Inner Peace (Through Superior Firepower) – Episode 008

[El_Chupacabra]

But its even scarier if they dont and the life the pliers create has to be balanced somewhere.

Well, considering the amount of death over the history of Erf, perhaps the pliers are correcting an imbalance that already existed.

[El_Chupacabra]

HORSECOOKIES! I think there's a reason Clay isn't a Master.

So, following his theory, what happens to the number that was created? Once used, where does that number go? Poof, it disappears? Or back into the pool, waiting to be used again?

This is the flaw: if there is a pool of numbers to draw upon, and it is of infinite size, drawing one number out does not reduce the number of numbers in the pool, because infinite - 1 is still infinite. That means the pool must be finite under Clay's theory. If that's true, then drawin g any number out changes the odds that that number will be drawn by someone else, and that would brutalize the Mathamancers and Predictamancers. Right? Beeeeeeep... wrong answer.

Mathamancy is about probabilities. If someone changes the odds of one number appearing vs another, they aren't screwed... they aren't even phased. Good statisticians know how to account for differing probabilities of the appearance of one number vs. another: they do not require all numbers to be equally probable in order to calculate odds. It's harder, but only by a little bit, and Mathamancers have magic to do those complex calculations for them.

As for Preictamancers... they're tight lipped about how they work, so we don't know how changing the odds of survival of one unit over another will affect their Predictions. If they are seeing the future, then they're seeing the future based on whatever does happen (not what is most likely), so changing survival odds won't affect them at all.

No, I'm not buying what Clay is selling here. It may be his way of understanding Luckamancy's fickleness, so to him it may be true, but I suspect a Master will have a completely different view.

Pure speculation: I'll bet a Master class can choose whom the roll is stolen from, ensuring a boon for your Side and a curse for your enemy simultaneously.

Well, it could be as simple as a penalty to future "rolls". Short-term gains at the cost of reduced luck elsewhere... Makes Sense.

[El_Chupacabra]

I think that Clay may be hitting on another factor as to how Erfworld has been engaged in "Perpetual War".

If twisting Luck tends to inevitably draw repurcussions and long-term failures to sides, perhaps that's how the Titans planned on making sure there never was a "final victory" where one side conquered all. I do suspect that one goal of the "Titans", if they exist, was to make sure Erfworld was in perpetual conflict, and having one side's Luck cave at critical points due to either early or excessive abuse of Luckamancy by one side, or via other side's manipulation of the same, would ensure that even the most competently run side would eventually fall apart.

[Chit Rule Railroad]

This is the flaw: if there is a pool of numbers to draw upon, and it is of infinite size, drawing one number out does not reduce the number of numbers in the pool, because infinite - 1 is still infinite. That means the pool must be finite under Clay's theory.

It's not an infinite pool, it's more like an infinite sequence. If Clay wants the next number received from the sequence to be a four, his magic traverses the sequence until it finds a four, and swaps whatever would have been the next number for that four.

If Clay is right that the magic "doesn't look very far", then there's really more than one sequence, some "closer" than others. I speculate that when Clay casts Luckamancy, a random number is taken from the most local sequence and used to determine whether to steal luck from that sequence or from the next closest sequence. Then the same check is repeated for that sequence, and so on.

[Dancing Cthulhu]

An interesting update, I am enjoying these alot.

I find the decay Wanda senses about Clay and Delphie interesting, I am really curious of the cause. As far as I remember no one else in the world as been portrayed as giving off such an aura, regarldess of age (in a world were aging and its affects are really an unknown). I wonder if it somehow relates to Wanda's croak sense (though she hasn't mentioned it in relation to her brother, so I doubt it is like Raistlin seeing everyone wither and die). Perhaps she is sensing Clay and Delphie have secretly given up - not in a way that would cause a disbanded, but are none the less gradually rotting away from the inside.

Hmm. I'm getting a distinct feeling that Clay doesn't actually know what he's talking about.

Heh, I have also gotten the impression he might not be the sparkliest die at the table.

Which is a nice touch. Magic- it works, but no practicioner actually understands how, or at least, no one has a very good picture. Very stupidworld-like, too.

It also means nothing with regard to my pet theory on how to interpret Luckamancy action. If I assume Clay doesn't know enough to provide a coherent model, what do I have to go on?

It would make sense, and we know casters (some at least) do enjoying debating, so there must be some disagreements and mysteries still unknown.

But I can put my tinfoil hat firmly on and say that there are a few Magicks in Erfworld that may be less than what they appear: what if Luckamancy, Mathamancy and Predictamancy were mostly bunk?

They could well be... heh, perhaps they have secretly been stagemancy all along.

That's an interesting theory Jackhammer, but it's flatly contradicted by this update. Clay is confident (for magic-theoretical reasons) that the lucky outcomes he invites are "stolen" from someone else, thus not disturbing the universe's probability distribution so to say. However, that the universe does not go very far to steal these rolls is something he only darkly suspects. Nowhere does he suggest the stolen lucky rolls has to come from the same side. And he certainly doesn't pick and choose which rolls to steal.

I wonder - Clay is firmly under the thumb of a predictamancer who comes off as a bit suspicious to me (understatement). I wonder if she has had any influence on his thinking or understanding of the secrets of luckmancy.

Assuming a widespread predictamancer conspiracy it would make sense for them to want people, especially those with a potential wild card power (as luck often is) to believe that in the big scheme of things all the luckmancy in the world isn't going to undermine predictamancy or mathmancy - the predictamancer says it will happen, it will - don't fight it, just accept it.

A bit "Clay, I have seen our side is doomed, shhh, there is nothing your magic can do to avert this, you know how luckmancy works. But listen, something greater can come from the destruction of our side if your play your cards right. Now listen closely, you know the warlord we are to pop based on the prediction I made to the overlord? Well *whisper whisper*"

Everyone seems to have realized that it's ok to get bad luck in battles you're going to lose anyway, but is forgetting that it's also ok to get bad luck in battles you're going to win anyway. If you don't need a good roll to win the battle, you might as well take those rolls and move them to battles where the outcome is less certain.

Assuming Clay is right with this that would depend on a side knowing which battles are certain wins or losses. Sometimes it is possible, others not so much. I guess with a predicatamancers it is easier but up till now we have gotten little detail on how, well, detailed a prediction can be. It is fine for them is they go for vague but certain:

Caster: "This city will fall"
CWL: "Damn! Why?
Caster: "That I can not say, all I know is the city will be lost"

So CWL will accept that and not waste juice on trying to save it. If they can provide great detail, or even moderate detail it seems possible smart cookies might see a way to avoid such a defeat (though some things are unavoidable, not everything is), which one would imagine would lessen the power predictamancers have - so far everyone seems to take their word as an absolute certainty (except young Wanda, ironically) - as far as I remember we are yet to see someone given bad news and respond with a "ok, what if I do this?".

So a Predicatamancer predicts a battle will be won (or it is obvious to a CWL), but how detailed is the knowledge? Even winning a battle could lead to heavy losses, deaths of warlords etc which might be avoided with a little luckmancy. And of course I guess luckmancy could apply to any "roll" a unit might take - an army might be going to win no matter what, but a warlord with a luck boost might get lucky on a spot check and reveal an ambush or foolamancy or something which will allow them to win much more convincingly or achieve something much greater. And of course if Clay is right I guess after using luckmancy bad and good luck could rub shoulders in a single battle that would have been won anyway as well as a battle that would have been lost, you're just doing your absolute best to ensure the bad luck doesn't fall on what you have classified as vital (or that what you have classified as vital has every chance to succeed in whatever).

[Dark Matter]

Oh, ouch.

From the description, that "4" was stolen from some future roll. That's fine and good... but...

Why does it have to be ONE roll??? I.e. what if he needs to steal a lot of future 4's to get one?

From Clays talk, they lose a LOT of unled types, enough to balance the effect of giving luck to the warlord.

Notice that picking when to be lucky is a huge effect, the implication is the unluck is huge enough to balance it, which isn't going to happen if "One Warlord Lucky = One Unled Stabber Unlucky".

Maybe a Master Luckmancer can steal luck more efficiently.

[drachefly]

Thus, something along the lines of "on average" or "we should expect losses around" or even a confidence interval are all reasonable information a Mathemancer could provide (I personally love the idea of hearing "Losses should be less than 15%, 19 times out of 20" from one). Even that's not quite proper, but I still like the sound of it.

Noooo... confidence intervals are for estimates involving unknown populations. When you know the population (ie. you can count your troops and the enemy's), standard deviation applies, but confidence intervals are irrelevant. Confidence intervals are used when sampling from a population, and so apply to exit polls, but not to a vote once it has been counted.

... If Mathamancy is being used to figure out what forces the enemy have, then yes, you do get a confidence interval. GR named 3 uses, one of which was a Confidence Interval. Nowhere was it said that the parenthetical example was an instance of a Confidence Interval.

[King Mir]

Oh, ouch.

From the description, that "4" was stolen from some future roll. That's fine and good... but...

Why does it have to be ONE roll??? I.e. what if he needs to steal a lot of future 4's to get one?

From Clays talk, they lose a LOT of unled types, enough to balance the effect of giving luck to the warlord.

Notice that picking when to be lucky is a huge effect, the implication is the unluck is huge enough to balance it, which isn't going to happen if "One Warlord Lucky = One Unled Stabber Unlucky".

Maybe a Master Luckmancer can steal luck more efficiently.

From the first page of book 0: "Zero always called, and someone would have to pay." The four won't be balanced by anything other than having exactly one less four in the future. otherwise it won't come out to the same average, the same balance.

[Kreistor]

Thus, something along the lines of "on average" or "we should expect losses around" or even a confidence interval are all reasonable information a Mathemancer could provide (I personally love the idea of hearing "Losses should be less than 15%, 19 times out of 20" from one). Even that's not quite proper, but I still like the sound of it.

Noooo... confidence intervals are for estimates involving unknown populations. When you know the population (ie. you can count your troops and the enemy's), standard deviation applies, but confidence intervals are irrelevant. Confidence intervals are used when sampling from a population, and so apply to exit polls, but not to a vote once it has been counted.

... If Mathamancy is being used to figure out what forces the enemy have, then yes, you do get a confidence interval. GR named 3 uses, one of which was a Confidence Interval. Nowhere was it said that the parenthetical example was an instance of a Confidence Interval.

No, that isn't how a Confidence Interval works. Confidence Intervals come into play when you aren't certain if the population you have sampled are representative of the whole. It's a second layer of uncertainty. But it is reliant on your sample being random in the first place, and on Erfworld it rarely will be.

In the case of Statistically predicting enemy troops, you need a random sample to start with. You can't use the Digger attack, for example, because it is not random. All units have the Digger special, so how many enemy units in the city have the Digger special? Statistics would say, "All," because your sample is 100%. But we know that if the entire army had that Special, it would have been a much larger attack. So we can logically say, "Few to none," but a Mathamancer can't take that sample and use it to get the true population.

On the other hand, in our world, we might be able to. Imagine a scenario in Normandy where there are 200 available soldiers and the Captain asks for 20 volunteers for a suicide mission. Once the Germans defeat them, they can look at the equipment on the US soldiers and determine which proportion of this company carries light machine guns, rifles, BARs, and SMG's, and from that develop expectations for other similar units (ie. it would be representative of an infantry company but not an airborne company). But you would remove the Sniper from the list, because you know they are rare, and almost always one will be on such a mission. The use of volunteers, instead of selecting men for particular reasons, makes the sample random and potentially representative. There is a confidence interval, based on the German intelligence's estimate size of the company.

[name lips]

For the record, the worst flame wars I've EVER seen on the internet involved arguments over statistics and probability. Usually between people each of whom partially knew what they were talking about.

Now we have magic mixed in.

Say we are going to flip a coin. Probability says it has a 50-50 chance of being heads or tails.

The person flipping the coin would agree. He doesn't know ahead of time what the flip will be. He knows for certain that the event is random.

But in the next room is a Predictamancer. She uses a bit of juice and predicts the coin will come up Heads.

The person flipping the coin is unaware of the Predictamancer. He has no indication, before or after the flip, that the future has been observed.

Is the flip still random at the time it is made?

[gameboy1234]

Why are people so concerned with Luckamancy infringing upon Mathemancy's territory? Let's see if I can counterpoint this in a more organized fashion than I tend to.

I gotta weigh in here with the opposite opinion.

Firstly, since a universe with perfect probability (infinite outcomes, drawing with replacement, etc) is always uniform regardless,

This very specifically is not true.

let us reject this as the law for Erfworld for discussions sake. This is reasonable as, with Erfworld being a world with "game physics" it could just as simply work as a deck of cards without replacement, then reshuffled when done, or a computer's "random" number generator which, at some level, is always deterministic.

Now, working under the assumption that actions come from a finite "pool" of possibility does not undermine Mathemancy,

Again, very much not so.

There's quite a large amount of mathematical work that's been done on analyzing computer psuedo-random number generators of various types. I guarantee you any of those things Clay says he's doing would show up in a mathematical analysis. For example, using the example given, a "stuck" or "streaky" PRNG is a well known problem and would quickly be detected. A PRNG that produces large streaks of 4's and 1's would NOT be considered random, even it it averages out to 2.5. There's many techniques for detecting this and other sorts of problems. A simple average or even standard deviation is not the be-all and end-all of PRNG correctness. I'll refer you to Donald Knuth's The Art of Computer Programming, Vol. 2, Seminumerical Algorithms for more information.

I'll elide the rest of your post there, but suffice to say that advocating "infinite draw" or the average as the only thing that matters is pretty naive. There's lots of things that could go wrong, and an PRNG that always gives a straight flush to one player and one of a kind to another would be considered broken by anyone, no matter what its average or how big its "draw."

In game terms, I think it should work like this: Mathemancers should be able to tell you the odds, and tell you after the fact if Luckmancy was used to skew the odds. (This is detecting out of order rolls, or streaks, or whatever.) Depending how good they are, they might be able to do this real time, or it they're not so good possibly only after a battle was finished.

A really good Mathemancer should be able to pick up on enemy Luckmancy during a fight and tell their Overlord "Oh, they're using Luckmancy here to boost, those rolls are way messed up. Let's disengage from that battle and play defense to limit our loses. Over here now, their Luckmancy is costing them, so let's push ahead and cause some damage." This might require a level 12 master class Mathemancer, or it might require something a lot less, depending on how Rob sees his world.

My 2 schmuckers.

[King Mir]

Although you can pick up statistical biases by observing results and comparing them to naive prediction, I doubt a battle would have enough data points to provide aany kind of confidence that luckamancy is used. For things larger than a battle, you might have enough points, but you'd just be proving that the enemy has a luckamancer, which isn't particularly useful to know.

[gobe]

Is the flip still random at the time it is made?

I think it should still be considered random. In the sense that random events still do have an outcome. Predictamancy is the magic of knowing in advance what will happen, but it doesn't affect the outcome per say (that would be luckamancy, obviously). It's because of the outcome that the prediction is made, not because a prediction was made that an outcome occurs.

Although you can pick up statistical biases by observing results and comparing them to naive prediction, I doubt a battle would have enough data points to provide aany kind of confidence that luckamancy is used. For things larger than a battle, you might have enough points, but you'd just be proving that the enemy has a luckamancer, which isn't particularly useful to know.

I agree with gameboy1234, and somewhat disagree with the above. Of course it depends on the scale of the battle, but there is still a lot of rolls being made, since one happens for every action of every unit on both sides. Also, this is magic, so maybe you can see more than only the rolls and their stats, sequences, etc., but even something about the "nature" of some of the rolls, i.e. if they were tampered with, on a magical level. But perhaps this would be lookamancy instead of mathamancy.

[Saladman]

I find the decay Wanda senses about Clay and Delphie interesting, I am really curious of the cause. As far as I remember no one else in the world as been portrayed as giving off such an aura, regarldess of age (in a world were aging and its affects are really an unknown). I wonder if it somehow relates to Wanda's croak sense (though she hasn't mentioned it in relation to her brother, so I doubt it is like Raistlin seeing everyone wither and die). Perhaps she is sensing Clay and Delphie have secretly given up - not in a way that would cause a disbanded, but are none the less gradually rotting away from the inside.

If it were just Delphie I'd take it as a sign of treachery. If she found a way to go up to the edge without actually turning or disbanding, decay could be the result. Clay makes that a little less likely, though being under her command it's possible he's just suffering the effects of not doing the best he can for his side, even if he doesn't know it.

Or to elaborate on your idea, perhaps Delphie has Predicted both their deaths, and either it's due real soon now, or the knowledge weighs them down.

[BLANDCorporatio]

For the record, the worst flame wars I've EVER seen on the internet involved arguments over statistics and probability. Usually between people each of whom partially knew what they were talking about.

Psst. Statistics and probability aren't proper math. There's a gang called the Blo- I mean the Bayesians, and a sect called the Frequentists, and they kill each other on sight.

Say we are going to flip a coin. Probability says it has a 50-50 chance of being heads or tails. {But a Predictamancer knows what the outcome of a specific roll will be.}

Is the flip still random at the time it is made?

Stop right there. What is random(ness)?

Because if you would define randomness as "not obeying a (causal) pattern", funnily enough, it's still random. Imagine this. I generate 1000 numbers, randomly. Truly random, by whatever definition you care to apply, and no predictamancer in the universe will know my next number.

NOW, I'm going to use that random sequence of 1000 numbers to determine whether a simulated coin falls heads or tails. I'm going to show the whole sequence to a "Predictamancer", whereas I'm going to give Average Joe only one number at a time.

This way, the Predictamancer will always know for sure what the coin will do, whereas Joe would not. OTOH, the Predictamancer could apply statistical tests on my sequence to tell whether it's random. And yes, that makes sense mathematically. You can have a whole sequence laid out in front of you (like, say, a shuffled deck) and still ask "is this random"?

[BLANDCorporatio]

To put it another way, Fate does not exclude Arbitraryness or Randomness.

Fate is as if the whole of existence is a movie. All frames already exist, only one of them is on the screen right now, but all frames have already been defined.

Nonetheless, all frames may be like TV static, with no patterns linking them and no pattern existing in a frame.

Causality (or rather, determinism) then is a stronger assumption than Fate. Not only is the film already made, but connections exist from one frame to the other and as a consequence of that, between pieces of the same frame if they are sufficiently close.

[gameboy1234]

Although you can pick up statistical biases by observing results and comparing them to naive prediction, I doubt a battle would have enough data points to provide aany kind of confidence that luckamancy is used. For things larger than a battle, you might have enough points, but you'd just be proving that the enemy has a luckamancer, which isn't particularly useful to know.

No, I don't have access to Knuth right now, but I'm sure I recall (I think they're called) confidence intervals for chi-squared tests for sample sizes as low as 10 and 20. It's harder, and you need to use a larger confidence interval, because for example it's fairly possible in a short fight between two pikers one guy gets two or three 4's in a row, but you don't need huge amounts of data to develop some sort of picture about your data.

But in a larger fight, with ten's or hundred's of units per side, you're going to generate a lot of numbers just in the first round. I'm quite certain a decent mathemancer, if such analysis is possible at all, could spot something "fishy" or out of whack very quickly. This sort of thing is never 100% of course. The opponent could just have a lucky round or two. But a good mathematician, and a good mathemancer, does not believe in luck; in our experience there's no such thing as luck (only Luck), and we keep our trusty blaster at our side too.

(I'm assuming that the system Clay, and Rob, describe ultimately works a lot like most table top war games. Both sides roll fist fulls of dice, "casualties" are removed, there's a few options for other play, then the next round happens and fist fulls of dice are rolled again. This is done until one side breaks or is eliminated. If you could record and analyze the rolls, it should be possible to spot say loaded dice really quickly, real time, right there on the battle field. The first round should be enough to tell you something is probably "up.")

[pSycHOtic chICkeN]

Interesting. So am I to understand that Luckamancy cannot be used to jinx an opposing force but only to boost one's own side? And even that only by "stealing" one of your own side's good rolls and exchanging it with whatever you were supposed to roll at the time? I kind of like that mechanic. Hmm.

Episode 007 said the exact opposite:

Clay sniffed again. “Yeah, kind of. Or jinx the enemy...

[ParsonIsOP]

:shock: This update provides a deep revelation on some key aspects of the plot.

If you put the following together
1) In order for one person to benefit from luckamancy, other people need to receive bad luck .
2) We know that there is at least two characters that are destinied by fate. Parson and Wanda.
3) Fate seems to protect people by using Luckmancy.

You realize that suffering is going to always surround these two. No wonder Wanda's sides always fell. No wonder she said she had to suffer so much to get her arkentool. No wonder she said Parson is giong to face so much hardships in his life. This is an actual Erfwold mechanic, and not just Wanda's personal beliefs. Erfworld suddenly seems much more cruel. Parson has a huge fight ahead of him.

Good update Robb. I would say the last two updates have been the most important ones yet.

Actually, you don't know that Fate is the same as Luckamancy. But I can see why it would make Wanda such a fatalist.

A major major theme in Erfworld is that it's a zero-sum game. And that's what this is trying to imply.

[pSycHOtic chICkeN]

The way Clay talks about numbers being stolen reminds me of things I have heard gamblers say. The gamblers that lose money on slots, not pro poker players who used advanced mathematics. Gamblers on a losing streak will claim that their "bad luck has almost run out". There is a belief that past events will effect the probability of the next event. This belief is not based on any type of sound mathematics. I am sure Rob has encountered real people with this idea. It is conceivable that in an Erf World casino it would actually be best to gamble your last chips in order to recover your losses. Or maybe you should bet low until the losing streak runs its course and then bet high and recover all when the winning streak starts.