How to write no rules

[Murtak]

On a 3d6 roll, being blinded should be maybe a -3 or -4.

What does that even MEAN Frank? That bonus has an inconsistent effect Dependant on other bonuses and the target number.

What Frank means is this (all numbers made up on the spot):

1) You decide on a default hit chance for a sample combat (say, 60%)
2) You decide on how much of a penalty being blinded should give you (say, going from 60% to 30%)
3) You check what applying the same effect again gives you.

With a d20 system you go from hitting on a 9+ to hitting on a 15+. Do it again and you are off the RNG.

With a 3d6 system you go from hitting on a 10+ to hitting on a 13+. Do it again and you are still on the RNG, though barely.

[PhoneLobster]

1) You decide on a default hit chance for a sample combat (say, 60%)
2) You decide on how much of a penalty being blinded should give you (say, going from 60% to 30%)
3) You check what applying the same effect again gives you.

You missed something there Murtak.

This is a unit conversion error.

Frank is declaring a modifier should be a 30% difference. He then converts that to a bonus value in two systems. In one of them that bonus value is constant across the entire range.

But in the other one it isn't he isn't actually as you later say "doing it again" when he adds +3 a second time. "Doing it again" would be to further modify the odds by 30% and convert that into a new bonus again for the now modified value of bonuses for the different part of the range.

He misses that step making what amounts to a basic unit conversion error. He misses it because in the 3d6 situation like the example where you start at a target number of 10+, modify odds by whatever bonus for 30% value you actually CAN'T modify odds by another 30% value because there isn't that much margin in percentage value left!

This is almost as good a slight of hand equation as Sir Hugo Rune's Disproof of the Work Ethic. Which is to say that most primary school kids should be able to see where Wally is if they just stare at the picture long enough.

And THIS sort of REALLY BAD reasoning is why I dismiss "bell curve" mechanics as both stupid and really opaque.

[Murtak]

Of course "halving your chances" again by applying the same numerical modifier is just as impossible with the d20. It is entirely up to the game mechanics designer as to how one should handle multiple modifiers.

Your "doing it again only works when you substract 30%" example falls apart when you consider that doing it the first time halved your chance and suddenly doing it yet again kills your chance of succeeding completely. If DnD miss chances were penalties to the d20 roll instead Blur + Mirror Image would translate into +20 AC.

Not that this is necessarily a problem. 3d6 has issues too, they are just different. But Frank's point remains: Applying modifiers to the roll pushes you off the RNG much faster when you use a single die.

[PhoneLobster]

Applying modifiers to the roll pushes you off the RNG much faster when you use a single die.

Your claim has no fucking basis in fact you moron.

In the example system the RNG of the 3d6 is actually smaller that is a fact.

Modifiers to the result push you off faster. That is a fact.

The various percentile values in changes to the odds of success of each of those modifiers doesn't fucking change that because when you talk about the RNG and adding modifiers directly do dice rolls, you aren't talking about the fucking percentage values.

The only thing 3d6 does is change how much of that RNG has reliable and observable impacts. Shrinking the part of the RNG that any bugger gives a shit about.

Frank is using some simple slight of hand where he goes from talking about a percentage chance modifier, converts it to a flat bonus to roll, then pretends he is talking about another percentage chance modifier of the same value without performing the appropriate conversion back to roll modifier again.

You don't get to convert from odds of success to a simple bonus to roll and then keep that value when the conversion value for the odds of success for that bonus changes.

It's basic fucking numeracy.

4x10 does not equal 4x2. You are doing the same thing as taking the same 4 centimeters from the middle of a logarithmic graph and claiming it represents the same value as 4 centimeters from the end of a logarithmic graph.

LEARN UNIT CONVERSION.

[Draco_Argentum]

You don't get to convert from odds of success to a simple bonus to roll and then keep that value when the conversion value for the odds of success for that bonus changes.

Yes you do. A system with two penalties that aren't mutually exclusive and with each individually a 30% reduction in success rate. Thats a very plausible setup.

Frank's claim is that the bell curve system lets you apply both penalties and stay on the RNG and the flat one doesn't. Its not rocket science.

[PhoneLobster]

Frank's claim is that the bell curve system lets you apply both penalties and stay on the RNG and the flat one doesn't. Its not rocket science.

Utterly central to his claim was the part where he got to add +8 to the 1d20 one and +4 to the 3d6.

And he justified that by a unit conversion error.

THAT isn't rocket science. It's a fucking bare faced cheating.

I am SO fucking pissed with Frank. He does nothing but pull this sort of inconsistent farce these days.

[Absentminded_Wizard]

I don't buy PL's blanket hatred of bell curves in all systems, but he has a point about their effect on transparency, especially in a game targeted toward liberal arts majors who took Math for Dummies 101 for their gen-ed requirement. Since those are the people who would most be attracted to rules-lite systems, 3d6 is probably a bad idea for those games.

And I agree with PL about dice pools. That's probably a better example of a system that doesn't do what many of its proponents think it does. To wit, dice pools aren't "more intuitive" than fixed RNG systems. They make everything about the system complicated to the point that, if a math geek sits down with the liberal arts majors and min-maxes the system, the LA people won't be able to catch up at all. And that's not even getting into how the old variable-TN systems completely screw up transparency.

[MartinHarper]

Let's talk about 3d12, rather than 3d6. That way the standard deviation is more comparable to a d20, and PL might understand the argument.

What does that even MEAN Frank? That bonus has an inconsistent effect Dependant on other bonuses and the target number.

Target DC 16. Penalty -4 => 5% chance of success
Target DC 16. No Penalty => 25% chance of success

Target DC 6. Penalty -4 => 50% chance of success
Target DC 6. No Penalty => 70% chance of success


Target DC 26. Penalty -4 => 0% chance of success
Target DC 26. No Penalty => 0% chance of success

In the first case the penalty reduces the number of successes to a fifth of the previous rate.
In the second case the penalty reduces the number of successes by a much smaller proportion.
the the third case the penalty has no effect.

Penalties have inconsistent effects with a flat d20 too.

[Murtak]

Your claim has no fucking basis in fact you moron.

Look, Mr. Snookelfink, I am fine with you yelling insults at me, but would you mind providing some facts, or even a single one to support your "argument"? I will settle for an example even.

In the example system the RNG of the 3d6 is actually smaller that is a fact.

As has been pointed out multiple times to your tiny brain now the number of possible results is smaller. The actual range of all RNGs is always one.

Modifiers to the result push you off faster. That is a fact.

Why yes, if you take the same number, which actually represents a larger shift on the RNG with less possible results it does push you off faster there. Exactly as, for example, Frank pointed out. That is not contended, you doodledork.

The various percentile values in changes to the odds of success of each of those modifiers doesn't fucking change that because when you talk about the RNG and adding modifiers directly do dice rolls, you aren't talking about the fucking percentage values.

Except that most humans actually are talking about percentages, or rather, talking about "if I do x, how will that affect my odds?". And when a given +1 modifier to the roll can do as little as absolutely nothing (going from needing to roll 1+ to 2+ with a 1 being an autofail) and as much as killing off your chances altogether (going from succeeding on a 20 to going to 21) that question stinks. It also sucks when you are trying to give some example modifiers and have to realize that your +2 circumstance modifier will do absolutely nothing to one PC and will absolutely cripple the other. I don't even get why this is so hard to understand.

The only thing 3d6 does is change how much of that RNG has reliable and observable impacts. Shrinking the part of the RNG that any bugger gives a shit about.

You know, those edges of the 3d6 system you don't care about ... guess what? Those are everything the fucking d20 consists of. Tiny 5% slices. Meanwhile the edge parts of the 3d6 system are 3% and 6% per step. Huge difference there, sure.

Frank is using some simple slight of hand where he goes from talking about a percentage chance modifier, converts it to a flat bonus to roll, then pretends he is talking about another percentage chance modifier of the same value without performing the appropriate unit conversion.

So you are proposing that instead of having flat modifiers we have algorithms in our player handbooks, like "recalculate the to hit roll so as to halve the chances"? Because that is the only way a modifier will stay constant as a percentage. Of course we will have to account for modifiers which are supposed to actually stay constant as a flat modifier.

Short version: Flat modifiers have a different impact depending on where you are on the RNG. No matter whether you are on the d20 or 3d6 RNG. Pretending the percentages don't change just because your prefered RNG has a fixed step size does not change that.

You don't get to convert from odds of success to a simple bonus to roll and then keep that value when the conversion value for the odds of success for that bonus changes.

Then why do you do it?

It's basic fucking numeracy.

Actually it is an unsolved problem. All we are doing is fucking around with half-fixes. Shadowrun 3rd edition came close, except for unacceptable threshold jumps. Most other systems aren't even trying. And then we have you, who doesn't even understand what we are talking about.

4x10 does not equal 4x2. You are doing the same thing as taking the same 4 centimeters from the middle of a logarithmic graph and claiming it represents the same value as 4 centimeters from the end of a logarithmic graph.

No, but close. What I am doing is to try to find a system where I don't have to recalculate percentages multiple times per die roll just to be able to have large modifiers while staying on the RNG.

LEARN UNIT CONVERSION.

LEARN TO THINK!

[PhoneLobster]

Murtak. You are an idiot.

3d6 goes from 3-18, 1d20 goes from 1-20.

Guess which is larger.

The average granularity for 3d6 is 6.6% increments which is very nearly the same as the 5% increments on a d20. If Frank, and you hadn't been failing at unit conversion the value he gives out as a +8 in the d20 range would have been a +6 in the 3d6 and would have defeated his entire argument.

Your entire post is irrelevant innumerate shit that does not address my basic, repeated, detailed and valid criticism of these unit conversion shenanigans. Behave or fuck off my thread already.

Martin harper. Your post's formatting and language is somewhat indecipherable. But I'm fairly sure you aren't even really engaging with the conversation at all.

[Murtak]

Ok, lets break it down to smaller numbers (and less math): 1d11+1 vs 2d6 (Yes, I am aware that a d11 is not exactly in wide circulation). Let's say you are midway on both RNGs (7+ to succeed on both of them). Given a +6 modifier you fall off both RNGs. That much is clear.

The discussed case is "what happens when I add multiple, individually large, bonuses?". Or, to put it in other terms, how high does a bonus have to be so I can actually notice it in gameplay, and how much of these can I pile on without leaving the RNG?

Let's say you define 25% as "a big bonus". That is a +3 modifier for the d11 and a +2 modifier for the 2d6 system. Doing this twice kicks you off the d11, you still stay on the 2d6.

And this matters, even though we are shifting from modifiers to percentages and back, because it is damn hard to put shifting modifiers into sourcebooks and expect people to be able to add those up in realtime. When you want to figure out a bonus for having the higher ground or a penalty for climbing a slippery slope you really want to set a fixed modifier and be done with it.

[PhoneLobster]

You are making the same conversion error again Murtak. Only this time it is more obvious because it's exactly the same bonus for both examples IF you convert consistently.

1d11+1 gives results from 2-12 It has an average increment of 9% per point of TN.

2d6 gives results from 2-12 and has an average increment of 9% per point of TN.

Where the fuck do you pull a 2 instead of a 3 from? From your cheating ass that can't do consistent unit conversion is where.

A +3 in the 1d11+1 is the same value as an "average" +3 in 2d6. If you cherry pick the large granularity portion of your 2d6 to convert that into a different smaller number I can just cherry pick the fine granularity end and convert it into a larger one.

It's a god damn mathematical shell game that is nothing more than a shallow deception. Same range, same average increment per point, same total points of potential bonus. Giving a smaller bonus to your system for no reason and saying "look it's a smaller bonus!" only proves you are an idiot.

[Murtak]

Where the fuck do you pull a 2 instead of a 3 from? From your cheating ass that can't do consistent unit conversion is where.

Look, calling me names to cover your inability or unwillingness to use your brain does not make you right, so I'd appreciate it if you at least tried to be borderline civil.

To answer your question:
A d11 has even steps of 9.1%. To get to a 25% shift in total you have to go 3 steps, no matter where you are on the RNG. Thus +3 for the d11 RNG.

On the 2d6 RNG it matters where you are, so I specified "in the middle". A TN of 7+ gives you odds of (1+2+3+4+5+6)/36 = 58%. A TN of 5+ gives you (1+2+3+4+5+6+5+4)/36 = 83%. 83-58=25, which is what was specified. Thus +2 for the 2d6 RNG.

[PhoneLobster]

so I specified "in the middle"

And you use that to make statements about "the end".

That is an invalid position.

I might as well use "The end" and say hey look. if our starting point is instead a target number of 2, then say a 10% difference is gosh golly, +2, while in the 1d11+1 it's only a +1, so hey twice as much room for that bonus on a d11+1!

That IS your exact fucking argument isn't it?

Your entire line of argument is an invalid false hood. A con game. And you don't even seem to grasp that!

You want to make statements about a % value of bonus effect across different points of the range you EITHER need to calculate the bonus for that percentage as it changes across the range OR you need to calculate the bonus from the average % value increment.

[Murtak]

And you use that to make statements about "the end".

That is an invalid position.

I might as well use "The end" and say hey look. if our starting point is instead a target number of 2, then say a 10% difference is gosh golly, +2, while in the 1d11+1 it's only a +1, so hey twice as much room for that bonus on a d11+1!

That IS your exact fucking argument isn't it?

Close. It is my exact same argument if your default position is for the character to be at the edge of the RNG.

[MartinHarper]

1d11+1 gives results from 2-12 It has an average increment of 9% per point of TN.

2d6 gives results from 2-12 and has an average increment of 9% per point of TN.

You're weighting the end of the 2d6 equally with the middle. However, 2d6 is more likely to give results in the middle, and therefore target DCs are more likely to be in the middle, so I would (at least) take a weighted average. The weighted average increment for 2d6 is ~11%.

[PhoneLobster]

Close. It is my exact same argument if your default position is for the character to be at the edge of the RNG.

But you are discussing the edge of the RNG. I only used the opposite side of the RNG so I wouldn't have to do it all as penalties and negatives.

You have seriously been discussing the area of the 2d6 RNG where the numbers are 11+, that IS the edge, and you have been discussing it using numbers derived from way back in the middle.

The weighted average increment for 2d6 is ~11%.

Which is close enough to 9% as to make little difference.

Though the justification for weighted average is highly questionable. To claim "You will have target numbers in the middle more often" is... highly questionable. Particularly in the light of Murtak discussing TNs of 11 on 2d6, Frank discussing TNs of 16 and 18 on 3d6 and the whole argument being about the "room" available for meaningful predictable bonuses before exceeding the range.

If you have to choose to limit the actual range of practical TNs to the mid range of the dice results in a 2d6 or 3d6 system then you only show that to be the only useful range these dice generate.

[Murtak]

You have seriously been discussing the area of the 2d6 RNG where the numbers are 11+, that IS the edge, and you have been discussing it using numbers derived from way back in the middle.

Of course I am discussing edge conditions. I never said I wasn't. I said my sample default difficulty is in the middle of the RNG. That does not mean all difficulties are in the middle of the RNG. And it certainly does not mean the edge cases are to be found in the middle of the RNG.

Heck, that was the whole point of this discussion: Starting in the middle of the RNG and proceeding towards the edge of it an add-multiple-dice system has more viable steps than a single die system. Viable meaning: using the same constant modifier and giving a noticeable effect for the average case. If you define the average case as "the edge of the RNG" or if you want your edge cases to have noticeable effects too then this won't apply.

[PhoneLobster]

Starting in the middle of the RNG and proceeding towards the edge of it an add-multiple-dice system has more viable steps than a single die system. Viable meaning: using the same constant modifier and giving a noticeable effect for the average case.

Frank, and then later you, defined your "viable increment" by selecting an increment with a specific percentage increment on odds of success. You don't need to redefine it now, you already defined it, that's the problem your stupid definition is blatantly false.

If you redefine "Viable Increment" to be a constant modifier for the average case you have to recalculate it according to my methods. Which is by the average increment, because that gives you the average value of the fucking increment you idiot, not by ANY specific cherry picked increment, because that only will give you the value of that increment in that specific cherry picked case. One entry is not a fucking average you twit.

And if you magically define "that bit over there" as your "average" by which you determine your "viable bonus" as you creep across the range your "constant modifier" is going to become less and less "viable". Because the part of the value that you originally used to measure it's viability isn't a fucking constant it's a fucking variable.

[Murtak]

Ok. Fine. Example: For a given task, which is in the middle of the RNG (50%, or just over if 50% is not possible), I want a modifier which makes this specific task half as likely to succeed (or, if that is not possible, a little less likely than half).

This is my main objective. It it also by far the most common case. Of course pretty much all systems handle this case fine. But I also have secondary objectives:

a) I don't want to have to recalculate modifiers. I will possibly tolerate some sort of addition of small numbers, but anything else is right out. I calculate the TN already, and even that stinks.

b) I want to be able to add multiples of these steps. After all, my characters will sometimes fight on unstable ground, in the dark, while fireworks are flashing all around them, with an unfamiliar weapon. I don't particularly care about the shifts in my likelihood to succeed, except of course that it should keep going down without reaching zero. The more of these steps I can add without leaving the RNG and the smoother their progression the better.

[PhoneLobster]

Basically all of your goals there are about having a fine granularity flat RNG.

They, mostly have shit all to do with "curvyness". And since "curviness" is in direct contradiction of goal a) and renders the constant used to define your viable modifier before that into a variable I suggest it is counter to your goals.

I'd say your best possible smoothness and largest possible number of steps would lean you toward a flat d100, a dice far too fine for my liking.

But that still doesn't really meet your goals because your stated goal is to 1/2 your chance of success for each modifier (not a linear progression) while simultaneously not having to recalculate anything (which you want a linear progression for). I'm assuming you mean to half your remaining chance each time in a non linear manner because otherwise your goal there is pretty unintelligible for the first place, because there are you know, only 2 actual 50% of total success chance increments in ANY 100% you care to describe...

And that WILL require something other than a flat d20. But it requires a very, very specific customized "curve". And NOT one of the ones already mentioned.

It also STILL fails to meet the sorts of transparency targets I set and still pisses me off no end with it's niggling little extremes that may as well not even be on the range at all.

And it's not at all what you've been arguing about with the great unit conversion con job.

[Murtak]

Basically all of your goals there are about having a fine granularity flat RNG.

No. I don't care about granularity, that comes for free when you increase the die size. And I don't want a flat RNG, because it fits my goals worse.

But that still doesn't really meet your goals because your stated goal is to 1/2 your chance of success for each modifier.

Again, no. I want to halve the chance for the common case.

[PhoneLobster]

No. I don't care about granularity,

But you said you wanted a larger number of finer sized bonuses!

And I don't want a flat RNG, because it fits my goals worse.

But you said you never want to recalculate the value of bonuses!

Again, no. I want to halve the chance for the common case.

But you said you don't want to recalculate the value of bonuses. If you pick a point in a curvy RNG to define your bonus then fix the size of the bonus, it's value fucking changes.

Do. You. Understand. Meaning. Of. Term. "Variable". Vs. Meaning. Of. Term. "Constant".

You seem to have those two things, totally fucking mixed up.

But then since you explicitly state you apparently want lots of granularity while simultaneously "not caring" about it I'm only able to assume you also have difficulty telling left from right, up from down, small from far away, and reality from imagination.

Overcome the double think, then come back and try again.

[schpeelah]

OK, let me sum up what was said here:
"Curve" RNG argument: stacking bonuses/penalties gives diminishing results, multiple individually meaningful modifiers do not push you completely off the RNG.
Obvious counterargument: similar result on a "flat" RNG achievable through a simple change: "for stacking bonuses/penalties, halve second modifier, 1/4 all subsequent ones" or similar.

"Flat" RNG argument: every number has the same percentage value instead of it depending on where on RNG it is, thus the system is easier to understand. From this stems also:

"Size of RNG" argument: "curved" RNGs have more "edge" numbers, so systems using them will more often see situations where chances of success/failure are marginal but not zero.

"3d6 is smaller than 1d20" specific argument: 3d6 not only has 4 less numbers than d20, 4-6 of these numbers have such small chances of coming up that you won't probably care about them, making 3d6 nearly twice smaller than d20.

Am I getting this right?

[Murtak]

Obvious counterargument: similar result on a "flat" RNG achievable through a simple change: "for stacking bonuses/penalties, halve second modifier, 1/4 all subsequent ones" or similar.

That would work, except rounding may get weird and anyways, why not use a curve to start with?

"3d6 is smaller than 1d20" specific argument

Take 3d8 then. Size and thereby granularity are arbitrary, only limited by our patience and the available dice. Similarly the steepness of the curve is arbitrary.