Quote from: jhkim;1130241I agree with you that 3d6 has a bell curve while 1d20 has a flat distribution. But the point is that 1d20 and 3d6 aren't the only choices. 1d10 also has less variance than 1d20. So let's look at real systems.

In D&D5, let's consider a Contest of Strength between a kobold (Strength mod -1) and Conan (Strength mod +5). So the kobold rolls 1d20 and subtracts 1, compared to Conan's 1d20 plus 5. There is a 73.75% chance that Conan will win, a 3.5% chance of a tie, and a 22.75% chance that the kobold will win. (Note that there was a previous claim that the kobold only had a 9% chance of winning, but I don't think that's right.)

Let's look at Interlock instead, which is the system for the Cyberpunk RPG (from R Talsorian). Here Strength goes from 2 to 10, with average 5. In a contest, each character rolls their stat plus 1d10. So the equivalent to a kobold would be Strength 4, while Conan is Strength 10. So here, there is a 90% chance that Conan will win, a 4% chance of a tie, and a 6% chance that the kobold will win.

That's a system with much less swing in it, despite not having a bell curve.

A bell curve 3d6 also has less swing than 1d20. Let's take GURPS. It's a little unclear what Conan's strength would be in GURPS -- there isn't a strict maximum and disagreement about what is a standard human max, and I don't have the GURPS Conan books. This thread rated him as ST 17, though. If we take GURPS as Conan with 17 ST compared to ST 9, then a quick contest of Strength will result that Conan has an 94.6% chance to win, a 1.56% chance of tie, and the kobold has an 3.8% chance to win.


I haven't checked all of them, but those numbers seem reasonable. I mentioned that the standard deviation of 3d6 is about half that of 1d20. I don't know where you're getting those mods from, though. I think it's more concrete to use real RPG systems.

I never used any of these systems, BUT shouldn't systems with bigger range (and variance) have bigger modifiers?  If I convert from 1-10 to 1-100, then a +1 is converted to +10. I think it should be 5-0.5=4.5 or roughly 5 for the cobalt, and 5+2.5 or roughly 8 for Conan if you want to approximately convert 1-20 to the 1-10 . At least that's how I would convert it; I would cut the modifiers in half and round the values.

Standard deviation is probably the best way to convert mods.

1d100: 28.87
1d20: 5.766
3d6: 2.958
1d10: 2.872
2d6: 2.415

Yes, a +1 in 3d6 means almost twice as much as a +1 in 1d20.

Quote from: Pat;1130263Standard deviation is probably the best way to convert mods.

1d100: 28.87
1d20: 5.766
3d6: 2.958
1d10: 2.872
2d6: 2.415

Yes, a +1 in 3d6 means almost twice as much as a +1 in 1d20.

It's a good place to start.  However, I think you then also have to examine how the range and mods are used in the system (some of which will be GM-driven, naturally).  For example, in D&D 5E, it's rare for the extreme bottom of the d20 range to ever be relevant in play.  Whereas some uses of Hero System are going to work hard to keep the effective range of results in the 7 to 14 range (by sitting on the modifiers).  The latter doesn't have much additional effect on the analysis, since we are dropping the same amount from the lower and the upper ends.

Quote from: Steven Mitchell;1130272It's a good place to start.  However, I think you then also have to examine how the range and mods are used in the system (some of which will be GM-driven, naturally).  For example, in D&D 5E, it's rare for the extreme bottom of the d20 range to ever be relevant in play.  Whereas some uses of Hero System are going to work hard to keep the effective range of results in the 7 to 14 range (by sitting on the modifiers).  The latter doesn't have much additional effect on the analysis, since we are dropping the same amount from the lower and the upper ends.

I think it's safe to say that most systems tend to use the upper half of the range more than the bottom half.

Quote from: Trond;1130260I never used any of these systems, BUT shouldn't systems with bigger range (and variance) have bigger modifiers?  If I convert from 1-10 to 1-100, then a +1 is converted to +10. I think it should be 5-0.5=4.5 or roughly 5 for the cobalt, and 5+2.5 or roughly 8 for Conan if you want to approximately convert 1-20 to the 1-10 . At least that's how I would convert it; I would cut the modifiers in half and round the values.

They're completely different systems, though. Each system uses different parameters to handle the range of ability modifiers. Interlock's range of modifiers are comparatively higher than D&D 5e's, despite using a lower die type at half the variable range. D&D 5e is also an odd case, since the system uses low modifiers, even compared to earlier editions of D&D, presumably to allow interaction between characters or enemies with disparate levels and allow low level/HD enemies, like goblins and orcs, to still pose some sort of a challenge to higher level PCs. Meanwhile Interlock's attributes and skills go up to 10 each, where an attribute of 10 (maximum unmodified human potential) is the equivalent of a D&D score of 20 (+5 modifier), and D&D 5e's proficiency modifier only goes up to +6 (which might be doubled with certain feats or class features, or modified by other factors).

However, older editions of D&D had skill or combat modifiers (or equivalent, like THAC0) as high as +20 or higher. The 5e modifier range is a recent trend based around a different set of assumptions on how to handle character abilities, where ability ranges are toned down for the sake of balance.

Quote from: GeekyBugle;1130253Now, take Interlock and switch 1d10 for 2d6.

And in a contest between Conan and a Kobold (how did the both of them end in the same world?) the result is automatic, Conan wins.

There's a reduced chance, but it is not automatic. The kobold has 4 Strength and Conan has 10, so (for example) if Conan rolls a 2 and the kobold rolls a 12, the kobold would win by 4 points.

With 1d10, the kobold has a 6% chance of winning.

With 2d6, the kobold has a 2.7% chance of winning.

Quote from: jhkim;1130305There's a reduced chance, but it is not automatic. The kobold has 4 Strength and Conan has 10, so (for example) if Conan rolls a 2 and the kobold rolls a 12, the kobold would win by 4 points.

With 1d10, the kobold has a 6% chance of winning.

With 2d6, the kobold has a 2.7% chance of winning.

It is automatic, unless there's a chance of Conan slipping on a banana peel and thus loosing. It's the prerogative of the GM (and a long held tradition) to not ask for rolls on stuff he considers doesn't need it. So in arm-wrestling between Conan and a Kobold (Unless especial conditions are mentioned), Conan wins 100% of the time.

Quote from: GeekyBugle;1130326It is automatic, unless there's a chance of Conan slipping on a banana peel and thus loosing. It's the prerogative of the GM (and a long held tradition) to not ask for rolls on stuff he considers doesn't need it. So in arm-wrestling between Conan and a Kobold (Unless especial conditions are mentioned), Conan wins 100% of the time.

But die roll variance isn't just something that comes up solely in the case of Conan and a kobold. It's something that influences how the whole game plays out, for all attributes and skills and tasks.

Conan (20 Str) arm-wrestles an 8 Str kobold. The mechanics say Conan wins 74% of the time, but the GM overrules and says it's 100%.

Conan (20 Str) arm-wrestles a 10 Str average peasant. The mechanics say Conan wins 70% of the time, and maybe the GM overrules and says it's 100%.

Conan (20 Str) arm-wrestles a 12 Str typical soldier. The mechanics say Conan wins 66% of the time. Does the GM overrule?

Conan (20 Str) arm-wrestles a 14 Str opponent. The mechanics say Conan wins 62% of the time. Again, does the GM overrule?


The GM can overrule and impose a 100% sometimes, but presumably at some point they use the mechanics as written, and then we jump back into the same high variance probabilities. So faced with increasing strength opponents, Conan might jump from 100% to just 62% chance of winning.

It is an intentional feature of high-variance systems that it's easier for low-skill characters to contribute, and there's still tension over the die roll even if a character is high stat/skill.

Quote from: Trond;1130260I never used any of these systems, BUT shouldn't systems with bigger range (and variance) have bigger modifiers?  If I convert from 1-10 to 1-100, then a +1 is converted to +10. I think it should be 5-0.5=4.5 or roughly 5 for the cobalt, and 5+2.5 or roughly 8 for Conan if you want to approximately convert 1-20 to the 1-10 . At least that's how I would convert it; I would cut the modifiers in half and round the values.

Quote from: VisionStorm;1130287They're completely different systems, though. Each system uses different parameters to handle the range of ability modifiers. Interlock's range of modifiers are comparatively higher than D&D 5e's, despite using a lower die type at half the variable range. D&D 5e is also an odd case, since the system uses low modifiers, even compared to earlier editions of D&D, presumably to allow interaction between characters or enemies with disparate levels and allow low level/HD enemies, like goblins and orcs, to still pose some sort of a challenge to higher level PCs. Meanwhile Interlock's attributes and skills go up to 10 each, where an attribute of 10 (maximum unmodified human potential) is the equivalent of a D&D score of 20 (+5 modifier), and D&D 5e's proficiency modifier only goes up to +6 (which might be doubled with certain feats or class features, or modified by other factors).

However, older editions of D&D had skill or combat modifiers (or equivalent, like THAC0) as high as +20 or higher. The 5e modifier range is a recent trend based around a different set of assumptions on how to handle character abilities, where ability ranges are toned down for the sake of balance.

As VisionStorm says, the point is that different systems play out differently. If you want to play D&D, then play D&D. When you use a different system, then the mechanics will produce different results. In Interlock, there is less comparative variance. This means that if I'm playing Cyberpunk, then my superstrong solo will more reliably succeed compared to the weak netrunner. This can mean less tension over the die roll, and more situations where you need a particular character to succeed.

Quote from: jhkim;1130381But die roll variance isn't just something that comes up solely in the case of Conan and a kobold. It's something that influences how the whole game plays out, for all attributes and skills and tasks.

Conan (20 Str) arm-wrestles an 8 Str kobold. The mechanics say Conan wins 74% of the time, but the GM overrules and says it's 100%.

Conan (20 Str) arm-wrestles a 10 Str average peasant. The mechanics say Conan wins 70% of the time, and maybe the GM overrules and says it's 100%.

Conan (20 Str) arm-wrestles a 12 Str typical soldier. The mechanics say Conan wins 66% of the time. Does the GM overrule?

Conan (20 Str) arm-wrestles a 14 Str opponent. The mechanics say Conan wins 62% of the time. Again, does the GM overrule?


The GM can overrule and impose a 100% sometimes, but presumably at some point they use the mechanics as written, and then we jump back into the same high variance probabilities. So faced with increasing strength opponents, Conan might jump from 100% to just 62% chance of winning.

It is an intentional feature of high-variance systems that it's easier for low-skill characters to contribute, and there's still tension over the die roll even if a character is high stat/skill.

Lets talk arm-wrestling for a bit. It involves more than raw strength, it involves skill (technique) and determination and pain tolerance.

Now lets examine your examples:

Conan (20 Str) arm-wrestles an 8 Str kobold. The mechanics say Conan wins 74% of the time other times it's a draw and the Kobold wins how often?, but the GM overrules and says it's 100%. The GM overrules the mechanics because he takes into consideration those other factors, and now lets look at your numbers in D&D you said the Kobold is STR-1 while Conan is STR+5 that's already 6 points difference just by the mechanics. So Conan is already at a 6 points advantage, now lets talk technique, me thinks Conan would have more experience in a human sport plus Kobolds are known for their "physical ineptitude", now lets talk determination, from the SRD : "Kobolds are craven reptilian humanoids that commonly infest dungeons. They make up for their physical ineptitude with a cleverness for trap making." Craven = Cowardly and you're telling me it has the same determination than Conan?

As a GM I take all that into consideration and say the result is automatic, Conan Wins and gets to roll to see if he broke the Kobold's arm.

Only way I could call for a roll is if there's other so far unmentioned circumstances.

The other cases I would need to know more about the situation, I might call for a roll or not, I might even give an automatic win to Conan's opponent. But just by what I know so far Conan beats the peasant. I call for a roll on the other 2.

Because this is an RPG not roulette.

Quote from: Cloyer Bulse;1130040High wisdom provides some resistance to mental attack forms involving will force. This makes sense because people who practice religion are more resistant to despair, anxiety, and other attacks against the mind.

Not sure about that at all. It almost seems more the opposite. Native Americans and Australian Aboriginals are notoriously prone to 'deaths of despair'. In Africa it's widely said that white Europeans are immune to black (in both senses) magic - neither vulnerable to it, nor able to employ it.

Quote from: VisionStorm;1130049Specially when we consider that chimps are technically stronger than humans in real life, which means that just because a creature is small that doesn't mean that they're automatically weak.

I remember looking at the bull chimps in London Zoo and realising that their torsos were basically human sized (perhaps not surprising - we only diverged 4-6 mya) and not that much smaller than the gorillas! The idea that chimps are small is a bit of a myth; they're more like D&D Dwarves - short but not 'small'.

Quote from: S'mon;1130428I remember looking at the bull chimps in London Zoo and realising that their torsos were basically human sized (perhaps not surprising - we only diverged 4-6 mya) and not that much smaller than the gorillas! The idea that chimps are small is a bit of a myth; they're more like D&D Dwarves - short but not 'small'.

The reason it's a myth is because all the chimps we see on TV and in movies are immature. And the reason for that is because chimps lose their playfulness when they mature, and become aggressive, and insanely strong. Young chimps are easier to work with, and you're less likely to lose an arm.

Quote from: Pat;1130450The reason it's a myth is because all the chimps we see on TV and in movies are immature.

Ah, right! Thanks!

Yeah, you don't want to mess with chimps.

Quote from: S'mon;1130427Not sure about that at all. It almost seems more the opposite. Native Americans and Australian Aboriginals are notoriously prone to 'deaths of despair'. In Africa it's widely said that white Europeans are immune to black (in both senses) magic - neither vulnerable to it, nor able to employ it.

Human intelligence comes at a severe cost: the existential crisis. Animals know nothing of the future, they know nothing of themselves, therefore they are inured to the evils of the world. But humans can be crippled by despair and self-doubt. If a people are afflicted by widespread despair, then they are subject to extinction. Religion seems to counteract this fundamental failure of the human mind. ALL human cultures have religion, therefore it seems that religion must perform a critical function.

Empiricism is a purely objective analysis of reality. However, it has a basic flaw: we are subjects, not objects; we live in the bivalent world of experience. Empirical thought can tell us the physical composition of a chair, such as its density and molecular composition, but it cannot tell us whether that chair is comfortable or uncomfortable. The mythological stories of religion tell us about the world we live in and they tell us how to navigate that world without our minds coming apart. They are first and foremost stories about us and our experiences with other humans. The Sky and Earth of Sumerian mythology are not the sky and Earth of science, rather they are archetypal personalities, categories of apprehension that we use to understand the world that we must navigate in order to survive.

Irreligious people are thus more vulnerable to crippling depression and anxiety. Intelligence in itself is not a shield, and in fact renders one more vulnerable. In our modern society, people rely more heavily on psychiatric medication to remain relatively functional sans the practices of magic and religion, but even so, depression and anxiety have continued to increase. The current mass hysteria, a stress test for our civilization and triggered so easily, shows how close we are to the total mental breakdown of our entire society.

One must remember however that superstition, a core element of pagan religion, is a double edged sword. On the one hand it provides resistance to anxiety, but on the other hand failure to perform the required rituals increases anxiety. Monotheism is an advancement, as it uses the conscious will, not superstition, as a shield (as in "the power of positive thinking") -- pay attention to the litanies and chants used in Catholicism, and sit in on a conservative Catholic service. Using the Rosary is just as effective at combating anxiety as any modern medication, if not more so.

Here is an example of how it works: When Trobriand islanders fish in a lagoon, they rely only on their science and technology to perform their task. But when they go out into the open ocean, a potentially chaotic environment which they cannot control and which provokes anxiety, they use magic and religion. This calms their anxieties and allows them to effect their science and technology without the diminishment of its efficacy. Thus, in this context, one can see that the use of magic is actually logical because it shows an understanding of how the human brain functions, not empirical understanding (i.e. not by using intelligence -- none of them have PhD's in psychology), but nevertheless that knowledge is embodied through the practice of their ancient religion (i.e. by using wisdom).

Belief is purely an act of will. Belief can be invoked by the rote practice of ritual, as in paganism, or it can be invoked by a conscious act of will, as in monotheism. Either way, it is a vital tool in the abnegation of the demons that haunt us.