Bring Back Probability Curves!!!

[FinnMcCool]

Let's take for the sake of argument, that the formula for calculating combat odds is A/(vA+vD)
where vA is the Defender's Attack value plus mods, and vD is the defender's Defense value plus mods.

The more I play this game, the more I realize something isn't right. It's purely an impression mind you,
so I'm actually posting about the player's IMPRESSION, and not any mathematical formulae. Basicly,
it boils down to the RNG and the esoteric factors of probability curves and variance. Please don't skoff,
and read on, fellow gamers: "probability curve" only happens when more than one randomizer is used.
If only one RNG is used, there is NO CURVE. And variance only refers to the range of the RNG.

There was a big hairy argument in a thread I posted earlier, regarding whether the odds formula is
accurate, since there are so many cases where a spearman can kill a tank. I was summarily cast down for
even suggesting such a thing, and I'm convinced Dangerboy is accurate in his description of the odds formula.
There is an interesting phenomenon we are witnessing here, though, and it hasn't been brought up. So I'll
break the ice.

They say there are three kinds of lies: lies, damn lies and statistics. If you arrange a combat between 500
Archers against 500 Spearmen, and tabulate the results, you will in fact have a STATISTICLY ACCURATE
description of the odds for these units' combat outcomes. But your findings will have very little to do with
what it's like to play the game. You have to play 500 combats to achieve these results. When you reduce the
number of events, an interesting thing happens. Variance becomes more and more significant. I'm using the
term "variance" out of context, but I'm using it in it's traditional sense, not in the specialized meaning used in
statistics. With no probability curve, any number has an equal chance of coming up in the RNG, which basicly
MAXIMIZES "variance". This doesn't change any statistical conclusions at all. But it means that in INDIVIDUAL
attacks (which are how we experience them in play) there is a large probability in any given single combat, that
my strong, elite unit will lose against a weak conscript. There is also an equally large probability that my weak
conscript will survive an attack from a strong, elite opponent. Hence we see events like a spearman killing a tank.

This shouldn't be eliminated. I believe it can happen (molotov cocktails, tank traps, etc) but I seriously suggest
it should be MINIMIZED. I've hashed out probability curves with professional designers, and they agree that a
curve gives the game rules greater control. With no curve (using only a single RNG) the game rules are literally,
"OUT OF CONTROL"... Spearmen kill tanks...

USE PROBABILITY CURVES. In any RNG line, use multiple RNGs within the range to create a curve, it helps add
to the player's sense of "predictability" and adds some value to strategy... rather than relying on randomness.

 

[warpstorm]

Well, if you and your opponent both have more than one hit point in the current system you are getting more than one RNG roll per combat (the minimum number of rolls is the lower number of hit points, the max is the total number of hit points for both units minus one). I don't see the difference for most combats (with the exception of the single hit point combatants where it is linear (but skewed towards the unit with the highest combat factor)). As you get more rolls, the outcomes will tend to form a nice bell shaped curve as it is.

Are you positive you understand how the combat system works? How many tanks have you personally lost to a spearman? I've lost exactly one. How many spearmen have been mowed down by my tanks? Countless.

 

[FinnMcCool]

Thank you warpstorm for your considered reply. I've had so many heated debates with designers and players both, about this very subject I was afraid I'd be run outta town under a hail of cabbages Some people actually like flat probabilities, saying it adds to variety. I've found that the people who like curved probabilities are the more obsessive strategists like me.

That said, you're partially correct describing combat. Only partially, and my initial post isn't meant to focus on combat only anyway. In general, any random decision made by the AI can become chaotic if a flat probability is used, and I'm hoping the Civ4 team will at least take it into consideration.

But regarding combat, my initial idea still applies. If you think about "a combat" as an event, sure, there are multiple RNGs, which gives it the appearance of a curve. But "a combat" isn't one event, it's many rounds, and in each individual round, there's that nasty flat probability. Similarly, if you consider ALL your combats as "combat" then yes, a probability curve will emerge, but only after MANY combats. Still, as the game is played, they're done one at a time, which makes statistics less meaningful (meaningless, actually...) I'm only suggesting introducing a curve in the initial equation, to give those wild results less probability.

And if a RNG is used in any other scenario (such as diplomacy? hm?) it definitely should be curved. Deeply. Adds to a little predictability. I get tired of being backstabbed by a "stalwart ally"...

 

[Civrules]

Yeah, it looks like the Civ IV combat system will have (almost?) none of the spearman defeating tanks.
Personally, I don't know if the land combat portion of Pirates! has anything to do with how it will be represented in Civ IV, but I've found that system they use in Pirates! to be very effective. It seems much more stiff. And I really like it.
All this combat thing becomes even more realistic when different variables are thrown in.

 

[FinnMcCool]

That's comforting to know, thanks.

I haven't played Pirates! but maybe I'll try it, now.

 

[The Last Conformist]

This is basically IbnSina's idea for a normal-distributed pRNG, and it's bad bad for the same reasons; it makes things less transparent, and instead of fixing a (perceived) problem - here the frequency of "odd" combat results, in the other thread that of culture flips - it changes something only tangentially related that will affect plenty of other parts of the game. Do we really want a combat system fix to affect what free tech we get when a Scientific civ hits a new era? Whether suicide galleys sink? Whether espionage missions success and what direction barbarians move?

 

[warpstorm]

TLC, you don't need to use the same RNG scheme for every random event. You could have a normal distribution for those events where it would make sense and a linear one for those more simple ones.

Finn, sorry for any antogonism. I'm just saying that with the current scheme it approximates a normal distribution with enough hit points per unit (of course this breaks down when there are two or less hits left).

Personally, I do like the current scheme.

 

[IbnSina]

Warpstorm is right. One does not need to use the same pRNG for everything. It's just a function call - I could produce a half dozen different pRNG schemes in half an hour, if required.

Warpstorm is also right in that in enough trials of the current uniformly distributed pRNG we will arrive at normal results. I am quite satisfied with the current system when my SOD of 24 cavalry attacks an enemy city containing six defenders. Still, if a single veteran cavalry attacks a single veteran spear, as happens often behind the lines when enemies attack from overseas, then that is, at most, seven trials of the RNG - not enough for the Central Limit Theorem to be of any use.

Recently I had a game in which an enemy made a "sneak attack" that I had forseen. I had placed my city on a hill, and fortified a spear and an archer in it. My enemy attacked "without warning", using two warriors. Both warriors won, taking the productive city from me in spite of my planning. How is that fun?

It is hard for me to understand why we must put up with a combat system that gives predictable results for large battles, but which can utterly destroy our strategic planning and calculations in the small battles that take place behind the lines or at sea or early in the game. The game is not fun when careful planning and due consideration are made a mockery by a die roll. I don't think it is unreasonable to demand the same level of consistency in small battles as in large battles, and it is not technically difficult to implement it. I am at Firaxis' service, if they need help with this.

 

[ybbor]

Let's take for the sake of argument, that the formula for calculating combat odds is A/(vA+vD)
where vA is the Defender's Attack value plus mods, and vD is the defender's Defense value plus mods.

THE DEFENDERS ATTACK HAS NOTHING TO DO WITH IT!!! IT'S THE ATTACKERS ATTACK!!!

and there is no mods in the attackers attack

 

[Aussie_Lurker]

Whoah, take a 'chill-pill' Ybbor, you'll have an aneurism if you're not careful ! I'm sure he MEANT to say attackers attack. I can't remember the number of times I have said the exact opposite (or close to) what I meant to say-usually because I am writing too fast !
Anyway, as I have said-probably ad-nauseum -there are two key issues at work here.
The first is that the whole 'spearman vs tank' thing makes people think that this is LITERAL!! The fact is that I have NEVER lost a tank to a spearman however, I understand that this 'phenomenom' refers to a more general problem of clearly obsolete units winning victories 'against the odds'-sometimes with barely a scratch to show for it !
This brings me to the second issue, just because unit A cannot damage unit B (due to an excellent defensive position, for instance) it DOES NOT logically follow that unit B should damage unit A instead-yet this is EXACTLY what the current combat system assumes. That if unit A has only a 45% chance of hitting unit B, then unit B automatically has a chance of damaging unit A. What we need is a system which allows for a STALEMATE, where NEITHER side is able to score a decisive hit during a single attack 'pulse'. This way, your spearman can theoretically hold out, in its fortified mountain retreat, against a tank indefinitely. The tank, however, can keep pounding away at said spearman ad-infinitum with little to no chance of getting hurt itself. The decision then is if said spearman is worth the effort, or whether there are other units better suited to the task, thus freeing up the tank for more appropriate attacks!!
Anyway, thats how I see things, personally!!

Yours,
Aussie_Lurker.

 

[Synergy67]

I think you're really on to a simple and elegant solution to this conundrum, aussie. I like the idea of stalemates. I hadn't really thought of the problem with unlikely battle outcomes being so linked to the automatic damaging of one unit or the other instead of the possibility that no one takes damage. Good thinking. I wonder if the solution really is as simple as introducing this feature into battles?

 

[Aussie_Lurker]

Well, Synergy, consider this:

Under the current system, if a veteran tank went up against a fortified, veteran spearman, then the tank would have an (16/(16+4))=80% chance of scoring a hit. Now, in my system, this would STILL be the case, but the spearman would have a (1/(1+8))=11% chance of hitting on a counterattack. Now, consider these 8 random numbers I generated on my calculator:

0.33; 0.73; 0.81; 0.66; 0.95; 0.17; 0.95; 0.31.

Now, in the existing system this would result in tank hits, tank hits, spearman hits, tank hits, Spearman hits, tank hits-spearman dies. Now, I admit that this is NOT spearman beats tank but it does result in the tank losing 2 hp against just a lowly SPEARMAN (or half its HP's). Heaven help us if there are two or more of these spearmen on this particular mountain!!!! Or, worse still, imagine if it were a pikeman instead, the tank might actually be at risk of being killed-by PIKES!!!!

Now, in MY system, these same numbers:

0.33; 0.73; 0.81; 0.66; 0.95; 0.17; 0.95; 0.31

would produce the following result: tank hits, spearman misses; tank misses, spearman misses; tank misses, spearman misses; tank misses, spearman misses.

So, the combat goes a bit longer, as the veteran spearman has only lost 1hp but, more to the point, the tank has YET to lose a hp!
Lastly, this only accounts for an attack/counterattack system. If you reintroduced firepower, as well as scaling all of your hps over a greater range, then things would be even more cut and dried in favour of the much more advanced tank!!!

Yours,
Aussie_Lurker.

 

[warpstorm]

I like the possibilty of a draw. It just feeels right. This could slow down a drive without giving really wierd results (in the long run, there would still be the occasional really improbably yet still technically possible result).

 

[IbnSina]

Yes, draws could be good. It's one of the things I have always appreciated about football...

 

[jst666]

About the stalemate...

In one war strategy game, some quite crappy shareware on windows, there was a rather nice idea. If an attacking unit had let's say 4HP, and 4MP; while defender had 4HP. If the two units were 1 square apart, the attacker could in no way defeat the defender, cause it used 1MP for moving, and attack once, twice, thrice. Each attack would take one HP of the winner of the battle.

Something similar I might like to see in a CIV, in a sense that an attack would not necessarily cut through the defender, but just take his HP down. And the suffered unit would then be replaced by a next in stack for the next attacker.

 

[Enkidu_Warrior]

It's purely an impression mind you,
so I'm actually posting about the player's IMPRESSION, and not any mathematical formulae.

finn, your post begins with the above quote, stating that it is your perception that drives your frustration with combat results, and not game mechanics.

as such, dont you find recommending a game mechanic solution even just a little ironic? i do. ironic and ludicrous.

...in INDIVIDUAL attacks (which are how we experience them in play) there is a large probability in any given single combat, that my strong, elite unit will lose against a weak conscript.

[bolding added]
with the bolded statement, your lack of understanding of statistics is grossly apparent. comments such as this one are not only erroneous and misleading but also damaging to people's understanding of the game.

please dont make me give you a lecture on statistics. i do enough of that at work.

------------

on the other hand, aussie_lurker has an interesting suggestion.

my only concern would be war stalemate: that is, an inability to fully prosecute a war within the timelines of the game. it's bad enough that you can get stuck in an ancient age war lasting 1000 years (for example) with the current system, but a combat system including stalemate would require a radical re-working of timelines/turn structures in order to remain even remotely historically reasonable.

for example, maybe for each turn you have production calculated and set at the start, but then within each turn you conduct 5 "combat" turns, for units only.

however, it doesnt seem realistic that we could expect civ4 to involve any radical re-workings such as this. not "profitable".

EW

 

[Aussie_Lurker]

Well, Enkidu Warrior, I'm not talking about DRAWS in the overall combat sense, as we assume that a single civ battle is in fact a number of smaller engagements (or, at least, I DO !) What I am talking about instead is that within a combat PULSE (i.e. a single attack/defense action) there is a chance that neither side will come out with a damaging hit. Within overall combat, however, things will continue until either either side holds the field triumphant (i.e. one side completely killed or retreated) I accept, though, that even if this applies to just combat pulses, it WILL make each combat last longer, which is why I also strongly support a multi-unit combat system, where every unit in a stack fights against every unit in the other stack AT THE SAME TIME!!!

Hope that clears things up a bit !

Yours,
Aussie_Lurker.

 

[Enkidu_Warrior]

aussie_lurker - it sure does. i like the idea of multi-unit combat, as well. the possibilities of how that could work would make for more tactical thinking, which would of course create more strategic possibilities.... the more i think about it, the more i like it.

that said, i was getting pretty enamored with a mutliple unit-moves per turn idea, as this would overcome some of the silly limitations of the movement system... but there's probably better solutions for that independently.

EW

 

[Aussie_Lurker]

Having looked more closely at your post E_W, I must say that your idea for restructuring turns DOES have great merit. I, for one, have long backed the idea of every player having their 'non-combat' phase first, followed by the resolution of all conflicts resulting from the moves each player made. Then, it would go back to the non-combat portion of the next turn. Just because its 'radical' though, doesn't mean it won't be in!

Yours,
Aussie_Lurker.

 

[Admiral8Q]

Um? I find the probability in Civ3 perfect.