Inner Peace (Through Superior Firepower) – Episode 026

[BLANDCorporatio]

No, I don't think it can work like that. I mean fundamentally. A "stack" doesn't have Attack and Defense... the Units in the Stack have Attack and Defense. When a Unit fights another, it fights with its own abilities modified, not as a nebulous stack vs. stack comparison.

This is pointless nitpicking on semantics. In point of fact, there are several rulesets where the battle calculation goes "sum Attack for all units in the stack, then apply bonus whatever, then apply this other bonus, {this effectively is an Attack score for the stack as a whole} then apply some random factor, then factor in the enemy defense {that is, effective Stack defense} somehow" etc. Whether "in reality" every unit fights on its own, or whether you choose as a calculational convenience to compute equivalent stats for the whole stacks involved in combat, should not merit further discussion.

If the fight was stack vs. stack, then the order to "screen" would be unnecessary. It would be the decision of the Commander which units took damage. To Screen, the Unit needs that order, so there is physically something the unit must do, to whit, place itself in the way of an attacker.

This is so. It's not very popular to have screening units, or stacks, in PBP Erfsims at the moment because of the extra complication it adds when computing battle outcomes. There were some rules proposed that added screening, be it in a stack or with a stack from outside it, but these systems are not well explored as of now.

Also, I should note that even if screening were possible, it would still make more calculational sense to aggregate unit stats into a stack stat. One thing that current rulesets allow for is targeted attacks against a unit not at the top of stack. This is done by computing the damage the Attacker would normally do, using stack-aggregated stacks. Say the value comes out 20. And we want to croak a unit inside the enemy stack, which has 8 Hits. "Targeted" damage suffers a penalty of being halved (for regular units), so 16 of that 20 damage points is used to croak the 8H unit. The rest may be delivered either to the top, or we could target another unit.

Screening might work symmetrically, where a unit is supposed to block some targeted damage meant for another. But to first obtain that "budget" of damage points that will be dished out, stack aggregate stats are better to use.

No, it comes because of a magical relationship between the Caster and particular Units, but the description is that of Leadership, not pseudo-Leadership.

If you insist on splitting hairs I will insist on text quotations. And besides, what I was saying there is that the justification for stack bonus is different from that of leadership, or mancy-alignment, bonus. So one doesn't need to expect the various kinds of bonuses to behave the same (that is, be adequately represented by the same simplified model).

Remember this from the WotT: "6011856 The relative combat power by level is NOT logarithmic or exponential."

That's great, but I haven't proposed either logarithmic, nor exponential, relative combat power level increase by level (which is defined how, do you suppose? ratio of combat power level? which is defined how?).

The system is as simple as this: For both units, add Attack to bonuses from various Leadership sources, Dancefight Bonus, and other Bonuses. Add the two Attacks and Divide individual by total to get probability of First Hit. Damage done by weapon type, modified by a function of the Attack and Defense.

I fail to see how you derived that from the quoted WoT, but funnily enough something like that's been suggested. Specifically, I suggested we split "Damage" from "Attack" and treat Attack as a source of bonus, the way Heroes of Might and Magic does. Also, again for reasons of convenience, aggregate stats for the stacks involved, rather than individual units, are considered. There's however no "first hit" rule at this time. Not because it wouldn't make sense, but again because of keeping things simpler.

As for the Stacking debate in general, I believe the limitations include a physical proximity problem. Whenever a Warlord is splitting his forces, he has them re-stack. If proximity weren't an issue, they wouldn't need to do this. The easiest way to explain this is if each Stack has one member assigned as a squad leader. If units are too far from the squad leader, they lose the bonus and take a penalty. This would explain why entire armies aren't in a single stack when fighting on a front.

This is highly plausible.

Next issue (as far as forum gamers are concerned) is, how to implement something that behaves like that, in a ruleset that's simple enough so that resolving actions does not take forever? For example, the "proximity calculation" would be the first to go; nobody wants to compute the exact positions of the units in space, and whether they collide with each other. No, you just count them. Above this value, this is how the bonus decreases. KISS.

PS: Artemiss. Yeah, nice name for the Goddess of Hunting it is.

[Housellama]

Warning, this wall of text is bigger than than my usual walls of text.

A lot of this is stuff I'm just putting out to see if it gives anyone else ideas. I'm not heavily invested in any of these theories. I'm just tossing some ideas out for the you guys and gals to play with. So many things. Hard to figure out where to start...

I'm hard pressed to think of an in-canon example, but we rejected the retaliate only once rule in Erfsim for an obvious reason.

It only takes one unit (which may be a cheap-boop junk) to disable ANY stack if you only allow one retaliation. This is one exploit not even Parson used, ever, and would seriously damage the resulting game. So several retaliations are typical. Usually there's a fatigue mechanic, as long as the defending stack does not wipe out the attacker.

I guess I'll start here. In one of my hybrid examples, a defending unit could retaliate as long as it was standing. In the other, the defending force was split against each attacker. These aren't mutually exclusive. For the sake of argument, we'll assume that both of these are in place.

The question here becomes one of engagement. Have we seen examples where stacks could initiate an engagement with multiple units? I've looked and couldn't find one. Each stack engages a single stack. However, there's nothing preventing one stack from being engaged by multiple stacks. So here's the question: Does engagement work both ways, or is a one-way process? That is, can a stack that is being engaged by multiple stacks engage more than one of those stacks at a time? Are the statuses of "Engaging" and "Being engaged by" different, or is it just one overall status?

What I was responding to, in the passage of mine that you quoted, was a suggestion to have the Stack Bonus a number that is added to the sum of the attack of the units in the stack. So for example, 8 units get +7 bonus. Meaning, if all have 10 attack, the stack's attack, with bonus, is 87.

What you suggest here works a little differently. 8 units, with attack 10 each, would each get +7 attack resulting in the stack having a score of 136.

I'd make a further observation. You speak mostly of Leader bonus, not stack bonus. This matters. If the stack bonus results in a value that depends only on the stack size, not also the units' stats, then strong units are affected by it less; example, if a stack of Pikers with attack 1 has it such that each Piker receives +7 from the stack bonus, that's a huge improvement. If a stack of Dwagons with 20 Attack has each receiving +7, not quite as big an improvement, comparatively speaking. But if stacking increases the efficiency of Pikers by some ratio, you'd expect the same ratio of improvement to happen for Dwagons.

No, I don't think it can work like that. I mean fundamentally. A "stack" doesn't have Attack and Defense... the Units in the Stack have Attack and Defense. When a Unit fights another, it fights with its own abilities modified, not as a nebulous stack vs. stack comparison. The Unit has it's Attack+ Bonuses vs the enemy's Defense+bonuses, and vice versa. If the fight was stack vs. stack, then the order to "screen" would be unnecessary. It would be the decision of the Commander which units took damage. To Screen, the Unit needs that order, so there is physically something the unit must do, to whit, place itself in the way of an attacker.

This right here is why I think that stacks are limited to a certain # of units attacking at one time. Otherwise there's no incentive not to stack everything into one monster stack to get every bonus ladled on top of one another.

As for the Stacking debate in general, I believe the limitations include a physical proximity problem. Whenever a Warlord is splitting his forces, he has them re-stack. If proximity weren't an issue, they wouldn't need to do this. The easiest way to explain this is if each Stack has one member assigned as a squad leader. If units are too far from the squad leader, they lose the bonus and take a penalty. This would explain why entire armies aren't in a single stack when fighting on a front. If you only need to be close to 7 other members of the stack, regardless of stack size, you could retain the Stack bonus at +8 across the entire front even as losses were suffered. There has to be more to it, because on a frotn line, 16 units could easily be in close proximity to share a +8 bonus and resist losses reducing the bonus with each death.

I don't think that proximity is the only factor in what can and can't be stacked together, but I certainly think it is one of them.

I think that a lot of us (me included) are sometimes forgetting that the elementary particle, so to speak, of Erf combat is the Unit, not the Stack. Erfword is not a game, as we are sometimes wont to forget. It is a world with game-like rules, but it is, at its heart, a world. Units have stats, stacks are simply groups of units. The game-like rules give bonuses to units based on the stack, but each individual unit is what matters, what does all the actual action. This isn't just a semantic nitpick, because Erf isn't a game.

If we look at retaliation in that light, it's easy to see that yes, a unit should be able to defend itself against an attack at any point as long as it is engaged. It also makes sense that engagement is a two way street. If you engage someone, they are also engaged with you. So a unit can respond to an attack by any unit it is engaged with. However, unless there is a Special in play, a unit can only attack one other unit at a given point in time, but can attack a new unit anytime it is not actively attacking something. So retaliation is unlimited, but only one unit at a time. This also puts positioning into play. Sure, a unit can attack anything its stack is engaged with, but only if it can reach it. Space isn't going to magically warp to allow 20 people to stand and attack in a space big enough for 5.

We have been told that 8 units achieves the maximum stack bonus. We have not been told what that bonus is, something that I had forgotten. I knew there was a 8 unit limit, but I had assumed that the bonus was 8. Not so. So stacking bonus is unknown, just that it maxes out at 8. There must be some incentive to having multiple stacks, otherwise it wouldn't happen like that. However, looking at Wanda's Dance-Fight scene, it is entirely likely that every Uncroaked in that picture was in a single stack, with Wanda leading it. Otherwise they would be considered unlead stacks and wouldn't get the dance-fight bonus. So the idea that only 8 units can attack at any given time is out. This also reinforces the effect of positioning. There are hordes of people behind, but only the units at the line are actually doing anything.

Given all these things, it's likely that the stack bonus applies to everyone in the stack, but only 8 units 'count' toward that bonus. As a result stacks beyond 8 hold their bonus longer. It's also likely that there is some incentive that we aren't seeing to have multiple small stacks, rather than a single large stack. I suspect some combination of engagement rules and stack bonus effect. Perhaps the stack bonus is divided across the # of units in the stack? Some kind of diminishing returns curve where 8 is the perfect number? That would make sense as to why an 8 unit stack is preferable to a larger stack. The obvious problem with this idea is that as casualties occurred to a unit bigger than 8 units, the bonus to each unit would start to rise because the same bonus was shared across less units. That could lead to some very interesting tactical concepts. Another possibility is that the bonus level is additive as the number of units rise, but the effect is multiplicative, a ratio based on each unit's power. That eliminates the problem with unfair unit bonuses and possibly explains why it would be better to have multiple smaller stacks. You get more bang for your buck with lots of 8 stacks than you do with one big stack.

That's about all I've got for now. Thoughts?

Edit: Yes, I realized I contradicted myself. My idea evolved as I wrote and I forgot to take out the bits above. I could edit them out, but it might spark something in someone else, which is the point of this post

[MonteCristo]

Not that it likely matters, but I believe Rwanda's a queen, not an overlord. And the other casters lights went out. They may have turned or gone barbarian l, though I doubt it.

Actually that point matters A LOT!!!! Wow, none of us noticed that.
Rob has previously been VERY clear that the terms Overlord and King/Queen are distinct and different, so he wouldn't use Overlord on accident. The general term is "Ruler". So the fact that Wanda refers to herself as Overlord tells us something very important about the mechanics of Royalty...
It is almost explicitly stated that Wanda IS in fact Noble, but she was not popped as an Heir.
She was made Heir Designate, and when her father died, despite being Noble, she STILL became an Overlord rather than a Queen. This means that only units POPPED as an Heir become Queen/King.

I do not recall it ever being mentioned that Wanda was a noble.
Her father was an overlord which means that he was a non-royal ruler. Wand may be considered the daughter of the overlord and Tommy's sister, but there is nothing that says that either of them are of noble status. Wanda took the title of overlord because she is not a noble/royal

[raphfrk]

Wanda turns and offs Banhammer. Jillian then becomes overlord of FAQ and gets a detailed turn by turn report of the fall of FAQ that she is powerless to prevent. Is it any wonder she hates Stanley so?

I wonder if she knows what Wanda did. Since Wanda had turned, she probably just didn't register.

[BLANDCorporatio]

A lot of this is stuff I'm just putting out to see if it gives anyone else ideas. I'm not heavily invested in any of these theories. I'm just tossing some ideas out for the you guys and gals to play with.

Aye, it's a very instructive discussion, and it would pay to go in depth, while combining with other rules, suggestions from your post and Kreistor's; more time than I have available right now, but I'll take note of these things.

Wanted to comment on-

I think that a lot of us (me included) are sometimes forgetting that the elementary particle, so to speak, of Erf combat is the Unit, not the Stack. {snip} This isn't just a semantic nitpick, because Erf isn't a game.

No, "we" don't forget that the Unit is more fundamental than the Stack. Neither do "we" forget that Erfworld is a world (that happens to look like a game). But, "we" (whoever that is) are wargamers, and we are interested in simplified models. Just like you wouldn't simulate a warship in a game by keeping tabs on every sailor, but rather the ship as a whole, you aggregate unit stats into stack stats and use those thereafter.

And I was speaking of Erfsim rules whenever I spoke of rules in this thread (because, unlike Erfworld, Erfsims have clearly defined rules). It is therefore insufficient to say, "since the Unit is what has stats in reality, not the stack, it doesn't make sense to speak of Stack Stats". Just like it works to approximate a ship by one unit instead of a collective of parts and people, and just like one can often think of a gas in terms of a continuous fluid and not a collection of thingamajiggies bouncing around, the question should be whether this model is accurate enough for some purpose.

[Housellama]

Wanted to comment on-

I think that a lot of us (me included) are sometimes forgetting that the elementary particle, so to speak, of Erf combat is the Unit, not the Stack. {snip} This isn't just a semantic nitpick, because Erf isn't a game.

No, "we" don't forget that the Unit is more fundamental than the Stack. Neither do "we" forget that Erfworld is a world (that happens to look like a game). But, "we" (whoever that is) are wargamers, and we are interested in simplified models. Just like you wouldn't simulate a warship in a game by keeping tabs on every sailor, but rather the ship as a whole, you aggregate unit stats into stack stats and use those thereafter.

And I was speaking of Erfsim rules whenever I spoke of rules in this thread (because, unlike Erfworld, Erfsims have clearly defined rules). It is therefore insufficient to say, "since the Unit is what has stats in reality, not the stack, it doesn't make sense to speak of Stack Stats". Just like it works to approximate a ship by one unit instead of a collective of parts and people, and just like one can often think of a gas in terms of a continuous fluid and not a collection of thingamajiggies bouncing around, the question should be whether this model is accurate enough for some purpose.

I realized that as I was reading your post right before mine. I'm actually interested in the 'physics' of Erfworld, not the rules design for Erfsim. The two happened to overlap there. I understand and agree that in the Erfsim rules, things need to be streamlined. But like science, if your knowledge about what the continuous fluid does isn't accurate enough, it's time to pay attention to the collection of thingamajiggies. I guess it depends on how accurate is accurate enough. Certainly it can't hurt to look at the activity of the unit to help model the mechanics of the stack. Even if it's not relevant, it's certainly interesting. I'll make sure the different subjects are more clearly designated in the future.

As far as the 'we' goes, I've been working on officework, homework and this at the same time. My pronouns got confused. Consider it a royal we then. *crowns himself Lord of Cross-typing*

[0beron]

I do not recall it ever being mentioned that Wanda was a noble.
Her father was an overlord which means that he was a non-royal ruler. Wand may be considered the daughter of the overlord and Tommy's sister, but there is nothing that says that either of them are of noble status. Wanda took the title of overlord because she is not a noble/royal

Oh right you are, my bad, I forgot that Firebaugh was an Overlord as well.
But reading back, Wanda refers to herself as "Lady" moments after popping...which raises some interesting questions about the title of lord/lady. This may imply that there can be Nobility even when a side is not Royal, interesting possibility.

[Kreistor]

No, I don't think it can work like that. I mean fundamentally. A "stack" doesn't have Attack and Defense... the Units in the Stack have Attack and Defense. When a Unit fights another, it fights with its own abilities modified, not as a nebulous stack vs. stack comparison.

there are several rulesets where the battle calculation goes "sum Attack for all units in the stack,[snip]

There are Games that try just about everything. I'm looking for something that indicates that is how it operates. Parson's comment about Bonuses being the fundamental basis for power suggests that bonuses need to be maximized in effect. Adding bonuses to the Stack instead of the Unit minimizes the effect, and maximizes individual unit level. Stacking bonuses on top of 8xCombat (5 Bogrolls is 40, so +8 is only +20%) is far less effective numerically than stacking it on individual Unit stats (whereas +8 on Bogroll's 5 Combat is +140%).

Whether "in reality" every unit fights on its own, or whether you choose as a calculational convenience to compute equivalent stats for the whole stacks involved in combat, should not merit further discussion.

No, it's a fundamental mechanic. Never trivialize things like this -- the details on trivialized mechanics are exploitable.

It's not very popular to have screening units, or stacks, in PBP Erfsims at the moment because of the extra complication it adds when computing battle outcomes. There were some rules proposed that added screening, be it in a stack or with a stack from outside it, but these systems are not well explored as of now.

I can't see why it's that hard. It sounds in the game like screening simply ensures the screening units have to die first, so long as they are mechanically capable of screening. So a screened unit cannot be directly attacked because the attacker lacks LoS, so all Screening units must be killed beofre the Protected Unit can be targeted. Simple Line of Sight (LoS) mechanic.

Also, I should note that even if screening were possible, it would still make more calculational sense to aggregate unit stats into a stack stat.

No, it wouldn't. You run into Exploitational issues that way. For instance, you place a highly vulnerable unit (ie. Archer) in a stack with extremely defensive units (heavily armored knights), then place it on the front line. Your stack can't kill the vulnerable Archer despite being in direct melee contact, but the Archer can snipe your Warlord. To target individual units of any type, you must do Unit vs. Unit combat. Since we know targeting is possible for Warlords and for Stacks with Leadership, we must abandon the Stack level concept. It is unwieldy to have two mechanics where one will suffice, and we must have targeted damage, so we may as well kick out the Stack damage mechanic entirely.

"Targeted" damage suffers a penalty of being halved (for regular units), so 16 of that 20 damage points is used to croak the 8H unit.

Yeah, calling BS on that. Unwieldy and unnecessary. KISS. There's no indication in the comic of targeted damage being lower than normal, so adding it is speculative. And complex.

Screening might work symmetrically, where a unit is supposed to block some targeted damage meant for another.

You've abandoned the concept of "missing"? Artemis made it clear that attacking is not 100%, with her misses. With a Miss mechnic, you can implement it in two ways.

1) Cannot target a unit that is being Screened.
2) Automatically miss a unit that is screened and roll "to hit" on a screening unit.

Pick one. Both work well.

But to first obtain that "budget" of damage points that will be dished out, stack aggregate stats are better to use.

No. Complex and useless, and not supported by comments in the comic.

No, it comes because of a magical relationship between the Caster and particular Units, but the description is that of Leadership, not pseudo-Leadership.

If you insist on splitting hairs I will insist on text quotations.

This started with talking to Sizemore. He told me that Casters are Commanders, and can lead stacks, but they almost never do. Casters are too rare and valuable to risk, and they give no leadership bonus to the stack anyway. Only Warlords have leadership.

Makes sense. Except for certain exceptions. Like, say... the bonus those golems get if they're led by a Dirtamancer. Or the huge one to Uncroaked units being led by a Croakamancer(!). I need Wanda back, hard. Like half our troops are Uncroaked. So I talked to Maggie about it.

If you take Paragraph 2 out of context, then it sounds like the bonus is untyped. But it has context from Paragraph 1. Parson is talking about Leadership bonus here. If the bonus were of a non-Leadership type, then the word "Exception" lacks meaning. "Exception" only makes any sense in this context if the bonus is of a Leadership type. If the bonus was of a different type, then Parson would not be able to use the word "exception" if the type was any other than Leadership. Exceptions are tack ons to main rules, and since the only rule that has been mentioned is the lack of Leadership, then it must be a Leadership Rule exception.

Remember this from the WotT: "6011856 The relative combat power by level is NOT logarithmic or exponential."

That's great, but I haven't proposed either logarithmic, nor exponential, relative combat power level increase by level (which is defined how, do you suppose? ratio of combat power level? which is defined how?).

That WoT came from a discussion between myself and Rob. In it, I gave him an example of an exponential system and linear system. An exponential system, like Champions, has a damage function similar to: Finaldamage = Damage dealt- Defense. Where damage dealt < Defense, damage = 0. From high school math, you may remember that an exponential can be simulated with two straight lines. In this case, there is one line at 0 out to Defense on the graph, and then final damage is a line with slope = 1. A linear system has a constant slope that intercepts Defense at 0.

In this specific discussion, the topic was Leadership vs. Level. He confimed that Leveling was an Exponential system, where it takes more units of your own level to reach your next level (ie. It may take 2 Level 1 kills to reach Level 2, but 100 Level 9 enemies to get from Level 9 to 10.) But, the effect of +1 level was +1 Leadership, and Leadership +1 Leadership on a unit with 10 strength would increase effectiveness by 10%. Effectiveness being a nebulous term in this discussion... we didn't get into the nitty gritty of the mechanics involved... it was high level concept.

The system is as simple as this: For both units, add Attack to bonuses from various Leadership sources, Dancefight Bonus, and other Bonuses. Add the two Attacks and Divide individual by total to get probability of First Hit. Damage done by weapon type, modified by a function of the Attack and Defense.

I fail to see how you derived that from the quoted WoT, but funnily enough something like that's been suggested. Specifically, I suggested we split "Damage" from "Attack" and treat Attack as a source of bonus, the way Heroes of Might and Magic does.

There are literally thousands of ways Erfworld could be implemented, but only a limited number of statistics to work with. Rob chose "Combat" instead of the more typical "Attack" from DnD, which suggests the Combat stat serves multiple purposes, and he didn't want any association to DnD mechanics.

Also, again for reasons of convenience, aggregate stats for the stacks involved, rather than individual units, are considered. There's however no "first hit" rule at this time. Not because it wouldn't make sense, but again because of keeping things simpler.

No, you're not making things simpler. You're reducing dice rolls, but that isn't simpler, just faster. You're losing Erfworld specific mechanics in your quest for minimization.

As for the Stacking debate in general, I believe the limitations include a physical proximity problem.

This is highly plausible.

Next issue (as far as forum gamers are concerned) is, how to implement something that behaves like that, in a ruleset that's simple enough so that resolving actions does not take forever?

Remember that much of Rob's knowledge of gaming comes from computer war games,. not board games. For him, thousands of rolls per round is trivial. He can intend a computer mechanism for the combat calculations.

But I think you need to be a little more specific here. You're not talking about reproducing Erfworld here. You're trying to create a version of Erfworld that is simplified for board game

The game you should be looking at for an example of simplifying mass unit combat is Warhammer. Warhammer simplifies by using only one type of die -- the D6. (White Wolf simplified by using D10, but that's an RPG.) It had a series of rolls to determine if a unit damaged another. It involved a series of 4 rolls (I forget them all... Accuracy and Armor Save were 2). But you needed to do this for every unit, and each unit could attack more than once. How to achieve this?

Roll them all at once. Only units of a particular type were permitted in a force (except for the leader which was rolled on different coloured dice). Add up all the attacks and take that many dice. Roll to hit vs. a number from 1-6. All dice that roll below are discarded. Re-roll the same dice for the next effect. You always re-roll the highest numbered dice. Same mechanic over and over until you had the number of actual hits. Multiply by damage the weapon does, and remove enough units to cover the damage. Repeat for each stack. Handled hundreds of units in a battle, sometimes, but most were 20-40. Conceptually, you're limited only by the number of dice you own. The slow bit is separating out the dice to re-roll, but if one player takes the misses and the other the hits, it speeds things up.

For example, the "proximity calculation" would be the first to go; nobody wants to compute the exact positions of the units in space, and whether they collide with each other.

Simple solution. Units have to be within X cm's of each other. Use a protractor and make a cone of diameter X. Move forward the unit you want on the left, and place the left-most edge of the disk on the ground below that unit, with a cone edge along the enemy front line. All your units must be inside that cone to retain the bonus. You can also use a string, but that works better with pewter units than unweighted plastic. (Glue a bolt to the bottom and it stabilizes.)

No, you just count them. Above this value, this is how the bonus decreases. KISS.

But does not simulate Erfworld mechanics. You can't claim it's Erfworld if you are using highly speculative mechanics. Rob has had the opportunity to mention that Targeting reduces damage (during Artemis' commentaries), and declined. Means it doesn't exist.

PS: Artemiss. Yeah, nice name for the Goddess of Hunting it is.

Can't believe I didn't catch that before. Kicking myself.

I'm actually interested in the 'physics' of Erfworld, not the rules design for Erfsim.

Then why are you looking for simple mechanics. Rob can use complex ones in erfworld because he doesn't actually roll any dice.

[quote = "Oberon"]It is almost explicitly stated that Wanda IS in fact Noble, but she was not popped as an Heir.[/quote]

No, there is absolutely no indication that Wanda is Noble. Any Commander can be made Heir to a Side, including non-Royals to a Royal Side (Stanley popped a lowly Pikeman).

Nobles are popped by Royal Sides, and Royals trace lineage back to the Titans so do not pop randomly. It's that simple.

But reading back, Wanda refers to herself as "Lady" moments after popping...which raises some interesting questions about the title of lord/lady. This may imply that there can be Nobility even when a side is not Royal, interesting possibility.

Hamster was given title without being Noble. Titles can be given, or in Wanda's case, taken. Parson is Lord Hamster. Wanda is Lady Wanda. Lady, in this case, is a form of address, like Ms, Miss, or Mrs., instead of an indicator of Title.

[Chit Rule Railroad]

If her father had died when she was the overlord, it would have been mentioned. Assuming that rulers can't abdicate, she knew he was dead because she became overlord, and that's why there was no further mention of it. Plus there was a delay between the promotion and becoming overlord.

I agree that Wanda believed that becoming Overlord meant that her father was already croaked, but it's possible that she made that assumption not because abdication is impossible but because she believed her father would go down fighting. So whether it is possible to abdicate is still unclear.

[Keighvin1]

Wanda made no assumptions, readers made assumptions. What Wanda knows, in as much as we know what she knows, is that she became Overlord, and then felt people ceasing to exist. She mentioned pretty much every named character other than her Father, so we have made the, quite logical, assumption that he was dead by the time she took over. Not even the concept of abdication was brought up in the update.

[BLANDCorporatio]

Parson's comment about Bonuses being the fundamental basis for power suggests that bonuses need to be maximized in effect. Adding bonuses to the Stack instead of the Unit minimizes the effect, and maximizes individual unit level. Stacking bonuses on top of 8xCombat (5 Bogrolls is 40, so +8 is only +20%) is far less effective numerically than stacking it on individual Unit stats (whereas +8 on Bogroll's 5 Combat is +140%).

Strawman there. The system you use to disparage stack-stats is not the one I used. Your system says "apply +8 to the attack of every unit". My system would say: "add all the attack of the units in the stack, then {add number of units * 8 (if you want a flat +8) OR you multiply the sum by 2.4 (if you want the bonus to each unit to be 140%)}".

At the level of bonus effect, this is functionally the same.

No, it's a fundamental mechanic. Never trivialize things like this -- the details on trivialized mechanics are exploitable.

This betrays a certain disconnect between our two goals here. More on this near the end of the post.

It sounds in the game like screening simply ensures the screening units have to die first, so long as they are mechanically capable of screening. So a screened unit cannot be directly attacked because the attacker lacks LoS, so all Screening units must be killed beofre the Protected Unit can be targeted. Simple Line of Sight (LoS) mechanic.

Or even simpler, put the screening units in front, in the stack order. If you don't have targetting rules, that allow damage to skip stack order, that's all you need.

Look, ideally you'd take into account each and every movement of each and every bone in each and every unit. I trust this looks obviously impractical, so you first combine all of the unit into a whole, rather than a collection of parts, then aggregate further into stacks etc.

You run into Exploitational issues that way. For instance, you place a highly vulnerable unit (ie. Archer) in a stack with extremely defensive units (heavily armored knights), then place it on the front line. Your stack can't kill the vulnerable Archer despite being in direct melee contact, but the Archer can snipe your Warlord.

This was very elegantly handled by Erfsims. In order for Ranged units to fight as Ranged, they must be stacked exclusively with Ranged units. (Some exceptions: Mounts are allowed to be not ranged, if the riders are, so as to allow for Horse Archers; Riders can be not ranged, if the mounts are, to allow for something like the Dwagon Knight riding some ranged flying lizard; and the commanding Warlord may be not ranged, but will not contribute damage in this case).

Since we know targeting is possible for Warlords and for Stacks with Leadership, we must abandon the Stack level concept. It is unwieldy to have two mechanics where one will suffice, and we must have targeted damage, so we may as well kick out the Stack damage mechanic entirely.

Nope, here's how it goes. Use the stacks' (usually, again to KISS, combat is kept between two stacks) aggregated stats to get the damage budget. Most of the time, this is simply dealt in stack order, so there's no need for anything else. Other times, some of this is reserved to target a certain unit, the rest being dealt in the usual fashion. And you never need to deal with the complication of who exactly dealt which blow to whom.

Yeah, calling BS on {target damage penalty}. Unwieldy and unnecessary. KISS. There's no indication in the comic of targeted damage being lower than normal, so adding it is speculative. And complex.

No indication in the comic, maybe. To say it's "unnecessary", or "complex" means you haven't thought things through.

The typical Warlord has much less Hits than the typical firepower of a collection of units. So if the units can gang up on one Warlord, they'd always be toast. Two ways to go about this. Introduce maneuvering rules, account for what each of the units is doing, roll initiative, hit, and damage for each blow- this is what Erfworld most likely does, and what you advocate. OR, so that we can get things going, use the aggregate stack system above so that combat calculation doesn't take forever. BUT, in this second system, you need some way to represent the cost of maneuvering your units in place to snipe at a Warlord. Which is why targeted damage against Warlords is divided by 4.

As to complexity: stack A deals X damage to stack B, but the owner of stack A decided to allocate some of that damage to hurting/croaking the Warlord in stack B. Then, the amount selected from X is taken away, divided by 4 and the result dealt to the Warlord; the remaining damage in X is then dealt to B in stack order.

You've abandoned the concept of "missing"?

No. Random factors with a fairly large spread account for that.

With a Miss mechnic, you can implement it in two ways.

1) Cannot target a unit that is being Screened.
2) Automatically miss a unit that is screened and roll "to hit" on a screening unit.

1) is what I previously suggested in my post before this, you'll find. 2) is functionally equivalent to 1) in the kind of systems we use.

Makes sense. Except for certain exceptions. Like, say... the bonus those golems get if they're led by a Dirtamancer. Or the huge one to Uncroaked units being led by a Croakamancer(!). I need Wanda back, hard. Like half our troops are Uncroaked. So I talked to Maggie about it.

The bonus is question is not explicitly said to work as a leadership one. Further, the croakamancy one is larger than dirtamancy, so they work differently. Yes I do notice you say

If you take Paragraph 2 out of context, then it sounds like the bonus is untyped. But it has context from Paragraph 1. Parson is talking about Leadership bonus here. If the bonus were of a non-Leadership type, then the word "Exception" lacks meaning.

No, "exception" means that, while Casters don't usually give bonuses to stacks by acting as their commanders, there are cases in which they do. There is no indication that caster bonus works the same as the bonus that Warlords give.

In it, I gave him an example of an exponential system and linear system. An exponential system, like Champions, has a damage function similar to: Finaldamage = Damage dealt- Defense.

My gosh, the word exponential sure has changed meaning since last time I used it when not referring to the exponential map of the Lie algebra on (R^n, +). Because apart from (R^n,+) and its algebra, no way Damage dealt-defense is exponential. But anyway, you probably refer to experience gain, not the damage calculation function, when you say exponential.

From high school math, you may remember that an exponential can be simulated with two straight lines.

Gosh again, if your Highschool taught you that the exponential function may be approximated by two lines, how come you're dead set against the idea of aggregating stats? The latter is a much better approximation to its target than the former is to its own.

In this specific discussion, the topic was Leadership vs. Level. He confimed that Leveling was an Exponential system, where it takes more units of your own level to reach your next level (ie. It may take 2 Level 1 kills to reach Level 2, but 100 Level 9 enemies to get from Level 9 to 10.) But, the effect of +1 level was +1 Leadership, and Leadership +1 Leadership on a unit with 10 strength would increase effectiveness by 10%. Effectiveness being a nebulous term in this discussion... we didn't get into the nitty gritty of the mechanics involved... it was high level concept.

Exponential increases in experience is something one can (and often does) work with, sure. And in the rulesets we use, 10% increase in "effectiveness" (aka, damage dealt) for every level the warlord has is indeed what happens. That's exactly how we compute leadership bonus.

Whether you apply the 10% increase to each unit's stat, or to the stack as a whole, is the same.

There are literally thousands of ways Erfworld could be implemented, but only a limited number of statistics to work with. Rob chose "Combat" instead of the more typical "Attack" from DnD, which suggests the Combat stat serves multiple purposes, and he didn't want any association to DnD mechanics.

D'you have WoT on that? And didn't YOU yourself suggest, in your previous post,

The system is as simple as this: For both units, add Attack to bonuses from various Leadership sources, Dancefight Bonus, and other Bonuses. Add the two Attacks and Divide individual by total to get probability of First Hit. Damage done by weapon type, modified by a function of the Attack and Defense.

Doesn't this require that "weapon type" be an extra info needed to compute the damage dealt, and that Attack (or as you called it now, Combat) and Defense are not enough?

you're not making things simpler. You're reducing dice rolls, but that isn't simpler, just faster. You're losing Erfworld specific mechanics in your quest for minimization.

Yes. And your point is what? Seriously, what is it? The kind of stuff I'm describing is typical of wargaming and even, heck, Engineering. The kind that builds bridges and houses after bars of materials that are treated as having aggregate "stats" like elasticity and hardness. There's no such thing. But the approximation works for the purpose. Nobody will design a house by trying to simulate interatomic interactions, and in a PBP forum game, we'd rather avoid having to roll several times for every blow a unit makes.

Why is this so hard to get?

But I think you need to be a little more specific here. You're not talking about reproducing Erfworld here. You're trying to create a version of Erfworld that is simplified for board game.

Apparently it isn't hard to get. Yes, that's what I'm all about. And I was always specificly referring to Erfsim rules, not Erfworld rules (which I don't know anyway).

The game you should be looking at for an example of simplifying mass unit combat is Warhammer. {snip} But you needed to {roll dice} for every unit, and each unit could attack more than once. How to achieve this?

{Roll, roll, roll again, gently down the stream ...}

What we currently use is a spreadsheet. You have the unit stats plugged in, the formulas for aggregate stack stats always work the same, and then there's one roll involved to get the random factors. If the combat is melee vs. melee, or ranged vs. ranged, done! Ranged vs. melee requires two such rounds (assuming the melee survives). It's much simpler, and much faster, than what you describe.

Units have to be within X cm's of each other. Use a protractor and make a cone of diameter X.

Dude. Play by forum. We exchange text files, game status is stored in text files (usually by hand because none of us had time to spare to code a proper comp-assistant), and combat is handled by spreadsheets.

But {your system} does not simulate Erfworld mechanics. You can't claim it's Erfworld if you are using highly speculative mechanics. Rob has had the opportunity to mention that Targeting reduces damage (during Artemis' commentaries), and declined. Means it doesn't exist.

On the latter point, of targetting penalties- the cost, as explained above, is to account for maneuvering around units in the opposing stack.

On the former point, is it appropriate to represent a computer as a collection of ideal logic gates? Or as a collection of logic circuits? Or as a set of motherboard, processor, RAMs? Or simply care about the programs currently running? Or a house or bridge as a collection of lumped up solid bodies? Or as an indivisible entity part of a larger thing like a city or road network? Or a warship in a wargame as one unit? Each of these is an approximation.

Not just wargaming, but also Engineering routinely uses approximations, lumped-parameter models, instead of accounting for every elementary particle in a system. Heck, real gases are often described as "ideal gas, but with correction factors in the laws". As approximations are wont to do, they work in a certain range and not in others. Even so, one often keeps using variations on the same approximations, because not using them is impractical. To extend the range, you sometimes introduce parameters (like correction factors for gas laws, or targeting penalties).

So here's the rub. You want to know Erf physics. Fine. I want to develop Erfsims. Fine. You point out that a behaviour in Erfsim rules does not match what we see in Erfworld. Fine. I suggest a fix- if the resulting behaviour matches observation, then fine regardless of whether the fix looks "unphysical" to you.

Example, targetting penalties. They account for the fact that a unit inside the stack is protected by other units, and to damage it one needs to focus time aiming, or maneuvering around defenses etc, thus reducing the time they have available to just flail around against immediately available targets. The result is that targetting is left for highly-powerful targets, or when an ambush provides a bonus to attack, which gels with the rest of the system.

I'm actually interested in the 'physics' of Erfworld, not the rules design for Erfsim.

Then why are you looking for simple mechanics. Rob can use complex ones in erfworld because he doesn't actually roll any dice.

Oi! I wasn't the one what said the quoted text. Just making sure that's understood.

[0beron]

It is almost explicitly stated that Wanda IS in fact Noble, but she was not popped as an Heir.

No, there is absolutely no indication that Wanda is Noble. Any Commander can be made Heir to a Side, including non-Royals to a Royal Side (Stanley popped a lowly Pikeman).

Nobles are popped by Royal Sides, and Royals trace lineage back to the Titans so do not pop randomly. It's that simple.

I wasn't saying she was Noble because she became Heir Designate, I'm WELL aware that any unit can be promoted that way.

But reading back, Wanda refers to herself as "Lady" moments after popping...which raises some interesting questions about the title of lord/lady. This may imply that there can be Nobility even when a side is not Royal, interesting possibility.

Hamster was given title without being Noble. Titles can be given, or in Wanda's case, taken. Parson is Lord Hamster. Wanda is Lady Wanda. Lady, in this case, is a form of address, like Ms, Miss, or Mrs., instead of an indicator of Title.

We don't KNOW that. Right now, we have seen Noble as a term used distinct from Royalty, rather than the 2 being used interchangeably. (similar to the Overlord and King/Queen usage, being similar but very distinct). So all I'm suggesting is that our current assumptions about what defines "Noble" and what the title "Lord/Lady" means MAY be wrong. Note that Lord Hamster was given that title once he was appointed Chief Warlord. Wanda assumed the title before she had any rank such as Chief Caster.

Also, I feel compelled to point out that the post I quoted was Kriestor's 666th post haha :p

[Kreistor]

It sounds in the game like screening simply ensures the screening units have to die first, so long as they are mechanically capable of screening. So a screened unit cannot be directly attacked because the attacker lacks LoS, so all Screening units must be killed beofre the Protected Unit can be targeted. Simple Line of Sight (LoS) mechanic.

Or even simpler, put the screening units in front, in the stack order. If you don't have targetting rules, that allow damage to skip stack order, that's all you need.

Except that in the comic the Warlords order "Screen for X". They don't screen for everything, just one particular type of danger. In fact, since they do Screen for only one specific threat, it may be that they can only screen for on threat at a time. Hmmm... will have to watch for that in the future.

Look, ideally you'd take into account each and every movement of each and every bone in each and every unit.

Contra-indicated by the Stat "Hits" and the fact Units can fight well with missing limbs.

You run into Exploitational issues that way. For instance, you place a highly vulnerable unit (ie. Archer) in a stack with extremely defensive units (heavily armored knights), then place it on the front line. Your stack can't kill the vulnerable Archer despite being in direct melee contact, but the Archer can snipe your Warlord.

This was very elegantly handled by Erfsims. In order for Ranged units to fight as Ranged, they must be stacked exclusively with Ranged units.

Unfortunately, we've seen mixes of units in stacks. Artemis and her knights. Archer with Sylvia and her dwagons.

Since we know targeting is possible for Warlords and for Stacks with Leadership, we must abandon the Stack level concept. It is unwieldy to have two mechanics where one will suffice, and we must have targeted damage, so we may as well kick out the Stack damage mechanic entirely.

Nope, here's how it goes. Use the stacks' (usually, again to KISS, combat is kept between two stacks) aggregated stats to get the damage budget. Most of the time, this is simply dealt in stack order, so there's no need for anything else. Other times, some of this is reserved to target a certain unit, the rest being dealt in the usual fashion. And you never need to deal with the complication of who exactly dealt which blow to whom.

When you need one Rule, adding a second to do the same job is inherently more complex. No matter how simple the second Rule is, it's more than a system with one fewer Rule and that's not KISS.

Yeah, calling BS on {target damage penalty}. Unwieldy and unnecessary. KISS. There's no indication in the comic of targeted damage being lower than normal, so adding it is speculative. And complex.

No indication in the comic, maybe. To say it's "unnecessary", or "complex" means you haven't thought things through.

No, I have. Two rules is more complex than one, no matter how simple the Redundant Rule is. The Stack level combat is not necessary, but Targeted damage is. We must then have a Unit vs. Unit system. No matter how simple, a second mechanic to achieve the same goal is unnecessarily adding weight of more Rules.

Makes sense. Except for certain exceptions. Like, say... the bonus those golems get if they're led by a Dirtamancer. Or the huge one to Uncroaked units being led by a Croakamancer(!). I need Wanda back, hard. Like half our troops are Uncroaked. So I talked to Maggie about it.

The bonus is question is not explicitly said to work as a leadership one. Further, the croakamancy one is larger than dirtamancy, so they work differently. Yes I do notice you say

It doesn't need to be explicit because of the surrounding context. That a number is numerically different from another does not suggest a different mechanic.

If you take Paragraph 2 out of context, then it sounds like the bonus is untyped. But it has context from Paragraph 1. Parson is talking about Leadership bonus here. If the bonus were of a non-Leadership type, then the word "Exception" lacks meaning.

No, "exception" means that, while Casters don't usually give bonuses to stacks by acting as their commanders, there are cases in which they do. There is no indication that caster bonus works the same as the bonus that Warlords give.

No, the context does not say that Casters provide no bonus. It specifically says provides no "leadership bonus". A lack of leadership bonus does not imply that Casters cannot give other bonuses, so the use of "Exception" cannot imply what you suggest. Further, we know that Casters (specifically Master Class Croakamancers) can provide other bonuses beyond Leadership (specifically Dancefighting) so Parson should not have been intending that implication. His discussion was about Leadership, not bonuses in general.

In fact, I'll speculate that Master Class Dirtamancers can Rock Out with their Golems.

In it, I gave him an example of an exponential system and linear system. An exponential system, like Champions, has a damage function similar to: Finaldamage = Damage dealt- Defense.

My gosh, the word exponential sure has changed meaning since last time I used it when not referring to the exponential map of the Lie algebra on (R^n, +). Because apart from (R^n,+) and its algebra, no way Damage dealt-defense is exponential. But anyway, you probably refer to experience gain, not the damage calculation function, when you say exponential.

An exponential can be represented by two straight lines with an error less than 5%. It's not my problem that you forgot that. And BTW, it wasn't me that used the term that way, but the creators of Champions (the Hero System), who all got their Masters degrees in Mathematics. I'm pretty much just laughing at this sarcasm as weak and petty.

From high school math, you may remember that an exponential can be simulated with two straight lines.

Gosh again, if your Highschool taught you that the exponential function may be approximated by two lines, how come you're dead set against the idea of aggregating stats? The latter is a much better approximation to its target than the former is to its own.

Yeah, my Engineering courses reiterated it for First Order system analysis. You only use the full exponential in Third Order Analysis and sometimes in Second. And I'll back that up with an Engineering Degree.

Sorry, but I'm just going to mock your ignorance of its use in Math, Physics, and Engineering. It's basic, it's useful, and it's applicable.

There are literally thousands of ways Erfworld could be implemented, but only a limited number of statistics to work with. Rob chose "Combat" instead of the more typical "Attack" from DnD, which suggests the Combat stat serves multiple purposes, and he didn't want any association to DnD mechanics.

D'you have WoT on that? And didn't YOU yourself suggest, in your previous post,

The system is as simple as this: For both units, add Attack to bonuses from various Leadership sources, Dancefight Bonus, and other Bonuses. Add the two Attacks and Divide individual by total to get probability of First Hit. Damage done by weapon type, modified by a function of the Attack and Defense.

Doesn't this require that "weapon type" be an extra info needed to compute the damage dealt, and that Attack (or as you called it now, Combat) and Defense are not enough?

Yes, but it isn't a stat of the unit, but the weapon the unit is carrying. Bogroll, at the time, was unarmed so his stat page would exclude weapon damage.

Further, you tend to list only stats that can change. If carrying a Sword does X base damage, and the modifiers all come from the Stat page, it's not necessary to list that constant in a Stat page. If the Stat page says "Piker", then base damage from the weapon is indicated by the fact he is skilled only with a "Pike". He is either dangerous because he is carrying a Pike, or useless because he is carrying something else.

you're not making things simpler. You're reducing dice rolls, but that isn't simpler, just faster. You're losing Erfworld specific mechanics in your quest for minimization.

Yes. And your point is what? Seriously, what is it?

My point is "Why are you arguing with me.?" I care about the Erfworld mechanics, not your version for your game. If you don't think that Stack vs. Stack combat happens in Erfworld, then keep that idea out of this thread. Start a Erfsim specific thread, and don't hijack this one.

In other words, take your business elsewhere. It's confusing, because it's difficult to know when you're discussing Erfsim and when Erfworld. "ErfSim" does not inherently imply a diverging goal from determining the Erfworld mechanics, but could indicate a system where the mechanics are as reliably implemented as possible, with unknown mechanics invented until Rob reveals the mechanics he is using. I am not capable of reading your mind or your intentions.

In other words, it is not clear what Erfsim's goals are. And that's YOUR fault.

The game you should be looking at for an example of simplifying mass unit combat is Warhammer. {snip} But you needed to {roll dice} for every unit, and each unit could attack more than once. How to achieve this?

What we currently use is a spreadsheet. You have the unit stats plugged in, the formulas for aggregate stack stats always work the same, and then there's one roll involved to get the random factors. If the combat is melee vs. melee, or ranged vs. ranged, done! Ranged vs. melee requires two such rounds (assuming the melee survives). It's much simpler, and much faster, than what you describe.

And non-visceral so boooooring.

Units have to be within X cm's of each other. Use a protractor and make a cone of diameter X.

Dude. Play by forum. We exchange text files, game status is stored in text files (usually by hand because none of us had time to spare to code a proper comp-assistant), and combat is handled by spreadsheets.

Then why the over-simplification? You've got the computer power to do unit vs. unit, and coding for Stack vs. Stack adds a second mechanic and adds, not subtracts, code. You are simplifying to reduce coding time? But certainly not by very much. It doesn't take longer to write Unit vs. Unit code instead of Stack vs. Stack... it saves processing power, which you should have in abundance.

But {your system} does not simulate Erfworld mechanics. You can't claim it's Erfworld if you are using highly speculative mechanics. Rob has had the opportunity to mention that Targeting reduces damage (during Artemis' commentaries), and declined. Means it doesn't exist.

On the latter point, of targetting penalties- the cost, as explained above, is to account for maneuvering around units in the opposing stack.

The justification doesn't matter. That you can create a reason doesn't matter. It's not in the comic and was not described where it should have been. Either you're screened, or you're not. It's a simple on-off mechanic.

On the former point, is it appropriate to represent a computer as a collection of ideal logic gates? Or as a collection of logic circuits? Or as a set of motherboard, processor, RAMs? Or simply care about the programs currently running? Or a house or bridge as a collection of lumped up solid bodies? Or as an indivisible entity part of a larger thing like a city or road network? Or a warship in a wargame as one unit? Each of these is an approximation.

Rhetoric.

Not just wargaming, but also Engineering routinely uses approximations, lumped-parameter models, instead of accounting for every elementary particle in a system.

See Exponential above. If you know we use approximations in some Orders of analysis, why are you mocking my use of an approximation? I am an Engineer. I know that your mockery is full of feces. What I don't get is how you know approximations are valid and you can simultaneously rationalize mocking their use.

[snip more Rhetoric]

So here's the rub. You want to know Erf physics. Fine. I want to develop Erfsims. Fine. You point out that a behaviour in Erfsim rules does not match what we see in Erfworld. Fine. I suggest a fix- if the resulting behaviour matches observation, then fine regardless of whether the fix looks "unphysical" to you.

No, keep your Erfsim out of Erfworld discussions. It has different goals from developing an accurate list of Rules from the comic, and a name does not imply that divergent purpose. Or at the very least, ensure you include disclaimers that indicate that accuracy is not your primary goal, since simplicity is.

[BLANDCorporatio]

Fortunatley, several large walls of text later, I don't need to produce another one to continue this.

irt. Kreistor

So here's what I see, and the evidence is in the previous posts.

I always talked about Erfsim rules, and why that wasn't clear from the start is your problem.

You invent purposefully bad systems to back up your points, and ignore the ways I suggested those issues are removed in a stack system (the stack bonus effect: either applied to each unit, or as a multiplier to attack sum (if the original was prop. to the unit stats) or by adding num units * bonus (if the original was a constant added to stats; you ignore the way mixed stacks are handled in the rules I described).

You say Erfsim rules have no place being discussed here and that you don't care about such nonsense. Fine, but so far you've contributed two large walls of text doing exactly that until I got that out of you.

You confuse a system with few rules with one that is simple to use. The Game of Life is simple (and Turing Complete!). I would not try and run the workings of a Game-of-Life computer by hand, or with spreadsheets, or whatever tools I have easily available now.

You ignore the fact that if Casters provided bonuses to general stacks (even if said bonuses are not called leadership), it would have been mentioned by now, in the quoted Klog even.

You invoke the creators of Champions (the Hero System) to defend why "A-B" is an exponential function. I don't know about the creators, or their math degrees. You on the other hand are using "exponential" wrong. And 5% approximation error? What does that mean, difference in value divided by the value of one or the other of the two functions? If that's the case then need I remind you that lim(x->inf) ((exp(x) - k*x) / (kx)) is infinite regardless of k if k constant? (Conversely, lim(x->inf) ((exp(x) - k*x)/(exp(x)) is 0).

Since that blows the 5% error into ridiculousness, you probably meant (this is me, giving you the benefit of the doubt), "within a certain range, you can approximate exp with two lines, and have this error". You might as well just use one line (the archetypal approximation for when working in small neighbourhoods of some position), or a constant.

But I digress.

The point here is that you entered in this discussion all like "this is not how the system works, you need to account for all the details" then switched to "but exp can be approximated by two lines".

Which means, you're just contrarian for the sake of it. Worse, what you do is GOOD, and whatever someone else does, even if it's conceptually the same, is BAD.

So I have a better suggestion. YOU put your typing fingers where your mouth is, and get your ideas implemented in code. The site may get renovated soon, it might include a gaming area, and it would be much more useful for everyone instead of this heated exchange.

[0beron]

*hides patiently in corner*

iiiiiiim just gonna wait over here for the dust to settle, and then hop in when it's all done to snag the resulting formula for use in my tabletop game :p lol

[Kreistor]

You on the other hand are using "exponential" wrong. And 5% approximation error? What does that mean, difference in value divided by the value of one or the other of the two functions?

The largest difference between the two straight lines and the exponential function is at the knee, where the two lines intercept. At that point, the knee is only 5% different from the actual value, and decreases as you proceed in either direction.

If that's the case then need I remind you that lim(x->inf) ((exp(x) - k*x) / (kx)) is infinite regardless of k if k constant? (Conversely, lim(x->inf) ((exp(x) - k*x)/(exp(x)) is 0).

Nope. The slope of the approximation kx = exp(x) (since exp(x) is its own derivative) at both ends of the graph, so

lim(x->inf) ((exp(x) - k*x) / (kx)) = lim(x->inf) ((exp(x) - exp(x)) / exp(x)) = 0

And that works in both directions, BTW. The slope of the line near 0 is technically also exp(x) as x-> negative infinity, which has the same result.

In the case of the game system, we're working backwards and reducing the tiny value of exp(x-defense) to 0 because the system lacks decimals. Technically, that results in 100% error, but relative to the other side of the graph, where x>>>damage, the error is trivial. Consequently, the error is not measured in this manner.

The maximum error is at the knee, not infinity or -ve infinity. At the knee point, you can see the largest deviation visually. And I don't have the equation on how to calculate it handy. Due to offset and slope (since
f_exp(x) = k*exp(mx+n)+C
is the set of equations we're considering), you can't measure it as a straight difference for a general set, because that method has a different error for every member of the set.

I believe the error is measured as area under the curve. I'm not going to look that up at this point. I'm not certain I have the text anymore, I'd have to look through a lot of books and may come up empty.

Since that blows the 5% error into ridiculousness,

Not so much. Nice try, though. But you forgot kx = exp(x) at x->infinity.

But you also need to remember that for the region over which you're considering, you will have two lines. If you zoom in on one region, or shift left and right, the two lines change slope to compensate. If you change the region, you change the approximation.

The point here is that you entered in this discussion all like "this is not how the system works, you need to account for all the details" then switched to "but exp can be approximated by two lines".

No, you are obsessing over the "two lines" thing. I am only answering YOUR questions and counters. I mentioned the exponential as a side comment in response to YOUR query about the discussion I had with Rob concerning exponential and linear effects. You prompted for it. It's not my problem that you don't like it and are obsessed with proving me wrong.

Which means, you're just contrarian for the sake of it. Worse, what you do is GOOD, and whatever someone else does, even if it's conceptually the same, is BAD.

This is the wrong place for your discussion. Normally, I don't have complaints about off-topic, but what you are discussing is very similar to a comic-based discussion about the known Rules. Maybe it was stated in your first post, but you didn't maintain a disclaimer. Contrary to popular opinion, I don't have time to read every post, and neither does anyone else. This subject is too close to the Rules Debate that you are going to have difficulties like this time to time. Blaming others for that is self-centered.

In other words, you need to take Erfsim discussions elsewhere. Erfsim should not have priority in the discussion threads over Erfworld Rules Debate.

So I have a better suggestion. YOU put your typing fingers where your mouth is, and get your ideas implemented in code. The site may get renovated soon, it might include a gaming area, and it would be much more useful for everyone instead of this heated exchange.

And I have s suggestion. Don't count your chickens before they hatch.

[Catalyst]

I have a question. Do we know that Delphie and/or Clay actually died? Would it look the same (the light going out) to the Overlord if the units turned instead of croaking? Either way she stops paying upkeep and does not keep track of them anymore.

[BLANDCorporatio]

Nope. The slope of the approximation kx = exp(x) (since exp(x) is its own derivative) at both ends of the graph, so

lim(x->inf) ((exp(x) - k*x) / (kx)) = lim(x->inf) ((exp(x) - exp(x)) / exp(x)) = 0

What Math are you using? You'll find that while exp is its own derivative, the derivative of k*x is k, the constant.

So applying l'Hospital's rule to lim(x->inf) ((exp(x) - k*x) / (kx)), you get that it is equal to lim(x->inf)((exp(x) - k)/k) where k is constant, which is infinity.

"Nice try though".

But seriously, LOADS of people would be eternally grateful to you if you got the rules you envision into workable code for Erfworld.com. Or even just for hobby use at home.

PS: you're not the only commenter here, and it's common practice for the reaction thread to include discussions on any range of topics. So that argument of yours that some topic doesn't belong here because you say so is baulderdash.

Just like your use of l'Hospital's rule. That's the thing with HS Math. It was so long ago.

Spoiler: show

I finally remembered where the "two lines for exp" (likely) comes from. I'm ashamed it took so long, yes: small signal analysis on diodes. But that's only valid in a small range, NOT as a global approximation for exp, which is what you suggest.

[0beron]

I have a question. Do we know that Delphie and/or Clay actually died? Would it look the same (the light going out) to the Overlord if the units turned instead of croaking? Either way she stops paying upkeep and does not keep track of them anymore.

That is an interesting (albeit unlikely) possibility! From what we gather, insta-turning is difficult and a high-level Turnamancy ability. I think it's more likely that they would have been captured first, and thus still lit-up, before later being turned.
It is possible that they turned willingly, but I find that mildly unlikely for Marie, and neigh impossible for Clay. Plus, Wanda knew that Delphi was in the tower, fighting, so a willing surrender is unlikely.
Good theory though, because it's very Rob-ish haha.

[BLANDCorporatio]

And just because why the heck not, let's compute:

Area under exp(x) from -infinity to x: exp(x), call it a_exp(x).

Area under k*x, where k is constant, from 0 to positive x is (k/2)*x*x. I'm doing you a favour starting at 0, since that part where x is negative is negative area and would reduce the area sum even more. Call this a_lin(x).

Relative error will then, as x grows to infinity: lim(x->inf)((a_exp(x) - a_lin(x))/(a_lin(x)) (I'm allowed to do this since for x positive a_lin(x) > 0) which by applying l'Hospital's rule is equal to lim(x->inf)((exp(x) - k*x)/(kx)) which I've previously established is infinite. So relative error (measured by ratio of difference of areas under the curve and area under the linear one) is growing unbounded.

If I were to compute the limit of a_exp(x) - a_lin(x)/a_exp(x), the limit at infinity is 1. 100% error under this metric. If I were to compute the limit at infinity of (exp(x) - k*x)/(exp(x)) , it's also 1 (damn typos!). Again 100% error. So as x increases, under this metric the approximation also gets rubbish.

I love shooting fish in a barrel.