the advent of Planes. Would we want this game play? I doubt.

 

[Buttercup]

Gotta say I don't mind the Civ 3 random element. It makes the game, err .. realistic. I once had a curragh that circumnavigated the globe despite being set upon by more powerful vessels along the way.

Doesn't the premise of this point contradict the in-game example?

Then Atishay takes the "realism" part of the quote and says:

Seconded. Without the randomness, the game just won't be as enjoyable. I agree it's frustrating losing armies to flips or losing elites to much weaker units but this same randomness helps cavs defeat stacks of rifles at the higher levels or a spearman to defend a border town for a couple of turns until reinforcements arrive. Also, knowing how a battle would end will simply make things too easy.

Which, again, just contradicts "realism" and is based on examples where denying realism is what you prefer. Are you more a poker fan than a chess fan? Do you think chess could be improved by 'random'?

You could, theoretically, finish a game without a single casualty. Is that an enjoyable idea. No, methinks.

Well, there are many games on the market that are tactics/strategy based and are quite easy to win, but their main draw for experienced players is seeing how many extra points you can score from completing the game with the fewest casualties possible, this concept being fully integrated into the game's design - so, yes, a lot of people think that "is an enjoyable idea".

 

[Lord AJ]

Which, again, just contradicts "realism" and is based on examples where denying realism is what you prefer. Are you more a poker fan than a chess fan? Do you think chess could be improved by 'random'?

I do think that in civ 3, the game is much more enjoyable without realism. This is clear from the reply I gave to ZergMaster. In the real world, cavalry would seldom defeat musketmen and longbows can reduce an army to half before it even gets a chance to strike. But if all this is implemented in this game, we'll end up having a handful of invincible units and several other weak units that'll distort the balance of the game. So, my opinion is that unrealistic game play isn't bad. In fact, it's what works the best for Civilization 3.

Well, there are many games on the market that are tactics/strategy based and are quite easy to win, but their main draw for experienced players is seeing how many extra points you can score from completing the game with the fewest casualties possible, this concept being fully integrated into the game's design - so, yes, a lot of people think that "is an enjoyable idea".

The concept may be enjoyable in other games. In fact even I have played the Age of Empires 2 and I enjoyed doing it. But it's implementation in civ 3 is, what I think, won't turn out to be fun.

 

[Theov]

Without randomness, it wouldn't be a game.
If you don't want to lose, bombard.

 

[Buttercup]

That's a really weird perspective. There's already virtually no random in the game, because since you know where the random is you just account for it by applying your own best method to remove the random - you're contradicting yourself:

"Without randomness, it wouldn't be a game" so I use "bombard" to minimise the random. Because you don't actually like random, otherwise you'd be happy to go toe-to-toe with just units, you only claim you like random because the game makes you feel intelligent by providing units that reduce the random.

And as a side note, I just finished a game where I had virtually no random whatsoever, I could have had any of 3 different victory conditions, of my choosing. The only random elements were:

Pollution - which I chose to minimise via refusal to build factories or hospitals.
Combat - I used Bombers exclusively to sink boats before troops could land and those that did got bombarded then Tanked/Modern Armoured, thereby minimising the random to its minimum. I let a few land to try and generate a General.
Military Leaders/SGLs - both positive random, I got 3 or 4 SGLs but no MGLs

The only event in the game which made me unhappy was an Elite Modern Armour getting red-lined attacking a red-lined Ancient Cavalry not fortified on a mountain. Well, to be fair, there were 3 AC on the mountain in various states of red-line and the MA took all 3 out, but the last one, which was red-lined, took my MA from 3hp to 1hp, which almost got a facepalm out of me had it died.

And this is where some people don't seem to understand random in games. Yes, things like positive random, such as SGLs, are cool in games. Yes, having 2 spearman face-off with unpredictable results is cool. Ok, we're all agreed, random can be 'fun' - but don't try to pull in the absurd random as in any way enjoyable - no-one, and I mean no-one, likes watching the best unit in the game struggle with Ancient Age crap. It devalues the entire point of the game...

 

[ZergMazter]

That's a really weird perspective. There's already virtually no random in the game, because since you know where the random is you just account for it by applying your own best method to remove the random - you're contradicting yourself:

"Without randomness, it wouldn't be a game" so I use "bombard" to minimise the random. Because you don't actually like random, otherwise you'd be happy to go toe-to-toe with just units, you only claim you like random because the game makes you feel intelligent by providing units that reduce the random.

And as a side note, I just finished a game where I had virtually no random whatsoever, I could have had any of 3 different victory conditions, of my choosing. The only random elements were:

Pollution - which I chose to minimise via refusal to build factories or hospitals.
Combat - I used Bombers exclusively to sink boats before troops could land and those that did got bombarded then Tanked/Modern Armoured, thereby minimising the random to its minimum. I let a few land to try and generate a General.
Military Leaders/SGLs - both positive random, I got 3 or 4 SGLs but no MGLs

The only event in the game which made me unhappy was an Elite Modern Armour getting red-lined attacking a red-lined Ancient Cavalry not fortified on a mountain. Well, to be fair, there were 3 AC on the mountain in various states of red-line and the MA took all 3 out, but the last one, which was red-lined, took my MA from 3hp to 1hp, which almost got a facepalm out of me had it died.

And this is where some people don't seem to understand random in games. Yes, things like positive random, such as SGLs, are cool in games. Yes, having 2 spearman face-off with unpredictable results is cool. Ok, we're all agreed, random can be 'fun' - but don't try to pull in the absurd random as in any way enjoyable - no-one, and I mean no-one, likes watching the best unit in the game struggle with Ancient Age crap. It devalues the entire point of the game...

Yes that's it. You took the words right out of my mouth. That's exactly what I mean about not liking random, and what I do like about it.

 

[Theov]

That's a really weird perspective. There's already virtually no random in the game, because since you know where the random is you just account for it by applying your own best method to remove the random - you're contradicting yourself:

"Without randomness, it wouldn't be a game" so I use "bombard" to minimise the random. Because you don't actually like random, otherwise you'd be happy to go toe-to-toe with just units, you only claim you like random because the game makes you feel intelligent by providing units that reduce the random.

And as a side note, I just finished a game where I had virtually no random whatsoever, I could have had any of 3 different victory conditions, of my choosing. The only random elements were:

Pollution - which I chose to minimise via refusal to build factories or hospitals.
Combat - I used Bombers exclusively to sink boats before troops could land and those that did got bombarded then Tanked/Modern Armoured, thereby minimising the random to its minimum. I let a few land to try and generate a General.
Military Leaders/SGLs - both positive random, I got 3 or 4 SGLs but no MGLs

The only event in the game which made me unhappy was an Elite Modern Armour getting red-lined attacking a red-lined Ancient Cavalry not fortified on a mountain. Well, to be fair, there were 3 AC on the mountain in various states of red-line and the MA took all 3 out, but the last one, which was red-lined, took my MA from 3hp to 1hp, which almost got a facepalm out of me had it died.

And this is where some people don't seem to understand random in games. Yes, things like positive random, such as SGLs, are cool in games. Yes, having 2 spearman face-off with unpredictable results is cool. Ok, we're all agreed, random can be 'fun' - but don't try to pull in the absurd random as in any way enjoyable - no-one, and I mean no-one, likes watching the best unit in the game struggle with Ancient Age crap. It devalues the entire point of the game...

With bombardment, I play the game and put the odds in my favor. Where is that contradicting?
Where do I say I 'like' random. I like randomness, but I like it also that I can play with the odds.

Your expamples of 'positive' randoms and 'negative' is just naive. You can expect to lose a tank to a spearman from time to time. But you also know - that will only happen once a Bengals Super Bowl appearance. Just because it makes you unhappy doesn't mean the dice should be thrown away.