How to write no rules

[Zeezy]

After five pages my position covers a lot more points than that but I can hardly say there is anything in your summary which is altogether incorrect.

In that case, while you were wrong* about 3d6 not being deeper than 1d20,** I do not see what it has to do with refuting your position as I worded it. Still, it was (and still is) a hot point of contention, and I want to put in my two cents.

*: Whether it be by failure to communicate, your facts being flat-out incorrect, or some other case. From what I'm seeing, it's probably the former case -- if not exclusively, then chiefly.

**: Depth, in this case, is defined as how many full standard deviations from the mean you can go before you leave the boundaries of the sample -- one with 1d20 (σ~5.766), versus two with 3d6 (σ~2.958); thus, 3d6 is twice as deep as 1d20. But Parthenon beat me to that, apparently!

[Parthenon]

My last post was possibly a mite combative. So I'm going to try and be a bit clearer and calmer.

I'm going to compare three methods of action resolution, each with a 50% chance of success: flipping a coin, 1d20 and 3d6, with a single penalty of about 50% miss chance, or blindness in D&D. If you have two such penalties your chance of success should be around 12.5%, so I'm going to compare each action resolution method to the hoped for chance to see if they work at all.

For the coin flip it is easy: add another coin flip and if both are heads you succeed. Bonuses of 50% can also easily be added and adding another penalty means just adding another coin with the expected and reasonable success chance of 12.5%. However there is a big problem: you can't have penalties other than 50%.

For the d20 you need a penalty of -5, which is close to the standard deviation. However there is a big problem: two such penalties means that it is an automatic failure with 0% chance of success as opposed to a 12.5% chance of success. Which sucks.

For the 3d6 adding a penalty of 2.96 changes it to an 80% chance of failure rather than 75% (a 60% penalty rather than 50%) so the penalty of -3 is actually slightly too large. But since we can't use 2.7 or whatever we'll continue to use -3. But what it means is that you can have two such penalties and still be on the RNG, admittedly with a 2% chance of success rather than a 12.5% chance of success.
Interestingly, given that a -3 penalty gives a 60% chance of failure we are actually looking at an expected 8% chance of success, which is a lot closer to the actual 2%.
So, this is better since you can have different sized bonuses, there is still an actual chance of success with two penalties and it is closer to what we'd expect to happen.

Since people are talking about higher granularity, lets look at that. For example lets use 3d10 compared to 1d30. The 1d30 has a mean of 15.5, a range of 30 and a standard deviation of 8.7. For the 50% penalty you'd need a penalty of -8. Two such penalties would be -16, or off the RNG.

Whereas with the 3d10, the mean is also 15.5, but has a standard deviation of about 5 and a range of 28. Damn, thats too big to round down. I was hoping it to be 4.3 or something. Oh well. Two such penalties are -10, which is still on the RNG, but with a probability of 3.5% (as opposed to 8%).

Once again, the difference is between automatic failure and 2-4%, while it is supposed to be closer to 12.5%.

Basically, you need a larger bonus with the d20 to do the same thing, and it doesn't fit what you want with just two of these bonuses. The 3d6 doesn't either, but it is still closer to what you want.

[PhoneLobster]

PhoneLobster thinks two is the same as a whole lot. Dumbass.

Those were sample graphs of normal distribution they appear in the article on mean deviation due to their significant relevance to the term standard deviation which is largely used to determine how steep a normal distribution graph will look.

If you were capable of clicking on that little linky on the pretty picture you would have discovered that actually the bell curve graph is very common.

...the normal distribution or Gaussian distribution is a continuous probability distribution that often gives a good description of data that cluster around the mean. The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known as the Gaussian function or bell curve...

And importantly the curves being discussed by Murtak and frank... are indeed bell curves that adhere to this exact definition.

And indeed do it better than most since effectively the RNG involved is nothing BUT a normal distribution generator.

Don't try and bluff me with your brief skim of the wikipedia article I linked you (brief enough to apparently neither understand it or even read the associated links). I did this and a hell of a lot more at a university level.

The standard deviation is a measure of spread that can be calculated for any group of data, not just bell curves.

Yes and no.

In that ANY set of data has a standard deviation you are, in a rather trifling manner.

But rather specifically Frank and co were describing LOW standard deviation normal distribution curves (3d6, etc...). If you intend to actually use the term to describe data including a 1d20 then you are going to such a HIGH standard deviation that you are not only rendering the term meaningless for this discussion you are effectively revealing that you and Frank have used the wrong term.

Talking about bell curves is MORE correct than discussing standard deviation as if it was a fixed term meaning LOW standard deviation, and indeed a rather specific and arbitrarily mapped curve at that, which is what Frank tried to do and what you now inexplicably defend.

Of course all this is still stupid because we have already at length discussed the actual odds of results occurring and the impact of all that on this thread.

Frank introduced the term "Standard Deviation" and waved it around like a distraction, and I responded with the term "Bell Curve" while talking to him about it.

Because talking about how many times you can add a term that merely gives you an idea of how lumpy the middle of a graph of probability distribution looks to the mean of that distribution before you exceed the maximum distribution... is fucking mathematical gibberish.

I am pretty confident it isn't even what Frank MEANT to talk about.

But it really doesn't matter because the DATA has already been discussed, the fact that it HAS a Standard Deviation and that it FORMS a Bell Curve is really fucking irrelevant. The numbers are there the behavior is there we already spent 4 pages discussing exactly that behavior

This is nothing more than a (poorly executed) attempt to bury the actual numbers and what they actually do in official sounding terminology that actually doesn't do anything other than describe the numbers we have already discussed.

It isn't even telling us anything NEW about the numbers already discussed. We already knew that they did that (well at least I certainly did, apparently it was news to Frank).

**: Depth, in this case, is defined as how many full standard deviations from the mean you can go before you leave the boundaries of the sample -- one with 1d20 (σ~5.766), versus two with 3d6 (σ~2.958); thus, 3d6 is twice as deep as 1d20. But Parthenon beat me to that, apparently!

Interestingly depth is NOT a term that you will find anywhere in those now rapidly more infamous wikipedia articles on Standard Deviation OR Normal Distribution. Indeed good luck finding the word "Depth" anywhere in the linked articles on various terms at all.

Not surprising really because it is not an especially valuable term to know, it is certainly not actually a valuable term here since it
A) Tells us nothing we didn't know already.
B) Is essentially an term invented on this very thread to describe a behavior that someone then declared beneficial. At no point has it been described WHY this behavior is beneficial.
C) Your invented depth term is especially interesting because by your own definition a Standard Deviation does not HAVE a "Depth" but a Bell Curve or Normal Distribution DOES have a "Depth".

But you know you apparently don't want to talk about bell curves and normal distributions, only standard deviations. So how the fuck we can start talking about this Depth invention of yours I have NO idea.

For the coin flip it is easy: add another coin flip and if both are heads you succeed

You are mixing your math in bad ways here. Using binary 0-1 number generators and an "And" condition really isn't a nice thing to add at this point. So even if the numbers involved are small and aspects of combinational logic and probability theory MIGHT sorta kinda brush on each other a bit... lets keep the combinational logic out of it for everyone's sanity.

And really if it's easy for you to "And" a coin flip to a coin flip why can't you "And" a coin flip to a 1d20 or even a 3d6? I mean. That actually IS what the d20 system does in some cases after all.

But that departs from telling us importantly what is DIFFERENT about 1d20 and 3d6 rolls. Adding an additional layer of obfuscation for no specific benefit. So again, lets not do that.

And so you describe a scenario where you once again equate a +3 bonus at several points in a 3d6 range to a +5 bonus in a 1d20 range.

1) This is nothing new to this thread. People have been doing that since page one. It is incorrect because a +3 bonus is NOT equal to a +5 bonus over the range you are discussing. It is NOT a fair or accurate comparison of bonus values over the discussed ranges.

2) You know that because you actually TALK about how the value changes. You even describe, for a change, why you apparently think that is a good thing.

So, this is better since you can have different sized bonuses, there is still an actual chance of success with two penalties and it is closer to what we'd expect to happen.

Lets see what you expected to happen...

with a single penalty of about 50% miss chance, or blindness in D&D. If you have two such penalties your chance of success should be around 12.5%, so I'm going to compare each action resolution method to the hoped for chance to see if they work at all.

(aside from the fact that you arbitrarily decided upon multiplicative rather than additional factoring of modifiers, which remember is bad in RPGs because players don't like multiplying and dividing things in their heads lets just carry on with your declared goal/"expected outcome"...)

a penalty of 2.96 changes it to an 80% chance of failure rather than 75% (a 60% penalty rather than 50%) so the penalty of -3 is actually slightly too large.

So lets see. is it what was "expected"/desired from the FIRST increment of the "50%" modifier?

No.

So lets take a little note of that. "3d6 mechanic did not perform as desired on first application of modifier due to weird and shitty numbers involved in its increments of percentage chance of success".

So lets check how it performs on the SECOND bonus application.

you can have two such penalties and still be on the RNG, admittedly with a 2% chance of success rather than a 12.5% chance of success.

So lets see. is it what was "expected"/desired from the SECOND increment of the "50%" modifier?

No.

So lets take a note of THAT down. "3d6 mechanic did not perform as desired on SECOND application of modifier due to weird and shitty numbers".

But wait you have a tiny explanatory note...

Interestingly, given that a -3 penalty gives a 60% chance of failure we are actually looking at an expected 8% chance of success, which is a lot closer to the actual 2%.

Oh a revised expectation. Somewhat out of left field since we are arbitrarily declaring we must never ever revise expectations bonuses on a 1d20 mechanic in any way, but lets run with it and...

...oh no!

Even the REVISED expectation is not met and instead encounters a chance of success one QUARTER of the desired goal!

So lets take THAT down as a note "Even when cheating by revising expectations the 3d6 mechanic STILL did not perform as desired".

I wonder why that is. Could it be because as an approximation to a Bell Curve[/i] the results of the 3d6 behave like a Bell Curve and instead of producing the results you declared (entirely arbitrarily) as desirable over those produced by a simple transparent 1d20 mechanic just so happened to be... oh yes... that's right... the results that I expect to be generated by...

A BELL CURVE.

Now do you want to have a discussion about how a basic mechanic that has only a 2% chance of success is a generally either bad or insignificant thing to build your RPG system around including?

Or how 1d100 would be a much nicer way of doing that? (should the need to do it inexplicably arise)

Or do you want to pretend you know something about maths again so I can rip you apart in public again?

[Username17]

Goddammit PL. A Normal Distribution is not the same as a Standard Deviation. It is a useful thing to have when you're talking about Standard Deviations, because in a Normal Distribution the distances between the standard deviations are fixed numbers that you can add together easily.

Rolling a pile of dice and adding the results approximates a normal distribution rather closely, at least for the first two standard deviations, which is by definition going to be most of your data set. Thus, rolling a pile of dice and adding them is a good way to transfer linear bonuses into standard deviations for abut +/-2 Standard Deviation.

But you don't get to say that bell curves and standard deviations are the same thing. You don't get to say that you meant one when you said the other. It makes you look like you have no idea how statistics work.

So cut all your bullshit. Show that you know what a standard deviation is, how it works, and why it is important, or shut the fuck up. Because you really haven't shown that other people are misrepresenting math. You've shown that you don't know what you are talking about.

-Username17

[NineInchNall]

Did you know that "separation of church and state" isn't in the Constitution? Those leftist commie bastards will tell you it is, but do a word search in an online version of the Constitution and see what you find: ZERO results! Good luck finding it anywhere in either the Constitution or Declaration.

[Parthenon]

Hmmm.... you're right that it multiplying probabilities isn't the most useful for most people. I'll have to think on that one.

But the standard deviation of the d20 is 5.77. 60% of the values fall within one standard deviation. Compare that to the 3d6. 67% of the values fall within one standard deviation. So we're comparing 60% to 67%. (Hmmm... looking at the numbers I've made a big mistake- the bonus I was talking about should have been +/- 2, not 3. That would have made the chance of success 5%. Which as you point out still isn't the expected value, but is still infinitely better than the d20)

A similar proportion of the expected values of the d20 falls within one standard deviation of the d20 as falls within one standard deviation of the 3d6. So, they can be used on both as a useful indicator of spread.

Saying that standard deviation is only applicable to the bell curve and they are synonymous is retarded.

[Murtak]

Interestingly depth is NOT a term that you will find anywhere in those now rapidly more infamous wikipedia articles on Standard Deviation OR Normal Distribution. Indeed good luck finding the word "Depth" anywhere in the linked articles on various terms at all.

Of course not. All mathematical models have an infinite depth. The entire concept is useful only in finite, predefined but random data sets.

Did you know that "separation of church and state" isn't in the Constitution? Those leftist commie bastards will tell you it is, but do a word search in an online version of the Constitution and see what you find: ZERO results! Good luck finding it anywhere in either the Constitution or Declaration.

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof

Edit: wrong thread, NIN?

[NineInchNall]

Nah, it was the right thread. Specifically I was mimicking PL's bit about depth not being in the wiki pages.

The point being that I consider his statement equivalent to the (commonly repeated) claim about "separation of church and state".

[Kaelik]

1) WTF you all need to die in a fire.

2) Nin, I see your comment just as easily reflecting you bitching about bell curves as him bitching about depth.

3) All this bull shit about standard deviations and depth and picking numbers at the middle of the graph specifically to punish flat distributions for no reaso at all is really dumb.

How about one person who is supporting 3d6 because of it's standard deviation depth bullcrap explain to me why the exact same arguments they have been using cannot be used to demonstrate that 20d4 is superior to 3d6?

[NineInchNall]

2) Nin, I see your comment just as easily reflecting you bitching about bell curves as him bitching about depth.

Saying "X = Y" when it most certainly does not is not the same as saying that an article talking about X says nothing about the results of X. It's exactly like saying that since the actual phrase I mentioned doesn't appear in the Constitution, the Constitution doesn't have anything about it.

How about one person who is supporting 3d6 because of it's standard deviation depth bullcrap explain to me why the exact same arguments they have been using cannot be used to demonstrate that 20d4 is superior to 3d6?

EDIT: What Souran says below.

[souran]

How about one person who is supporting 3d6 because of it's standard deviation depth bullcrap explain to me why the exact same arguments they have been using cannot be used to demonstrate that 20d4 is superior to 3d6?

Actually, the nature of the argument is such that people arguing for 3d6 ARE saying that 20d4 would be better, or at least that it would be a resolution mechanic with more of the attributes they are in favor of.

However, at the same time 3dx is a small enough number of dice that people can use the dice to get results quickly - and rolling infinite X sided dice is not an option.

[TavishArtair]

Any number of dice that you can fit in the palm of your hand and roll easily, be it 1 or 5, is not a problem. So there's no real significant difference in terms of encumbrance between 1d20 and 3d6. There is between pretty much anything else and 20d4.

Myself, I prefer 2d10, if only because the curve is slightly easier to memorize and has the nice effect of making both 2 and 20 a "1 in 100" roll.

[Username17]

If you are rolling 7d6 instead of 3d6, you can get 3 standard deviations in with linear bonuses, instead of just 2 for 3d6 or just 1 for a d20. That's an improvement.

Whether that improvement is worth rolling 7 dice and adding the totals up is another deal altogether. As it happens, it's not. But if you were making a computer game out of the deal, that would be pretty exciting. In fact, you'd probably end up having the computer roll like 15d100 or something, so you could get a lot of granularity and a lot of statistical depth.

For table top gaming though, you have limitations. You want statistical depth and you want granularity, but dealing with more numbers is a pain in the ass. Dealing with more dice is a pain in the ass. 3d6 and 1d20 are both perfectly fine concessions to the reality of the difficulty of doing this sort of thing.

-Username17

[mean_liar]

3d6 and 1d20 are both perfectly fine concessions to the reality of the difficulty of doing this sort of thing.

My entire world just came thundering down, crashing into fragments of ruin.

[Username17]

3d6 and 1d20 are both perfectly fine concessions to the reality of the difficulty of doing this sort of thing.

My entire world just came thundering down, crashing into fragments of ruin.

I don't see why. No one here is saying that you have to use 3d6, or that you have to use a curved RNG at all. It's just being said that it's an option, and that it has rather well defined effects on what is possible and how the game treats linear bonuses. Remember, this entire tangent got started when PL took a dump on his own thread with this:

I dislike the effects of "bell curve" rolls in ANY RPG mechanic. I think they are unpleasant, opaque and largely don't do what most of their proponents think they do. I regard the whole bell curve thing more as a sort of wanky zombie fad rather than a productive or sensible design decision.

Which if he'd just left it "I dislike bell curves in my mechanics" would be fine. Some people like getting extreme results all the time. It's a personal preference issue. We tend to tell each other to suck a barrel of cocks but to live and let live about that sort of thing here. But he kicked it up a notch. He said that curved RNGs don't do what their proponents think they do. And that's just a testable claim. So we tested it. We went to a god damn GURPS board and looked at what bell curve proponents actually thought the bell curve did. And you know what they thought it did? They thought it made numbers near the center very common and numbers near the edge very rare. They thought it made the first couple of bonuses very important, and made the next couple of bonuses much less important without actually canceling them entirely. And you know what? That's exactly fucking right. That is in fact, exactly what bell curves do.

Which would leave PL on totally fine grounds if he wanted to say "Fine, but I still think they suck and I don't want to use them." Or something. But he hasn't backed down. He has instead increased the shrillness of his tirades until I don't think even he knows what the fuck he's talking about any more.

He's so bent on not giving any ground that he's gotten into outright fraud - such as deliberately conflating normal distributions and standard deviations. The fact is that no one was ever making the completely ridiculous point that he had to like bell curves. The point was always simply that his tirade that the people who liked bell curves had to stop liking them went too far. And he's been an irrational dick about that point ever since. He is wrong. It started as an extremely minor point, that he could have conceded in just a single sentence, but he has blown it up into a thread consuming flame war, because he is an asshole.

-Username17

[PhoneLobster]

So cut all your bullshit. Show that you know what a standard deviation is, how it works

Really after my latest post I find myself wondering if YOU know what a standard deviation actually is.

Because it is clear you are talking about the behaviour of a particular Normal Distribution and just using the words Standard Deviation like they mean something important other than what they mean.

A Standard deviation is, approximately, how much on average results in your data set deviate... from the average.

It is used as a tool to determine where most of results in your distribution fall.

YOU are deciding it is a useful tool to define a bonus increment you find important to add multiple times to an RNG for a role playing game.

But lets look at what that decision actually does for a minute.

You use the mean of your probability distribution as your starting point.

You move along the GRAPH a number of points equal to the Standard Deviation because thats the increment size you have arbitrarily defined as good.

(lets note in passing here that standard deviation as a value has no meaning outside of this first increment, there IS no such thing as "a second standard deviation", that is, oddly non-standard)

By adding that increment you have taken ALL of the average results generated by you RNG and put them behind you.

With one single increment of the size of the arbitrary mathematical term you have chosen in an innumerate attempt to look cool the ONLY results left on the RNG are ones which fall OUTSIDE of the average result.

That's by definition, that's because that's what a Standard Deviation is, it isn't a term meaning "Bonus that is cool to add multiple increments off" it is a term meaning "Range beyond a single increment of which it is really quite unlikely for a result to fall".

Further because you ARE working with a low standard deviation on a BELL CURVE Normal Distribution the potential points on the Probability Distribution that remain have only a few results which are particularly likely to come up and decrease in value from here on at an exponential rate.

The fact that you think I'm conflating Standard Deviation and Normal Distribution is just hilarious. Because I've been talking about Normal Distribution because your reference TO the behavior of a Normal Distribution by means of a Standard Deviation is incorrect As I have pointed out PRIOR to your post of accusing me of conflating the two. Stop waving around "Standard Deviation" Frank. You don't know what it means and you are sounding like a totally innumerate idiot.

Also.

You don't get to say I'm wrong JUST because I made a broad statement about curvy dice mechanics being shit. You actually have to SHOW them to be good at some point.

Which means yes, you do actually have to answer Kaeliks question.

How about one person who is supporting 3d6 because of it's standard deviation depth bullcrap explain to me why the exact same arguments they have been using cannot be used to demonstrate that 20d4 is superior to 3d6?

[Username17]

Dude, we answered Kaelik's question. You can add more granularity and more statistical depth by rolling more and bigger dice. More and bigger dice are also a pain in the ass, because you have to find them, roll them, and add them. There is a utility function which will be different for different people and groups for what is the limit where adding more granularity and depth is no longer worth the hassle and confusion. 20 dice is a frankly silly piece of hyperbole, because even people who really love granularity and minutiae - like Rolemaster players - shy off at more than 6 or 7 dice.

It is incredibly exhausting to try to talk to you. But since you are at least trying to have a civil discourse in some tangible manner, I should reward that behavior by talking back.

There is for every data set a standard deviation. For randomly generated data sets, like ones we make with random number generators and fair dice, the data sets will look nicely theoretical. And that makes doing statistics on them easy and fun. There is always going to be a modifier you can add that will shift your chances approximately one standard deviation. It is the number that is the difference between where the next standard deviation is and where you are.

On a d20, that number is largely unknowable. If you're starting at DC 11, you need a +6 bonus to shift one standard deviation, and you'll need a +3 to shift another standard deviation. In short, the statistical meaning of the bonus is not the same. So to achieve the same statistical effect on the data set, you need to change the physical value of your die modifier.

On 3d6, that number is more knowable. Starting at DC 11, you need a +3 bonus to shift one standard deviation, and from there you'll need another +3 bonus to shift a second standard deviation. It breaks down after that, but it means that within a fairly broad fraction of the RNG, you can add a static modifier to the die roll and have that have a fixed statistical effect no matter where you started.

That's it.

-Username17

[TarkisFlux]

Didn't he already do that when he wrote

If you are rolling 7d6 instead of 3d6, you can get 3 standard deviations in with linear bonuses, instead of just 2 for 3d6 or just 1 for a d20. That's an improvement.

Whether that improvement is worth rolling 7 dice and adding the totals up is another deal altogether. As it happens, it's not. But if you were making a computer game out of the deal, that would be pretty exciting. In fact, you'd probably end up having the computer roll like 15d100 or something, so you could get a lot of granularity and a lot of statistical depth.

For table top gaming though, you have limitations. You want statistical depth and you want granularity, but dealing with more numbers is a pain in the ass. Dealing with more dice is a pain in the ass. 3d6 and 1d20 are both perfectly fine concessions to the reality of the difficulty of doing this sort of thing.

or is that not a valid answer since it doesn't specifically use 20d4 in the example?

[PhoneLobster]

or is that not a valid answer since it doesn't specifically use 20d4 in the example?

It is not a valid answer because it doesn't tell us why the much talked about complexities and behavior of the 3d6 is good but the 7d6 is bad.

Essentially it is an admission on his part that that behaviour is not worth the complexity... but only at an arbitrary line he draws. And apparently draws after a mechanic (3d6) that is so complex it causes him to make up a new definition of Standard Deviation and it's usage that isn't actually (for good reason) recognized by real mathematicians.

It is the number that is the difference between where the next standard deviation is and where you are.

There IS no such thing as a "next standard deviation" anything outside the FIRST standard deviation is not a standard deviation it is, definitionally, a deviation that is non-standard.

On a d20, that number is largely unknowable. If you're starting at DC 11, you need a +6 bonus to shift one standard deviation, and you'll need a +3 to shift another standard deviation. In short, the statistical meaning of the bonus is not the same. So to achieve the same statistical effect on the data set, you need to change the physical value of your die modifier.

On 3d6, that number is more knowable. Starting at DC 11, you need a +3 bonus to shift one standard deviation, and from there you'll need another +3 bonus to shift a second standard deviation. It breaks down after that, but it means that within a fairly broad fraction of the RNG, you can add a static modifier to the die roll and have that have a fixed statistical effect no matter where you started.

You are not describing a behavior/attribute that mathematicians call Standard Deviation.

There is no such thing as a second standard deviation. More to the point adding multiple standard deviations does NOT do what you claimed originally (having some sort of desirable or even KNOWN modifier to chances of success each time it is applied as a modifier) and the term does NOT exist in order to describe that behavior.

If you apply Standard deviation as a bonus ONCE we know what it does because of the nature of the term. Beyond that we no longer even have any information about what it does without discussing Normal Distributions or the actual data on your Probability Distribution.

Thats because Any deviation beyond the standard deviation... is non standard.

[Username17]

You are not describing a behavior/attribute that mathematicians call Standard Deviation.

There is no such thing as a second standard deviation.

Wat?

In statistics, the 68-95-99.7 rule, or three-sigma rule, or empirical rule, states that for a normal distribution, nearly all values lie within 3 standard deviations of the mean.

Starting at the Mean, one standard deviation is a 34% bonus, the second standard deviation is a 13% bonus, and the third standard deviation is a 2.7% bonus. With a bell curved data set, you can generate those numbers with an iterated static bonus, and with uncurved random number generation you can't.

You saying that there is no such thing as a 2nd standard deviation is simply counterfactual.

-Username17

[Murtak]

It is not a valid answer because it doesn't tell us why the much talked about complexities and behavior of the 3d6 is good but the 7d6 is bad.

Again: 3 dice is an arbitrary number. Six-sided dice are an arbitrary choice. By fiddling with the number and size of the dice you can fiddle with the shape and granularity of the generated RNG curve. 3d6 happens to be a choice that does not require rolling many dice, or adding large numbers, that uses the most common dice and generates numbers close to the d20 you favor.

[PhoneLobster]

In statistics, the 68-95-99.7 rule, or three-sigma rule, or empirical rule, states that for a normal distribution, nearly all values lie within 3 standard deviations of the mean.

That is NOT however multiple standard deviations or increments of standard deviations. It is just describing how close to the standard deviation the data in the Probability distribution falls.

In the mean time that is not standard deviation that is indeed the three sigma rule and is part of you guessed it Bell Curve behavior. But when I responded by discussing Bell Curves you fucking ranted and blew your top and said I understood nothing and you were going to put your fingers in your ears and scream until I misused the term standard deviation.

Standard deviation for a normal distribution is a number. We can discuss things in proportion to it and in that case use it to describe part of the shape of a BELL CURVE. Effectively the three sigma rule (ie, not Standard deviation) is describing the bell like flex to the edges of the curve.

But still why do we suddenly care? We discussed this already you know. That curve, those numbers, 4 pages worth before you started confusing Standard Deviation with Normal Distributions.

I mean sure yes on a BELL CURVE and ONLY on a BELL CURVE...

Starting at the Mean, one standard deviation is a 34% bonus, the second standard deviation is a 13% bonus, and the third standard deviation is a 2.7% bonus. With a bell curved data set, you can generate those numbers with an iterated static bonus, and with uncurved random number generation you can't.

... but again why the hell is this a GOOD THING?

Those numbers are FUCKING SHOCKING for a functional transparent RPG base mechanic. People do not know those numbers, people do not want to and often cannot do division or multiplication let alone the math to derive those numbers.

Where the hell do you get off just describing "well these numbers exist" and from that concluding that they are therefore really good numbers to use for a specific task?

The Fibonacci sequence exists. I can sit down and describe it and actually it is easier to do the math for at least a short portion of it. What the hell is different to your current argument and me doing that to then declare it is a good base mechanic for an RPG?

By your methods the Fibonacci sequence is clearly a great means of adding cumulative bonuses to your RNG for an RPG hey! I mean it exists, I can describe it, therefore bonuses now are simply cumulative progressions along the Fibonacci data set and all players are going to be really happy with that and it will do good things!

You saying that there is no such thing as a 2nd standard deviation is simply counterfactual.

No. There is an Absolute Deviation[/b] that is twice the size of the standard deviation.

Standard deviation itself is a range you fall inside or or outside of. That is it.

[TarkisFlux]

Actually it said that the 7d6 was good and the 15d100 was better but that they were a pain in the ass to do at a table and add up and so were impractical for actual play. Seriously PL, do you want a fucking cost-benefit equation for it? Here, I'll try, cause I'm bored of work and am still kicking around in my head for an easy counting function for the WotG dice states.

If you desire a system where adding the same static number means less to your odds of success the more times you do it for any single given roll, (and if you don't you go single die flat and move the fuck on) then you go over the following decisions. The number of dice you roll is going to be based on how many times you want to be able to add a small but significant (which is also arbitrary and subjective, but a standard deviation seems to be the one chosen here lately) static modifier without going off the RNG weighed against the additional time each die will take when you add them up. The size of the die you use is going to be based on the granularity and number of result states you want weighed against the time it takes to add potentially bigger and more divergent numbers up. There you go.

So yes, at some point the behavior is not worth the complexity because of the added time it takes to roll dice and add them. But if the behavior is desirable (which I understand you do not think it is) then some amount of added complexity is a worthwhile price for it. Where the additional complexity isn't worth the added behavioral benefit is a fucking design / preference question that has no objective answer. If the game is going to be played on a computer where it takes you an insignificant time to add and you want lots of bonuses and lots of result states, you take the 15d100 or 500d1000 or whatever fits your desired result states and bonus math most effectively. If you expect the game to be played by people and understand that there are people out there who take forever to add up fireball damage you go with something a lot smaller in dice and die size to speed things up.

So the answer as to why 3d6 is better than the others is "it's not, but it's a "perfectly fine concession to the reality of the difficulty of doing this sort of thing".

[Kaelik]

1) I thought that 20d6 was actually the sort of shit that high end specialized dice pools through in Shadowrun already, so I figured 20 is a number people actually use.

2) The impression I was getting is that smaller dice sizes are better, because the smaller the dice size, and the more dice you have, the smaller the numeric bonus to travel 1 standard deviation or whatever, and so the more "depth" a system has, that was why I choose d4s in the example.

3) If you think that person X's statement about standard deviations makes them look innumerate, or like an idiot, or like an innumerate idiot, turns out, you are wrong. No one looks like that to what I will call "the average" because I have no damn basis for determining which of you is correct.

So actually, one of you is just misleading people who read this shit and aren't into this stuff.

[TarkisFlux]

Kaelik - dice pools (otherwise called dice and hits systems) like in shadowrun are substantially different from dice and add systems like the 3d6 and XdY systems being discussed at the present here.

In shadowrun you never add up your dice, you just roll them and look at how many of them are at or above a particular value. You care about the number of them that are at or above this value and compare that against the TN. And it's much easier to just pull out the number of d6s that are 5+ from a pool of 20 and count them than it is to add all of that shit up. If you get a bonus on this at all, it's a bonus number of successful dice.

In a dice and add curved system like gurps you add them up and hope you rolled well (which is actually low in that system, but whatever). Adding more dice increases the range of values you might get, but also increases the odds that your total falls closer to the mean. Using bigger dice increases the range of values you can get in the end, and changes your curve in a very specific and predictable way. But adding that shit up takes time, and the more dice you have and the bigger the range of values on them the longer you spend doing that. Which may or may be worth spending at the table to get the effect you're looking for.