battle calculator

Do you have suggestions or ideas for improvement, post them here and we will them out.

Re: battle calculator

Postby KGB » Wed Apr 11, 2012 5:07 pm

Fordus,

Fordus wrote:KGB misses the point... As long as it's possible to know battle mechanics and individual battle strenghts, calculators cannot be disallowed. You can try to prevent their use, but it'll probably fail.

Hiding bonuses won't make calculator obsolete or unusable, it would just require bit more assumptions based on experience


Except that if you hide all the numbers for the bonus's and individual units, randomize the maximum dice roll and add new features like buying extra strength units no calculator can help you. Yes, it can give you an 'estimate' of the odds, but it can't give you the true odds since it won't know them. The difference between being 70% or 80% likely to win is quite a lot so if you can just obscure enough information to put a 10% fudge factor in the game it will make calculators vastly less useful. So yeah, you can make some assumptions but thinking you are 90% likely to win when you are only 80% could cause your hero to die.

Fordus wrote:As for your poker example, online players have programs to calculate exact odds. Some sites try to prevent it, but it's easily circumvented by smart phones, secondary computers or some other means.


I don't play online poker for this reason. Also the other reason I don't play online is I can't pick up a persons 'tell' when they aren't physically there. Face-to-face games are a whole other animal from online play. I liken online poker to playing games with the AI and face-to-face games being ladder style.

Maze wrote:"Good"(*) news! Battle calculator will become available (probably) this week with the release of Warbarons 0.8!


As noted in that thread I think this is a bad decision for the game. Ultimately, the moment that 'simultaneous turn' mode comes in another Beta I will stop playing anything but those games simply to avoid the calculator which besides providing exact odds, punishes the defender due to fight ordering.

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Re: battle calculator

Postby LPhillips » Thu Apr 12, 2012 5:27 am

Simultaneous/speed games may become the new standard if people really do lean on the calculator. Playing by numbers is for people who aren't in it to play the game, but rather to feel like they've won. That is the difference between people with KGB/Moonknight's point of view, and people who argue endlessly that as long as someone might gain an advantage over them by peeking, the wizard's curtain must be torn down so that everyone can see.

Some of us want to play a strategy game. The most apt analogy to Warbarons is indeed Poker: the death knell to Warbarons will be the day it becomes online poker, gaming by numbers. Then all strategy and intrigue disappears, and it is basically equivalent to the button-pressing grindfests which dominate the attention of millions of pubescent children online already. Warbarons is more than gaming by numbers, and the legacy it continues is more than that. I don't think you understand the price of what you're asking when you demand to remove the mystery from the game and begin to hold players' hands to try to make everything equal and fair.

(note: I'm not being ambiguous, I'm being extremely precise. If a person's understanding about "mystery" and "intrigue" is ambiguous, then my comments will appear so. Please inform me of any way I can help us to come to a mutual understanding, such as elaboration of terms.)

---------

Many of the posts and arguments are in good faith, but a generous portion of them are also laden with latent elements of modern thinking: Everything must be made equal so that no one is at a disadvantage. This is moronic and boils down to removing all incentive for the individual to strive; in fact it punishes effort and striving by removing its natural rewards.

We have no duty to level the playing field with aids like battle calculators. Some of us are smarter than others, and we all think differently than others. I'm a creative analytical thinker, and KGB is a utilitarian analytical thinker (to oversimplify matters). We approach different problems different ways, and our different thought patterns and capabilities produce different conclusions. In short; I'm unpredictable but effective, he's coldly precise in the crushing manner of WWII's German Army (the most effective fighting force in history). We get to have fun because we're different. A battle calculator is a step toward gaming-by-numbers, where our choices are made by calculating the odds and not by strategy, wit, nor even human thought. It's linear. It's a deadzone for thought and for any elevated form of entertainment.
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Re: battle calculator

Postby hungrytales » Thu Apr 12, 2012 10:06 pm

KGB,

this is my delayed answer to the big post where you dissected my argumentation point by point (I feel flattered you took time to do that, btw). As it seems we ventured dangerously close to tl;dr area I'll try to be brief(ish).

First section was about my missing an actual description of exact battle phases being posted on the forum. If you meant the thread titled 'Beta4 Bonus System Question' - it's indeed long and a little convoluted too, but I thought I followed it through well enough and came out with nothing definite. But maybe I did miss sth. Guess there's no other way, no willing soul wanting to prevent this and I'll have to look there again :P. Nevertheless at least one thing is certain - it's clear I was aware of the thread. In my request for battle phases info I happen to quote one of LichKing's posts from it.

OK, let's move further. Last section - well, I wasn't aware you actually propose to change dice without a proportional change of units' strengths! I must say I'm kinda shocked :shock: . It's nothing short of changing the game rules on the fly. Now, if you propose to introduce some factor which influences battle odds in such a way as to reflect/simulate some real-life (or fantasy-life for that matter) mechanic/property - ok, that's fine. But even then I WANT TO KNOW how that factor works. Only then it becomes a part of the rule set and therefore a part of the game. Otherwise it's not a game it's randomness, it's pure chance, it's turning from a nice strategy with clear set of rules to a "game" of coin-tossing and hell I don't like it :evil: .

And that in turn prompts me to move another step to comment on the rest of your post which actually boils down to: MORE RANDOM. That was what I actually meant by pointing you to the 90% rule thread where (I'm still pretty sure of it, but I still haven't checked) you argued for LESS RANDOM (and hence justified 90% rule existence). I honestly think, KGB, you kinda shoot yourself in the foot coming back to those poker analogies, because that way I even don't have to bother with my own examples, cause, seriously...poker? Well, that's is EXACTLY the point. Sure I don't want Warbarons anywhere near the poker's league of randomness in games.

If someone showed up at a Hold-em Table with a poker book that contained all the odds for the hands or had a computer program that listed those odds and advised you of the bets to make you'd be asked to leave.

Sure you'd be asked to leave. Those odds are ALL the strategy there is in poker. It's not the case with Warbarons. Completely, totally, outrageously NOT. And we ought to strive for it to remain that way.

This is also why I put in the wish list the ability to buy production with extra strength because with hidden numbers no one would know when you bought better units and when you didn't and so no calculator could work out the odds.

So this is the point? Really? So no one knows anything? Nevermind in-game choices, strategic decisions, tactics employed? Fine. Make it so. Next logical step: let's make FOW permament.

[edit]
KGB, it's from your next post:
Except that if you hide all the numbers for the bonus's and individual units, randomize the maximum dice roll and add new features like buying extra strength units no calculator can help you. Yes, it can give you an 'estimate' of the odds, but it can't give you the true odds since it won't know them. The difference between being 70% or 80% likely to win is quite a lot so if you can just obscure enough information to put a 10% fudge factor in the game it will make calculators vastly less useful

Sorry, I can't read it with a straight face :). What you propose will make brains vastly less useful too.

[edit2]
LPhillips,

It's funny how people can disagree :). Also - it's a good read, your post. My main beef would be - you make
it sound like those odds are EVERYTHING. And it's so untrue :>. It cannot be true, otherwise I'm pretty sure we wouldn't be here.

So let's assume I have the calculator. I know better how to structure my army, I know better what I'm doing but still this knowing won't help me any bit to decide:
- should I go on an offensive or a defensive?
- should I employ a hero or upgrade city walls?
- should I stock up cash for allies or invest in production?
- should I risk leaving a city defenseless for an important edge in conquering another one?
- should I raze/plunder/capture?
- should I empoy this or that unit?
- should I...

As you yourself stress - we all differ. We all have knacks for different behaviour. From your description it seems in MBTI you would be an NTP and KGB surely is an NTJ. Well, I'm NFP (creative synthetic thinker), and my game is never cold. I rant and rave in the chat when my opponent amazes me or unnerves me or scares me to sh*t and those cold-blooded NTs don't even answer with one word they just sneer at me in silence. We all differ :). And that is the best part.
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Re: battle calculator

Postby LPhillips » Fri Apr 13, 2012 5:00 am

Hungrytales,
I took the MBTI.
I failed.

All joking aside, the odds of battle are not the whole game. That's true, and it's a very important consideration. But the valid arguments brought against a battle calculator seem to boil down to this:

1) Players should never be encouraged to run simulations for every possible outcome of specific battles.
2) Corollary to 1), the advantage is already on the side of the offensive player in many ways; allowing them to simulate the battle until they achieve the best possible result is quite nearly a game breaker. The only mitigating factor is that players have equal opportunities at taking advantage of this imbalance.
3) A game where players are compelled to plot out the numbers and make their decisions based on percentage odds (and yes, we'd be compelled if our opponents were consistently doing so) dives headfirst into the tedious world of gaming by numbers. Everything would take a backseat to having the right odds when you reach the frontline. It would penetrate all the way back to unit purchase, and the game would be formulaic. I'm not speaking of the abolishment of strategy, but of its reduction in value toward the trivial. Formula supersedes intellect, and boredom replaces our enjoyment :(

KGB, I see the obvious detriments of a variable battle dice system, and it seems to me that they greatly outweigh the proposed benefits. In the event that such a system is introduced, we truly would see the experience earned by long-time players lose its value. Hidden statistics for units should be enough, but completely hidden statistics is a high price to pay for a calculator. It's probably enough to make the calculator null in competitive gaming.
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Re: battle calculator

Postby Chazar » Sun Apr 15, 2012 5:07 pm

LPhillips wrote:1) Players should never be encouraged to run simulations for every possible outcome of specific battles.
Why? I, for one, disagree. Here are some reasons why I disagree:
1) Chess is an interesting game - even without any kind of randomness. Plenty of interesting games exist that have all open information and no randomness. Some people prefer randomness in their games, some don't - some like roulette, some like chess, most people like something in between, but it is just a matter of taste.
2) Warlords series games always had Battle Advisors, but I don't think the Warlords series was broken.
3) Warbarons is all about predicting what your enemy does, and having the right kind of forces at the right place at the right time. That is, for me, what strategy games are about, the more random influenced a strategy game becomes, the less interesting it is for me.

All a battle simulator does is to reduce the time effort to learn the rules of game:
An experienced Warbarons player has learned from numerous battles how the odds are (roughly). A Warbarons beginner who is brilliant at strategy games in general has a bad disadvantage there: the beginner needs play hundreds of game before he can become competitive - he does not need to get better at strategy, he just need to memorize the odds in order to be perceived as better - is this really what you want? I dislike games where you have an advantage just by tedious unintelligent memorizing. If a player is good at strategy, then he should also have a good chance of winning a game without going through dozens of hopeless games first.

A battle simulator allows to cut short on this: I can easily see whether or not four battle-blessed light cavalries have a chance at taking a 5-defence city defended by a spider. In this example, the odds are 49.3%. I still need to decide: do I risk it? Can I spend these four light Cavs elsewhere for a better gain? If I win, can I hold this city? If I loose, does it mean I loose the game as well? These are the true questions a player has to answer in warbarons. Knowing the odds is just memory.

LPhillips wrote:KGB, I see the obvious detriments of a variable battle dice system, and it seems to me that they greatly outweigh the proposed benefits.

This is a very silly suggestion, since it just increases the variance a little, but I can easily compute the odds like I did before - I just need to account for one more roll of the die. If the battle dice varies from 50-150 per battle, the odds in the above example reduce to 44.28% percent. So my calculator gave me pretty much the same knowledge, even with the more randomized dice. Nothing changed at all.
The question really is how much randomness do you want, and how much skill?
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Re: battle calculator

Postby LPhillips » Mon Apr 16, 2012 7:15 am

Chess is not comparable to Warbarons on any level. I'm sorry to be dismissive, but it's not. So anything said relating Warbarons to chess in the context of a qualitative comparison has to be thrown out as an irrational argument.

The ability to run a battle simulator can be good. That much we can agree on; I'm actually happy with that ability. The debate is that it must not be used in our real-time gaming, to dictate players' choices about what engagements to make. This is why I'd like all stats to be hidden from the player in ladder games. Transparency equates to boredom in a gaming model where slightly randomized outcomes are an integral part of the design. I thought that was clear. Warbarons is not a mathematical equation, as Chess is. If you want that, go and play Chess. The two simply are not at all similar.

Chazar wrote:
LPhillips wrote:1) Players should never be encouraged to run simulations for every possible outcome of specific battles.
Why? I, for one, disagree.

If players were simply going to run a simulation occasionally to try to understand the game better, I could agree with much of your post. But that's simply not how this will be used by most people, and anyone with experience with the gamer mentality knows this. People will literally ruin the game for themselves and others by simulating every possible method for conducting a particular encounter until they come up with the most beneficial outcome for themselves in order to artificially gain an advantage over others. This is a form of what is known as "grinding", where people spend excessive amounts of time on minor components of a game to gain a small advantage, ruining their own experience and the experience of those who choose not to participate in such behavior.

In short, a real-time battle calculator presents the possibility of completely ruining the game for casual players. It's likely to have the very opposite of the effect you proposed. As for the argument that learning curves are evil, we have no duty to make it easy for newbies to beat veterans. Here is one of the only legitimate comparisons to chess: do you expect a beginner to have any chance against a veteran? Put them in their own league if you're so averse to a learning curve, but removing the curve is the wrong direction to go. An invalid doesn't learn to walk in a wheelchair. The correct move is to prevent them from entering ladder games until they've played for 3 weeks, so they won't be stomped by heartless pointmongers (who also should not be able to collect points from newbies).

The best thing to do about the curve is to make ladder games not show up in the "Play" section for those who have not been here very long.
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Re: battle calculator

Postby Moonknight » Mon Apr 16, 2012 6:36 pm

Maybe instead of a battle calculator, players just need some battle examples, where all of the different kind of bonuses are demonstrated so that everyone has a better sense of how they work and the order in which they work.

I agree that something like that would be good to have, but not to the point of a user choosing the exact units and fight order.
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Re: battle calculator

Postby KGB » Tue Apr 17, 2012 1:20 am

HungryTales

Now, if you propose to introduce some factor which influences battle odds in such a way as to reflect/simulate some real-life (or fantasy-life for that matter) mechanic/property - ok, that's fine. But even then I WANT TO KNOW how that factor works. Only then it becomes a part of the rule set and therefore a part of the game.


I have said repeatedly, I 100% believe all the rules should be clearly explained to all players. However, this game is still in Beta and is repeatedly undergoing changes with each new update. So you must expect that the game will continue to evolve and will not be static in terms of the rules for combat. So having the dice change from D100 to D80-200 would be explained as a rule. But you would not know in any given battle which number between 80-200 was chosen. Thus a random factor of between 0-10% would be introduced to the final odds. This hardly changes the game to flipping coins.

So this is the point? Really? So no one knows anything? Nevermind in-game choices, strategic decisions, tactics employed? Fine. Make it so. Next logical step: let's make FOW permament.

Sorry, I can't read it with a straight face :). What you propose will make brains vastly less useful too.


I suspect English isn't your first language because it appears you didn't understand what I wrote. I want to increase brain use. I am doing this by making players actually learn the rules and use their game experience. You on the other hand want to decrease brain use by automating everything to do with combat. So that there is no reason to ever use your brain there. No need to figure out fight orders and how they work and when to change it (the calculator will do it for you) or estimate odds or figure out whether the opponent might have stronger units than normal (for example there will be no more need to scout an enemy stack with a single unit to see what it contains, just click and see what your battle odds are). Nope, just click on the enemy stack, see a magical odds rating saying something like 72% chance to win and then say 'yes' or 'no' to proceed with the attack. Talk about a dumbing down of the game. A calculator would be the saddest thing to ever happen to Warbarons because you lose:

1) Fight ordering (it might as well be taken out entirely since a calculator will figure out the optimum order for you automatically).
2) Scouting enemy stacks/cities (no need to use 1 unit to see the enemy, just click and wait for the calculator to show what your odds are then decide whether to attack or not).
3) No need to ever learn the rules or learn to estimate battle odds since it will be all spoon fed to you. This sadly seems to be the way society in general is going. No one wants to take the time to learn anything any more, they just want it all handed to them instantly.

Any by the way, there is a lot more to Poker than just learning the basic odds just as there is more to Warbarons than combat. You have to learn when/how much to bet, read peoples tells, bluff etc.

Chazar,

2) Warlords series games always had Battle Advisors, but I don't think the Warlords series was broken.


Yes, However those Advisers never gave exact odds. Rather they said things like 'This battle will be very evenly matched'. What does that exactly mean? The odds are exactly 50% or in the 40-60% range? you never quite knew.

Also, the Adviser was meant for SOLO PLAY. And I completely 100% support an adviser for solo play to help new players learn the game (as you noted). Some players in fact *might never* play another human, instead just preferring to play AI games. Nothing wrong with that at all. However once you move into the realm of games against other human players you must leave the adviser behind. Online DLR play strictly forbade the use of the Adviser and if you were found to have turned that game option on, you quickly were ignored when you wanted to get games.

An experienced Warbarons player has learned from numerous battles how the odds are (roughly). A Warbarons beginner who is brilliant at strategy games in general has a bad disadvantage there: the beginner needs play hundreds of game before he can become competitive - he does not need to get better at strategy, he just need to memorize the odds in order to be perceived as better - is this really what you want? I dislike games where you have an advantage just by tedious unintelligent memorizing. If a player is good at strategy, then he should also have a good chance of winning a game without going through dozens of hopeless games first.


This comment makes NO sense. I have never ever come across any strategy game anywhere that allowed newbies to compete with advanced players (can you name one?). I consider myself an above average strategy player but to say that I should be able to sit down at a Chess board with Gary Kasparov and have a good chance to win is absurd. But you are saying that in effect, I should be able to sit down with Kasparov and get a chess computer to help me play against him so that I can have a good chance to win. That's crazy. The battle calculator should be purely to help new players learn by playing solo games. It should not be used to allow newbie players to compete with players who have hundreds of games of experience. Experience matters especially in strategy games just as it does in real life (tell me, you trusting the Doctor fresh out of med school to perform his first ever triple bypass heart surgery on you just because he got the top grade in the class or are you going with the Doctor who has performed several hundred of them in his career but graduated middle of his class. I know who I am taking).

This is a very silly suggestion, since it just increases the variance a little, but I can easily compute the odds like I did before - I just need to account for one more roll of the die. If the battle dice varies from 50-150 per battle, the odds in the above example reduce to 44.28% percent. So my calculator gave me pretty much the same knowledge, even with the more randomized dice. Nothing changed at all.


While 44% to 54% (80-200 dice roll) may not seem like much since it's still roughly 50-50, I can assure you that 75% to 85% is a big deal. You went from 3-1 odds to 8.5-1 odds. That matters.

Also you are assuming you have all the numbers. What if that Spider is blessed? Then what? Or what if that Spider has 3 hits instead of 2? Or was maybe built with +2 strength so it's a 27 instead of a 25? Then what kind of numbers will you get? You'll get a range between 20% to 50%. Then how will you decide whether to attack?

See, right now in beta5 the game has static units. As in fixed strengths and hits. But many players including myself have been asking for the features in prior Warlords that allowed units to come built with extra strength or hits or acquire more strength from medals. If you don't show those values, then a calculator won't have any use because you can't know exactly what you face other than a Spider. And you'll have to rely on the fact that maybe you've already seen another Spider with 3 hits from that player or extra strength or blessed or all 3 and figure out what is most likely. Then you aren't even factoring in battles where there are lots of units on both sides and fight order actually matters...

To sum things up again for those not reading all these long posts:

1) The game should clearly state all the rules of combat on a nice easy to read page with some examples so players can understand how the combat works.
2) A battle calculator for solo games should be provided to help both new and veteran players experiment with combat.
3) A *nice to have* feature in solo games would even be a 'reload battle' option so you could experiment with reloading and trying out different fight orders.
4) Human player games should not have a calculator and it would be best if the numbers for your opponent were not revealed so that 3rd party calculators can't be reliably used.

KGB
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Re: battle calculator

Postby Fordus » Tue Apr 17, 2012 10:26 am

KGB wrote:1) Fight ordering (it might as well be taken out entirely since a calculator will figure out the optimum order for you automatically).


No matter how good the calculator, players would still have to make choices. Calculator just provides the odds, you'll still have to decide what are acceptable odds for different outcomes. Would you choose 20% risk of losing something big vs. 85% chance of losing 1 or 2 smaller units? Biggest winning chance isn't always best, and often it's 100% regardless of the fight order.

KGB wrote:2) Scouting enemy stacks/cities (no need to use 1 unit to see the enemy, just click and wait for the calculator to show what your odds are then decide whether to attack or not).


Providing calculator to everyone won't in any way affect scouting. What you are suggesting here is specific function that might or might not be implemented.

KGB wrote:3) No need to ever learn the rules or learn to estimate battle odds since it will be all spoon fed to you. This sadly seems to be the way society in general is going. No one wants to take the time to learn anything any more, they just want it all handed to them instantly.


Currently this one is everyones personal choice. Should you learn the odds, or do you use couple hours coding to get yourself a calculator. Providing artificial advantage to coders and other computer savvy people. Certainly everyone can make it, others just are faster than some. But well, eventually just minimal googling skills are all you need :twisted:

Yes, I understand that using more time to a game should give you some advantage, but does it have to be done in a way that is in no way related to playing the game?

KGB wrote:Also you are assuming you have all the numbers. What if that Spider is blessed? Then what? Or what if that Spider has 3 hits instead of 2? Or was maybe built with +2 strength so it's a 27 instead of a 25? Then what kind of numbers will you get? You'll get a range between 20% to 50%. Then how will you decide whether to attack?


Calculator can give "exact" probability as long as it knows value ranges (and preferably probabilities) of unknown variables. Or it can give range based on different combinations of unknown variables. However decision making won't differ all that much from basic 75% chance of winning, or 89% chance.

If anything, more random or semi-random variables gives more reasons to use calculator. If there's too many variables, mind can easily overweight some of them. Causing experience based "feeling" to be harder to learn and more often more wrong than currently. Now using calculator is skill itself, adding more random or unknown elements will make it require more skill while also giving more benefit compared to players not using calculator

LPhillips
I kinda agree with your arguments. However as actual battle is already random, and in my opinion minor part of the the game, I don't see any pressing reason not to include calculator. Fact that making own calculator and "cheating" that way is impossible to prevent and somewhat easy to do would however suggest that making one available to all wouldn't be bad idea.

I know that above statement is completely wrong approach to cheating, but let me restate that battle calculater is minor convienience item that is only bad if you let dictate everything. Using one will give only minor advantage, if any, over experienced player. Heck, it can easily do more harm than benefit if used carelessly and without thought/experience.
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Re: battle calculator

Postby LPhillips » Tue Apr 17, 2012 1:28 pm

First, Fordus, by the way your position changes from paragraph to paragraph, and your lack of objectivity, it seems like you're arguing just to argue. Some people enjoy that, but please remember that we are having an objective discussion here for the good of the project! Set a firm opinion, give reasoning, and stick to it! Now to the arguments...
Fordus wrote:I know that above statement is completely wrong approach to cheating, but let me restate that battle calculater is minor convienience item that is only bad if you let dictate everything. Using one will give only minor advantage, if any, over experienced player. Heck, it can easily do more harm than benefit if used carelessly and without thought/experience.


1) If you know that it is the wrong approach then why are you suggesting it? Maybe it's a minor convenience to you, but if provided carte blanc to young gamers then it becomes a crutch. I don't see it as a "maybe it's harmful to them, so let's give it to them" issue. (And what's with that logic anyway?) I see it as "it's definitely harmful to them, the community, and the project in general, so let's not give it to them!"
2) That leaves us with the current situation, where it's provided to elite players only as a minor convenience. This can easily be misconstrued as an unfair advantage, which is a pretty legitimate argument.
3) Finally, you have suggested that anyone can make a calculator, and that it is inevitable that we will see an underground movement of calculator cheaters. That is easily dismissed by providing the calculator on the site in limited ways, as suggested by KGB and others. If it is already available for playtesting in solo games, then most or all players will not go through the trouble of creating one to cheat in competitive games! Those with the intellect to make an accurate calculator won't have any need for one.

You also presented arguments toward KGB that were entirely contradictory to any understanding about the points I presented, particularly the idea of calculators being used to determine the best method of conducting any engagement by running repeated simulations. If you agree with me, then agree, but don't do it after contradicting me, apparently just for the sake of arguing with KGB on a false basis.

I don't think we would ever see KGB's worst described scenario, where one simply clicks on an enemy stack and gets a free Battle Advisor report, but it was suggested in an earlier post. However, scouting an enemy stack, inputting their precise stats into a calculator, and then manipulating your stack composition and unit order until you find the right combination to do the most damage (or win with the least loss to you) is a very real possibility. That is the scenario that we all wish to avoid. That is the scenario where the ability to vary unit strengths in minor ways, as KGB and others have suggested, becomes the death knell to mechanical gaming. It doesn't do you any good to try to fool around with the fight order for hours in order to gain an artificial advantage if you cannot predict the exact strengths of enemy units.

KGB, It is still my firm opinion that a varied dice system is not an effective solution. If we hide the unit strengths, isn't that enough?
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