Inner Peace (Through Superior Firepower) – Episode 026

[Oberon]

Don't forget, you can only make a stack of up to 8 units. Which is what you see in the art (+1 for Wanda).

I think it's actually +1 for the mount. I'd speculate that mounts don't count towards the 8 stack limit, or you'd only be able to have a stack of 4 plus their mounts. And I think we've seen larger stacks of mounted units before.

I dont think that is right. I believe the bonus stops at 8, but you can stack as many as you want.
It makes sense to only stack to 8 to maximize use of stacks.

You'd think so, but this is not necessarily true.
[snippage]
If you cannot split N into stacks of 8, say you have 15 units, it's actually better to keep them all together, so that they enjoy stack bonus(8), rather than one stack of 8 (full bonus) and one stack of 7 (lower bonus).

This is true only if there is no other limit. Such as the stacking bonus only being able to be applied to 8 units. You listed another couple potential limits that also make it make sense to keep stacks at 8.

We can finally put to rest that debate on whether casters can be heirs and overlords.
Yes they can. Next.

Yes, this is awesome. Charlie can be a caster Overlord, which is more esthetically pleasing to me than he being better than all other Thinkamancers only through the possession of the 'Dish.

[Stanley] is thoroughly bored as Overlord. He could be convinced to going back to Warlord, which he loved.

I don't think so. He is a megalomaniac and loves being in charge, even if it has some boring disadvantages. Can you see Stanley actually working for Parson, for example? Parson would probably be able to use him very effectively, but could Stanley abide by taking orders from the potato man?

And thank you to Rob for giving us a number on the Fellows. Over 500 is enough to wait out their decay. That's not trivial.

I'm looking for the 511 secondary reference. All I've got is travel sites... Anyone else?

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.

It's not 'retaliate only once' then, it's 'retaliate only against a single stack which has attacked you'. Then the cheap-boop unit dies so fast that the defender is free to retaliate again. But what it does do is allow the first stack of 8 pikes to engage the twolls, followed by the next two stacks, and probably only the first stack gets wiped out. Or the first and part of the second, perhaps. It can be a way to limit casualties without being a complete exploit. And don't forget that we've already seen Parson use a 'destack and rotate in fresh units' strategy to keep his casualties down.

On the topic of Wanda's status, I suggest it's possible that Wanda is STILL a barbarian Overlord/Heir. Does anyone have citations to prove Wanda is properly a GK unit?

Many. The most solid being Stanley relaying the account of her turning to GK. There's nothing to suggest that after turning she somehow acquired the status of barbarian again.

Best bot evar.

They do that crap to avoid checksum spam filters. By parking some random text in the spam, it changes the sum, and slips through.

I love shooting fish in a barrel.

And I love seeing a huge, flaming battle that I'm not a participant in.

[mortissimus]

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.

[snip] I think it's more likely that they would have been captured first, and thus still lit-up, before later being turned.

Does rulers know where captured units are? If so then Stanley knows exactly where Jillian sets up camp for the night.

Though of course there cold be a middle road where the ruler knows the units are captured but not more then that.

[BLANDCorporatio]

this is awesome. Charlie can be a caster Overlord, which is more esthetically pleasing to me than he being better than all other Thinkamancers only through the possession of the 'Dish.

I know! It's nice to see that such an arbitrary restriction (Casters can't be Overlords) does not apply.

Incidentally, on the topic of "we haven't seen situation X mentioned exactly so far, so whatever arguments of aesthetics and symmetry and common sense bear no impact on X being possible".

A mathematician, a physicist, and an Engineer are on their first trip, ever,through Scotland. They go by train, and after the vehicle gets inside Scotland, they notice, through the window, one black sheep grazing.

"A-ha", says the Engineer, "all sheep in Scotland are black!"

"No", says the physicist, "but there's at least one black sheep in Scotland."

"What makes you say this?" asks the Mathematician, "all we know is that in Scotland there is at least one sheep, at least half of which is black."

...

Ba-dum-tish.

[Oberon]

Does rulers know where captured units are? If so then Stanley knows exactly where Jillian sets up camp for the night.

When Jillian is setting up camp somewhere alone in the wilderness, she is no longer a GK captured unit. When Jillian is in the GK dungeon or otherwise held captive by GK units, GK pays her upkeep and it would make sense for the GK leader to know where she is.

[mortissimus]

We can finally put to rest that debate on whether casters can be heirs and overlords.
Yes they can. Next.

Yes, this is awesome. Charlie can be a caster Overlord, which is more esthetically pleasing to me than he being better than all other Thinkamancers only through the possession of the 'Dish.

It does dash my hope of being right in speculating that Charlie is a mind-controlled ruler and the person truly owning the Dish was his thinkomancer and mind-controller Bosley. Ah, well.

[mortissimus]

Does rulers know where captured units are? If so then Stanley knows exactly where Jillian sets up camp for the night.

When Jillian is setting up camp somewhere alone in the wilderness, she is no longer a GK captured unit. When Jillian is in the GK dungeon or otherwise held captive by GK units, GK pays her upkeep and it would make sense for the GK leader to know where she is.

Sorry, I was unclear. I meant in the near future of the comic when Jillian makes camp with Ansom and her other prisoners and Parson will want to retaliate and free as many as possible. Guess we will read that in a couple of years.

[jkosta]

because Trem is not a popped Heir

I suspect this is incorrect. I think that multiple Heirs can be popped and that they, along with any commander, can be the Heir Designate. It makes sense from a real world perspective, too: multiple royal children with valid claims to the throne are very often born, at least for the sake of redundancy, despite the later risk of fracturing the kingdom between them.

And because it doesn't make much sense for Slately to consider his non-heirs "sons". It's possible, but I just don't find that plausible.

[Curxzed]

"This group had no scouts. As they marched on, she hoped for an ambush, or any enemy encounter, so that she might spend her juice this turn making fresh units instead of hopelessly re-patching these. It was better than wasting the juice entirely, but there was only so much she could do."

So this finally puts to rest the rediculous notion that casters can save up juice, and the kingworld spell was two full turns (as in days) worth of juice. It was worth 2 casts of the turn (unit) spell.

called it.

[MarbitChow]

"This group had no scouts. As they marched on, she hoped for an ambush, or any enemy encounter, so that she might spend her juice this turn making fresh units instead of hopelessly re-patching these. It was better than wasting the juice entirely, but there was only so much she could do."

So this finally puts to rest the rediculous notion that casters can save up juice, and the kingworld spell was two full turns (as in days) worth of juice. It was worth 2 casts of the turn (unit) spell.

called it.

Kingworld could be a spell that has a cost when it is 'prepared' (day 1 - entering the trance) , and again when it is triggered (day 2 - triggering the spell to end the turn). The ability to save juice is not a necessary requirement for a spell to need nearly 2 full days of juice to cast.

[cheeseaholic]

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.

Clay seems possible, as he knows that the woman he loves is fated to join the side attacking them. I wondered if Delphie had gone barbarian since her light went out in the tower, which presumably has the portal.



Wanda shall be called Rwanda by me often until such time as I figure out how to turn off the auto correct on my kindle.

[Kreistor]

Yeah, Bland, that's wrong. Intercepting at 0 forces the approximation line to cross the exponential, and that's not allowed. The approximation is always below the exponential. You have to select the correct pair of lines, and they are not always y=0 on the left, because the left hand region can shorten and cause the left line to have a positive slope. The x-intercept shifts to the right as x increases, but the slope is definitely not k=exp(x), since that always intercepts at x-1.

I know you're impressing yourself with this math, but you aren't capable of analyzing it, because I can't give you the specifics anymore. I haven't used it in over two decades, so can't train you right now. Everything you're doing is Strawman because you're not approaching it from anything except my flawed memory and that's forcing you to make a lot of assumptions, and I can't give you the math you're demanding, because it's locked away in some textbook that's older than many readers here.

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).

And that's the fundamental mistake. The approximation line never crosses the exponential, but choosing intercept at 0 causes it to. It's not an arbitrary process, and I'm sorry that I don't remember the details to explain how you select the lines and intercept point based on arbitrary x range.

http://en.wikipedia.org/wiki/Exponential_function

Look down on the right for the graph where they demonstrate the derivative proof that the slope intercepts at x-1. This is not a graph where you choose the lines y=0 and y=x*exp(x_max). The lines will be closer to the two examples (extended to intercept each other).

Anyway, enough. Clearly you have simply forgotten the approximation, or were never taught it. But it is not wrong, and I really am only laughing at you as you try to "disprove" it. I know what I was taught, and I agreed with it at the time, so you're just blowing smoke on your own ego. Approaching it from extremes by using infinite points? It's an approximation. It is a fundamentally flawed to approach approximations from a perspective outside the realm of approximation. Approximations deal with specific cases, and they only work under given conditions. The Game example I presented fits the conditions, with suitably large range with the knee near the middle of the graph. That you can make it break down in other conditions is irrelevant.

Last post on this topic.

[Oberon]

Clay seems possible, as he knows that the woman he loves is fated to join the side attacking them. I wondered if Delphie had gone barbarian since her light went out in the tower, which presumably has the portal.

Why do people add such wild speculation to such a simple reading of the words? How hard is it to arrive at the conclusion that Delphie is dead?

Delphie was there in the tower, wounded.
In Wanda's head, Delphie's light went out as well. Gone.

A wounded caster, hard pressed (evidenced by the tiny count of other Goodminton units and the death of the CWL and other caster, either of whom might have been with Delphie during the attack), is finally killed by the attackers. At the time this occurred, Wanda was Overlord of her side. There's no hiding the unit status. She'd know if it turned, she'd know if it was captured, she'd know if it was dead.
Add suitably poetic language about a "light going out" and suddenly it's a tin foil hat frenzy as to what "really" happened... Let me clear it up: There was no inside job for the 911 attacks.

[cheeseaholic]

Clay seems possible, as he knows that the woman he loves is fated to join the side attacking them. I wondered if Delphie had gone barbarian since her light went out in the tower, which presumably has the portal.

Why do people add such wild speculation to such a simple reading of the words? How hard is it to arrive at the conclusion that Delphie is dead?

Delphie was there in the tower, wounded.
In Wanda's head, Delphie's light went out as well. Gone.

A wounded caster, hard pressed (evidenced by the tiny count of other Goodminton units and the death of the CWL and other caster, either of whom might have been with Delphie during the attack), is finally killed by the attackers. At the time this occurred, Wanda was Overlord of her side. There's no hiding the unit status. She'd know if it turned, she'd know if it was captured, she'd know if it was dead.
Add suitably poetic language about a "light going out" and suddenly it's a tin foil hat frenzy as to what "really" happened... Let me clear it up: There was no inside job for the 911 attacks.

I believe that Delphie and Clay died. But just because that's how it appears doesn't mean that that is how it is, and that is worth keeping in mind. I prefer to keep track of what is an assumption and what is stated as true, as well as keep an eye on other possibilities.

[Lamech]

Clay seems possible, as he knows that the woman he loves is fated to join the side attacking them. I wondered if Delphie had gone barbarian since her light went out in the tower, which presumably has the portal.

Why do people add such wild speculation to such a simple reading of the words? How hard is it to arrive at the conclusion that Delphie is dead?

Delphie was there in the tower, wounded.
In Wanda's head, Delphie's light went out as well. Gone.

A wounded caster, hard pressed (evidenced by the tiny count of other Goodminton units and the death of the CWL and other caster, either of whom might have been with Delphie during the attack), is finally killed by the attackers. At the time this occurred, Wanda was Overlord of her side. There's no hiding the unit status. She'd know if it turned, she'd know if it was captured, she'd know if it was dead.
Add suitably poetic language about a "light going out" and suddenly it's a tin foil hat frenzy as to what "really" happened... Let me clear it up: There was no inside job for the 911 attacks.

Would she know the differance? A captured unit seems to be officially on the enemy side. She certainly wouldn't know what happened to Clay. And Delphie certainly doesn't exactly seem loyal. What does she even have to keep fighting for? If she dies she can't protect Wanda, if she lives she can still run her manipulations. In fact, Wanda CAN'T die since of that fate crap. From Stanley we know an Overlord can tell the differance between being turned into food and normal croaking, but I that might also indicate he knows how much food he'll get. (Or a connection to the hammer). There is no reason to believe an overlord can truly tell the differance. They might be able too, but quite possibly not.

And yes, Clay especially probably turned. I mean the women he loves is on the other side soon. What do you think happened...

[Balerion]

I don't know why you would assume anyone was given a chance to turn. This entire circumstance reads as a lightning quick raid, with no one having time to react. Firebaugh barely managed to save Wanda, where he would have written out an entire note on proper paper if there had been a drawn out fight first (just to give one clear example of how we know that didn't happen).

This was raiders killing whoever they came across as soon as they found them. Level 3 and 4 adept class casters are common enough that no one is going to bother with the risks of attacking to capture instead of kill. Firebaugh himself was not given the ceremonial execution for an Overlord (a tradition we can infer from Ossomer's disgust at the downing of the tower), instead being cut down where he stood. Goodminton and everyone there should be assumed dead unless details come out that call that into question.

[BLANDCorporatio]

No Mr. Fish, you ain't wiggling out of that barrell.

To the following fragment I wrote in this post:

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?

you produced as response the gem here:

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

Which means that either you don't know Calculus, or you don't care to read my post when you respond to it.

Last post on the topic? Then let the last word be how your latest attempt to save face is wrong also.

I would love to point out that you started this debacle with "as you should know from HS math" (or words to that effect)*, you are now reduced to

I know you're impressing yourself with this math, but you aren't capable of analyzing it, because I can't give you the specifics anymore. I haven't used it in over two decades, so can't train you right now. Everything you're doing is Strawman because you're not approaching it from anything except my flawed memory and that's forcing you to make a lot of assumptions, and I can't give you the math you're demanding, because it's locked away in some textbook that's older than many readers here.

In other words, you attempted to make yourself sound smart by appealing to some misremembered old info you picked up somewhere, and now that you're called on the mistake, cannot produce the details. You laugh at my "ignorance", but are yourself ignorant when pressed for details. But at least you're happy.

{EDIT: *

Spoiler: show

Here is what you started this storm with:

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.

which as a double whammy doesn't really need limits to show that it is bonkers- wherever the line that increases intercepts the line at 0, the value of the approximation is 0; the value of exp isn't. The relative error (exp(x)-approx(x)/exp(x)) is 100% at that point, and all points where the line with 0 height coordinate is used.

}

Intercepting at 0 forces the approximation line to cross the exponential, and that's not allowed. The approximation is always below the exponential. You have to select the correct pair of lines, and they are not always y=0 on the left, because the left hand region can shorten and cause the left line to have a positive slope. The x-intercept shifts to the right as x increases, but the slope is definitely not k=exp(x), since that always intercepts at x-1.

{snip}

And that's the fundamental mistake. The approximation line never crosses the exponential, but choosing intercept at 0 causes it to. It's not an arbitrary process, and I'm sorry that I don't remember the details to explain how you select the lines and intercept point based on arbitrary x range.

Any line can be represented as k*x + c, where k is constant. Replacing this new expression for the line in the limit expression yields lim(x->inf)(exp(x) - k*x - c)/(k*x + c)) which by l'Hospital is also infinite. So just choosing a line and sticking with that line throughout (or choosing ONLY two lines, which in the limit to either infinity is the same to having chosen just one because only one of them will be used in that range) will result in a progressively worse approximation.

Approaching it from extremes by using infinite points? It's an approximation. It is a fundamentally flawed to approach approximations from a perspective outside the realm of approximation.

That's what I originally thought you were saying. But no, you went on to misapply l'Hospital and claim that the GLOBAL error of this approximation is 5%. This doesn't pass a basic sanity check. Your original suggestion (quoted in the EDIT-spoiler) doesn't even need limits to infinity to show how bonkers it is to claim that it has 5% error.

[Whispri]

If Wanda is part of an allied non-Capital Side in the Future Era at Gobwin Knob, then Parson pretty much stole her Scrolls and got outraged about it during the Battle for said City, what a complete and utter boop.

So where to from here for Wanda? The approaching cavalry suggests capture, but she's still the Lady Wanda Firebaugh, she still has full juice, she's defeated armies with a smaller stack than that. So if Clay did Boost her, well she might defeat this raiding party, which may in turn grant the forces needed to repel the second and so on. If so... might she end up allied to Haffaton? She can't poison them from without. I'm actually hoping she gets to spend at least a few turns exploring ruins and taming horses. Some time spent adventuring would look good on her.

If they have scrolls then there is no reason to think Faq was involved since scrolls can be purchased in the magic kingdom. Also another thing to mention is that Faq didn't send mercenaries to nearby sides, but sent them to far off sides; sides so far that most don't even know their existence. Futhermore is the fact that Jack would have to be away from Faq for many terms and there is no telling what scouts might pass by in that time. Also i feel safe in assume Faq's isolation status... i mean if Faq wasn't isolated then how did they become isolated? Kinda hard for them to make all other nearby sides to forget about their existence.

The alternative seems plausible considering how we already saw a pair of sides get into Goodmitten's airspace in a very sudden manner. hell the update even mentioned that frenemy and Quisling were now allies with haffaton. If they could invade and potentially conquer goodmitten by air once, they could do it again with haffaton's forces to aid them. Without the uncroaked, goodmitten doesn't have a whole lot and it would not take much to finish them; it may not even take a very large army to finish them

If? Yes, Scrolls can be bought for a pretty penny, Jack? He can make the booping things to order. As for the rest, Faq's distance from Goodminton is unknown and unknowable, it only needs to be close enough. Faq has a Predictamancer and again, Scrolls. On the subject of their isolation, their set-up requires multiple high level Casters in order to work and they don't grow on trees. Even if they are hiding, as long as they keep their Capital from being discovered everything's fine and, well, Foolamancy.

Frenemy and Quisling may have shown their true colours and allied with Haffaton, but the prior update made it clear that they'd pulled out of the area and Frenemy took a pasting last time in anycase. Their last attempt was defeated by a five Unit stack without the Fellows getting involved and of that stack only Wanda left the Capital. Furthermore, to pull off a stroke like this they'd have had to kept their forces within striking range of Goodminton, without being discovered by Boosted Scouts, for turns on end.

Every reference to the concept of "Turning". We know Warlords and Casters can change Sides.

But more specifically, Stanley's description of Wanda Turning to GK when he attacked FAQ. Wanda is clearly a full fledged unit of Gobwin Knob.

Yes we do. Rulers though... Can a Barbarian leader stop being a Barbarian without founding a Capital Side?

His description consisted of the word 'Bam', plus he's an idiot who was talking to someone he considered to be his intellectual inferior. Even if you're right, what's to stop Wanda saying 'I'm a Barbarian now' and walking away with the all the gems she can carry at any given point?

-Overlords (and thus their sides) can submit to another side! Ok, tecnically we still didn't saw it, but there's not other option. Wanda is overlord now. Wanda will, at least, become an unit for Faq and later on to GK. Hamster would've certainly noticed if Wanda was her own side.

Wanda stopped being an Overlord when Goodminton was destroyed, she's leading a non-Capital Side now, I don't think we actually have a term for that beyond 'Barbarian'. Anyway, Parson didn't realise the Gobwins and Hobgobwins were his allies until someone told him so. The same could easily be the case with Wanda, especially if she's actively using her magic to avoid... trouble. Stanley's Stanley after all.

[0beron]

[snip] I think it's more likely that they would have been captured first, and thus still lit-up, before later being turned.

Does rulers know where captured units are? If so then Stanley knows exactly where Jillian sets up camp for the night.

Though of course there cold be a middle road where the ruler knows the units are captured but not more then that.

I would imagine that a ruler knows that their unit has been captured, but not where. I've gotten the impression that the Natural Thinkamancy of Rulers is very limited, in fact I'm surprised that Wanda could tell Delphie was in the tower, but that may be because she was in the capital and not afield.
As for the capturing Ruler...I'm not so sure. They unit is not properly "theirs" because they can't issue orders to it. Sure, they pay it's upkeep, but I think that's almost more akin to erf-version of the Geneva Convention, except its a rule of the game rather than an agreement.

because Trem is not a popped Heir

I suspect this is incorrect. I think that multiple Heirs can be popped and that they, along with any commander, can be the Heir Designate. It makes sense from a real world perspective, too: multiple royal children with valid claims to the throne are very often born, at least for the sake of redundancy, despite the later risk of fracturing the kingdom between them.

And because it doesn't make much sense for Slately to consider his non-heirs "sons". It's possible, but I just don't find that plausible.

No, it is specifically stated by Slately that when Trem was popped, Jetstone had many Heirs but few Warlords, so they didn't waste the extra turns to pop him as an Heir. I don't know the exact page, but I'll post it when I find it.

Anyway, this point about Trem was only important because I was falsely speculating that if Trem ascended, Jetstone would lose its Royal status, based on Wanda's ascension, but I was overlooking other details (namely, that Firebaugh wasn't Royal)

[goodmorrow]

Wow. So many formulas and discussions over math, etc. I'm just still laughing at the dancing Un-Tommy joke.

For reference: http://www.youtube.com/watch?v=sZ-aRwEbp5I

[Kreistor]

If Wanda is part of an allied non-Capital Side in the Future Era at Gobwin Knob, then Parson pretty much stole her Scrolls and got outraged about it during the Battle for said City, what a complete and utter boop.

I think the "ownership" here is in question. Wanda had to get permission to buy clothes. She had the Scrolls, but they may not have been technically hers if they were bought with GK schmuckers, only in her care. Stanley was gone, and couldn't confirm that he knew of the scrolls existence. Wanda may not have felt obligated to inform Parson the scrolls were part of GK inventory.

So where to from here for Wanda? The approaching cavalry suggests capture, but she's still the Lady Wanda Firebaugh, she still has full juice, she's defeated armies with a smaller stack than that.

Check out Ben from Transylvito. Not a Vampire. Casters do wind up part of other Sides, and it is not obvious that they are always captured or Turned aggressively. Vanna joined FAQ willingly. Recruiting Casters from the MK may be a common method of getting Casters on your Side. Wanda can simply work with Haffaton for a while. wind up in MK when it falls, and then hire on with FAQ. How do they find her? Marie and her Predictamancy.

Frenemy and Quisling may have shown their true colours and allied with Haffaton

Groups like them have no "true colours".

Every reference to the concept of "Turning". We know Warlords and Casters can change Sides.

Yes we do. Rulers though... Can a Barbarian leader stop being a Barbarian without founding a Capital Side?

I don't see any reason why they couldn't. Seems a petty exception. They can ally, so I see no reason why they couldn't Turn.

His description consisted of the word 'Bam', plus he's an idiot who was talking to someone he considered to be his intellectual inferior. Even if you're right, what's to stop Wanda saying 'I'm a Barbarian now' and walking away with the all the gems she can carry at any given point?

We do not know that abandoning a Side is even possible. You can Turn, but there is no evidence of voluntarily becoming a Barbarian. If possible, any Caster in the MK would be able to just go Barbarian and stay there, so Rulers would ban the Portal. So no, I do not believe you can choose to abandon a Side.