Quote from: Lunamancer on July 15, 2022, 11:32:03 PM

Quote from: drayakir on July 15, 2022, 10:23:04 PM
Well, I mean I suppose you could have a percentile system that doesn't use a d100, but... I dunno. The problem with the d100 and the d20 that at a certain point your skill/stat doesn't matter. If the target number is 13, and you're at +6, you have very good odds of it, but there's still a decently high chance that you will fail. More, you still run the risk of failing really easy tasks that somebody at your skill level has no business failing. That's why I prefer bell curve stuff, since that distribution is more like a realistic skill distribution.

One thing I like about expressing odds as a percentage is it's a lot easier to highlight the severe analytical defects in what you're saying. Which I think is important because a lot of gamers would agree with you. And it's straight up incorrect.

Take GURPS. There you have the iconic 3d6 bell curve that gets gamers rocks off. It's simple. Uses dice that's familiar even to the normies. They can be added up quickly. And it's high enough resolution that the probability distribution actually looks like a pretty damn sexy bell curve. Nothing but great things to say about it.

How does that work in practice. Well, my guy as 12 Dex and a +3 in Stabbing Sword skill. So I need a 15 or under to hit. That's roughly a 95% (rounding to the nearest integer) chance to hit. Got it. Switch systems.

Now I've got my Lejendary Adventure Avatar with 75 Weapons Ability, and the Stabbing Sword has a Precision bonus of 20. That's roughly a 95% chance to hit. Same thing. Because "swingy" is made up nonsense when your answering a question of "Did you do what you set out to do?" Either you do or you don't. And the probability that you do always boils down to a percentage.

I know what you're saying. But muh modifiers!

So now GURPS man is going for the coveted called shot through the eye socket to the brain, bypassing the natural armor of the skull, for -10 to hit. Now he needs 5 or under. Drops the probability to 5%.

LA guy, not to be outdone, goes for the same shot. Aimed attack means -20 to hit. And then to bypass armor requires getting a special success--rolling under 1/10 the probability. So 95 - 20 = 75, so you have to roll 7 or less. 7%. Not really a huge difference.

And yeah, I know there's someone somewhere thinking "Ackchyually 7 hits in 100 is 40% more hits than 5 in 100." But when there's no frame of reference to say which is more correct we are in fact operating within the margin of noise. It's clearly a similar order of magnitude in the adjustments.


The trick that gets pulled in these sorts of discussions is every argument you can make is hypothetical. As such, it makes assumptions that usually are not applicable to an actual play situation. That's why I cite specific rules from specific systems. It's a waste of time to speak in generalities like this type of mechanic does this, but that other type of mechanic does that.

If you're talking about a situation that's relevant to the game, and if the game was play-tested, I have to think the problem arose at some point, was addressed, and is not an actual problem. Maybe some games weren't as rigorously tested and put together as others. An example of a bad game is just that--an example of a bad game. Not evidence of a bad mechanic.

Obviously it's all hypothetical. Ultimately it comes down to personal preference. But the thing happens with descriptions. If you're described as a "grandmaster" at a skill, you should never fail at a basic task. I prefer looking at the Shadowrun 4e system that does it much better. An easy task requires just 1 success. A character that is considered to be a grandmaster of something is going to have something to the tune of 14 dice not counting equipment bonuses. The odds of getting at least 1 success on that many dice is 99.66%. Sure you have the statistical fluke of rolling no dice on that many, but the odds are well, less than 1%. Now if we're using CoC as an example, at character generation, someone who represents the utmost master of a skill is... 75%? I think? It's been a while since I've looked at the system. Regardless, it doesn't even reach 90%. So, the Shadowrunner is going to have a good 20% odds of success on the bleeding edge researcher in CoC. It is also important to note that the CoC character has a flat 1% chance of failure. Then if we compare them to the poor D&D adventurer, they're just fucked. They have a flat 5% chance of failing any roll, but barring that, if we're looking at the modern edition, with it's "bounded accuracy" the character is going to have something to the tune of +5 to their primary skill at chargen (3 from stat at 17, 2 from proficiency). An easy task is a DC 10, so the starting character has a 25% chance of failure.

And all this is because the d100 can just randomly decide to fuck you.

Roll under systems are a little off-putting to some slice of the gamer population.  It's not an insurmountable problem with most gamers, but it is there.  Roll over percentile would be an odd duck. Not saying it can't work, but might be a little twisted in interpretation, possibly throwing out some of the intuitive benefits supposedly residing in using the percentile system in the first place.

There's no point in having the fine granularity of percentiles if your system doesn't take advantage of it.  Exactly how it does so can lead to some compromises.  In an attempt to write my "inspired by Dragon Quest" game, I found that using the fine grain of the percentiles to slow advancement was still useful, but for modifiers applied on the fly (e.g. typical combat or spell modifiers), I very much wanted to stick with 10% increments whenever possible, and 5% increments when the 10% was too coarse.  Playing around with +1% or +2% per some factor (e.g. shield rank) in DQ uses the heck out of the fine granularity, but that's also part of what makes it inaccessible.  Since "advancement" happens away from the action, it can afford to take advantage of the finer grain without it bogging everything down.  (Done well, such as in most of the later RQ editions and their variants, such fine grain advancement can also give a moderate sense of verisimilitude without a lot of complication, too.  DQ manages to throw that advantage away by inserting layers and layers of complication on top of an otherwise good system.)

Quote from: jhkim on July 15, 2022, 07:30:50 PM

3) Percentile stats make it difficult to express large differences like in high-power fantasy or superheroes, because values higher than 100% are counter-intuitive.

This is a lot bigger deal than it seems at first.  When just talking about it, seems like it would be something to work around, but when you start designing the game, turns out not so much.  That's because to take advantage of the full percentile range is probably out the door in reality, when mixed with slow, "realistic" advancement of a reasonably simple percentile system.  Be real, not many people are going to want to play a game where you start at 1% and work up slowly from there.  The skills are practically unusable for a long time.  And no system of which I'm aware does so.  They'll start off at some base, usually, in the 20% to 40% range, perhaps based on ability scores, or like DQ just set by fiat based on what the ability is.  Tolerances for what is good enough varies by players, but in my experience most players will tolerate a floor somewhere in the 25% to 50% range, depending on the rate of advancement.  So let's round all that off and say we've tossed out about a third of the percentile range right up front.  You have a similar (if narrower) dynamic on the upper end, that I won't elaborate upon since this post is already long.  So to make a long story short, your usable range is probably more in the 20% to 95% range, with the vast majority of abilities more in the 40% to 85% range.

(A similar dynamic is of course true for any mechanic, where the extremes of the range limit what you can do with it and shape the modifiers.  Once you get down small enough that your useful, typical modifier is +1 or +2 on a relatively narrow spread, say 1d20 or 3d6, no one expects fine grain anymore.  That's the subtle difference.)

Now combine all that.  We are trying to keep most starting points in the 40% to 85% range, allowing for modifiers that are usually in 10% increments, with characters that start on the lower end of that and very slowly work up to the upper end of it.  All doable, if a little flaky when several positive or negative modifiers send things out the 1-100 range.  But let's wave that off and say we can account for such exceptions with a tolerable level of complexity.  The resulting system might be really nice for that slow advancement.  If you start trying to live in the upper or lower ranges, or speed up advancement, all of your advantages and compromises hit the wall really fast.  You might be able to work around that to a certain extent by scaling something other than the percentile roll.  For example, higher powered characters don't advance skill rolls any faster than the usual slow rate, but what they do with success is more impressive.  Note that this is itself a compromise on the design that might seem a little contrived after awhile.

Trying to use percentile, roll under for a D&D style game would be about a useless as trying to make a d20 Star Wars (Ha!).  It's the wrong tool for the job.  Using it makes the most sense when you want incremental advancement and a fairly overt power cap.

Quote from: drayakir on July 16, 2022, 12:22:56 AM
Obviously it's all hypothetical. Ultimately it comes down to personal preference.

There are key variables that can turn the conclusions on their heads that hypotheticals have the luxury of excluding all "for the sake of argument" that are not excluded in reality. Sound analysis identifies those variables. And a sound hypothetical includes them. This isn't a matter of preference. It's a matter of accurate analysis versus obsession with a model.

QuoteBut the thing happens with descriptions. If you're described as a "grandmaster" at a skill, you should never fail at a basic task. I prefer looking at the Shadowrun 4e system that does it much better. An easy task requires just 1 success. A character that is considered to be a grandmaster of something is going to have something to the tune of 14 dice not counting equipment bonuses. The odds of getting at least 1 success on that many dice is 99.66%. Sure you have the statistical fluke of rolling no dice on that many, but the odds are well, less than 1%. Now if we're using CoC as an example, at character generation, someone who represents the utmost master of a skill is... 75%? I think?

I used to work with this 60 year old guy, one day he comes to work holding this big trophy. He won 2nd place national grandmaster body building competition. Sounds impressive, especially for a 60 year old. Until you find out that "grandmaster" was the name they gave to their division for older body builders who were past their prime. Kudos to the guy for competing and winning. The point is, that's a very different level of performance than coming in 2nd place in a tournament of grandmasters in chess.

I mean, I couldn't help but notice you mentioned an easy task requires just 1 success. So what does a hard task require? 3? 4? More? So you mean to tell me you could roll something that in game terms is called "success" and still fail? And yet you dare complain about how two different games might have different conceptions of a term like "grandmaster" that has no inherent or specific meaning?

It would be the easiest thing in the world to shit on everything you love picking on the stupid word choices of game designers.I prefer to take a more honest approach and look at the numbers to make sure I'm comparing apples to apples across systems.

Unless a task has an autofail range (and ones that do are not all that easy), if you have skill over 100 in LA and roll a 100, you roll a second percentile to dice against your points above 100. I don't know what "easy" means in Shadowrun. It could map to anywhere from a +20 to +60 bonus in LA. But whatever the skill plus the "easy" modifier, if it totals out to 166, then you've got a 99.66% chance to succeed. For point of reference, to achieve the highest ranks within an order (guild), the required score in the main skill has to be at least 131. So a 136 +30 easy bonus both fit's LA's idea of "grandmaster" and "easy" and yields the same probability. Apples to apples.

QuoteIt's been a while since I've looked at the system. Regardless, it doesn't even reach 90%. So, the Shadowrunner is going to have a good 20% odds of success on the bleeding edge researcher in CoC. It is also important to note that the CoC character has a flat 1% chance of failure. Then if we compare them to the poor D&D adventurer, they're just fucked. They have a flat 5% chance of failing any roll, but barring that, if we're looking at the modern edition, with it's "bounded accuracy" the character is going to have something to the tune of +5 to their primary skill at chargen (3 from stat at 17, 2 from proficiency). An easy task is a DC 10, so the starting character has a 25% chance of failure.

Two problems. What you're saying is grain-bitching. And what you're saying is also not true.

Every probability distribution approximates an S-curve just by virtue of the fact that probabilities are bounded. Yeah, even if the RPG doesn't have "bounded probability" probability is always bounded by 0 and 1. The question is what happens when you approach the bounds. Yeah, you could just say on a d20, 1 always fails, 20 always succeeds, and the curve goes horizontal at the 5% away from the bounds. A d100 system where 1 always succeeds and 100 always fails would similarly go horizontal, only at the 1% mark instead. But there could also be a tapering-out effect as I described with LA. But in all 3 of these cases, we're talking about a difference of less than 5% entirely attributable to the graininess of the mechanic. Now if I've correctly reversed engineered Shadowrun as you describe it, having only 1 die means 33% chance of succeeding as an easy task. What if you have two dice? You're going to skip straight to 55%? Sorry. You don't get to bitch about a rounding error within 5% while a rounding error in excess of 20% is fine.

And to the second point. It's just plain not true. When I play AD&D 1E, I can hit a magically held or sleeping character without any chance of failure at all. There's no whiff factor for things that are that easy. This isn't something that you will find emerging from the math. But it's how people play, and it is also there officially in the rules. Obsession over the model is going to make you blind to what is plain to see in actual play. You're simultaneously asserting that something that is noticeable and a problem, but also it won't be noticed and handled like a problem at the point of play. That's a thin line to tread.

QuoteAnd all this is because the d100 can just randomly decide to fuck you.

I have an old-school d100 I bought for $3 back in 1989. In all this time, it has never once rolled out of my dice bag under its own volition and then fornicated with anyone.

The d100 is just too big. Is there a meaningful difference between 71% chance of doing something, and a 74%?

I'll also note that I feel like going for d100 lends itself to either: Roll-under systems (feels bad & counterintuitive), or reducing attribute systems (also feels bad & counterintuitive).

What I like about d100 systems is they generally have you modify your target number before rolling, so success or failure is immediately apparent once you roll. d20 systems tend to have you add/subtract modifiers after the roll, so there's a short delay as you do the arithmetic. It's a primitive gambler mental thing that hits the right neurons and has nothing to do with the actual dice involved.

Quote from: Zelen on July 16, 2022, 02:59:11 PM
The d100 is just too big. Is there a meaningful difference between 71% chance of doing something, and a 74%?

I agree about there is no statistical difference between a few percentage points, but the 1s place is useful in tracking incremental skill improvement.

For me the basic problem is that I like probability not being obvious by simply looking directly at the numbers. I find it immersion-breaking to immediately know I have a 50% chance of failure when rolling my Arcane Lore 60 Skill vs. a -10 Difficulty Modifier. (Yes, if you're good enough at math or seasoned enough with the system you get a pretty clear sense of your odds anyway, but there is something a little different about how obvious percentiles make it.)

The double-digit mental addition or subtraction required for modifiers which use increments of other than 5% or 10% (and if you don't use increments other than that, it's simpler to go to the d20, as noted) is also, I think, a stumbling block for enough gamers that it's an immersion-breaker. And there are others who simply don't like roll-under -- I'm one of them; I wouldn't turn down a chance to play such a system if offered (and I spent years playing GURPS), but my preferences are always for the high roll.

None of this makes percentiles a bad or unplayable system. It's just reason enough for me to explain why they haven't driven all other alternatives out of the market.

Quote from: Jason Coplen on July 15, 2022, 11:18:17 PM

Quote from: drayakir on July 15, 2022, 10:23:04 PM
Well, I mean I suppose you could have a percentile system that doesn't use a d100, but... I dunno. The problem with the d100 and the d20 that at a certain point your skill/stat doesn't matter. If the target number is 13, and you're at +6, you have very good odds of it, but there's still a decently high chance that you will fail. More, you still run the risk of failing really easy tasks that somebody at your skill level has no business failing. That's why I prefer bell curve stuff, since that distribution is more like a realistic skill distribution.

Do you mean rolling high? I prefer roll under, personally. Both are percentile.

Bell curve ain't bad except for combat, which is a wild affair linear handles better.

With d100 % Rolls, I'm Always thinking about Roll Under; as in a 30% Chance of Success means, you need to Roll 30 or Under on d100.

Quote from: Jam The MF on July 16, 2022, 07:05:20 PM

Quote from: Jason Coplen on July 15, 2022, 11:18:17 PM

Quote from: drayakir on July 15, 2022, 10:23:04 PM
Well, I mean I suppose you could have a percentile system that doesn't use a d100, but... I dunno. The problem with the d100 and the d20 that at a certain point your skill/stat doesn't matter. If the target number is 13, and you're at +6, you have very good odds of it, but there's still a decently high chance that you will fail. More, you still run the risk of failing really easy tasks that somebody at your skill level has no business failing. That's why I prefer bell curve stuff, since that distribution is more like a realistic skill distribution.

Do you mean rolling high? I prefer roll under, personally. Both are percentile.

Bell curve ain't bad except for combat, which is a wild affair linear handles better.

With d100 % Rolls, I'm Always thinking about Roll Under; as in a 30% Chance of Success means, you need to Roll 30 or Under on d100.

I love the simplicity of it. You know your odds before rolling, meaning most players will roll regardless. I much prefer it to any game using "yes, but" rolling. I find it easier to roll, know your result, and move on. Too much dice rolling takes me out of the game.

Quote from: Jason Coplen on July 16, 2022, 08:05:46 PM

Quote from: Jam The MF on July 16, 2022, 07:05:20 PM

Quote from: Jason Coplen on July 15, 2022, 11:18:17 PM

Quote from: drayakir on July 15, 2022, 10:23:04 PM
Well, I mean I suppose you could have a percentile system that doesn't use a d100, but... I dunno. The problem with the d100 and the d20 that at a certain point your skill/stat doesn't matter. If the target number is 13, and you're at +6, you have very good odds of it, but there's still a decently high chance that you will fail. More, you still run the risk of failing really easy tasks that somebody at your skill level has no business failing. That's why I prefer bell curve stuff, since that distribution is more like a realistic skill distribution.

Do you mean rolling high? I prefer roll under, personally. Both are percentile.

Bell curve ain't bad except for combat, which is a wild affair linear handles better.

With d100 % Rolls, I'm Always thinking about Roll Under; as in a 30% Chance of Success means, you need to Roll 30 or Under on d100.

I love the simplicity of it. You know your odds before rolling, meaning most players will roll regardless. I much prefer it to any game using "yes, but" rolling. I find it easier to roll, know your result, and move on. Too much dice rolling takes me out of the game.

It gets straight to the point.  d100 is finite.  You can adjust in large increments, or in very small increments.  It is flexible for the DM.

A D20 system with +/- increments of 1 is mathematically the same as a percentile system that uses increments of 5%. 

The systems I'm more curious about are all of the games that stick to just the humble D6.  Dice pools or a single 1D6, or classic 2D6 get the most uses.   Or even a D36 system that uses the dice to generate a tens number from 10 to 60, and the other die is the single digit 1 to 6.  A range of 11-66, aka 36 possible numbers. 

All that work just to use common dice.  It's all probably unnecessary now that gaming dice can be bought at Walmart, or dice apps for your phone exist.  Hell, just use a web browser and search "dice roller" if you want. 

Still, I'm a sucker for easy to use dice mechanics.  Dungeons and Delvers Dice Pool Edition for example.  Attribute stats and skill levels are each a dice size, plus any other benefit are also a dice size.  Roll them, pick the best two and add.  Simple.

Quote from: Jam The MF on July 15, 2022, 07:13:11 PM
Having a % Chance of Being Successful at "X", is a very natural way of explaining things.

Why haven't Percentile-Based Systems won out in a big way, in the RPG market?

Thanks in advance, for chiming in.

I mean, technically, every game that uses dice is a % system, its just that d20 uses increments of 5% and is explained without using percent.   I think d100 has its place, its just easier to roll 1d20 than it is to roll 2d10 and turn it into d100,  or to roll an actual d100 and wait for it to stop rolling and then peek on the tiny sides for the correct number

I'll throw in a monkey-wrench...

MSH is a percentile based system that has built in mechanics that can make sure you almost always succeed (Karma). But the entirety of this discussion has been straight pass/fail mechanics based on the actual number... It is one of the most un-swingy games I've ever run. When people fail, it's almost always because they don't want to spend Karma.

How many percentile systems have graduated varying success when rolling percentile against an easy to use chart? With Karma mechanics (or whatever you want to allow to modify that roll on the fly) you can get one very streamlined and fun system.

Quote from: Jason Coplen on July 15, 2022, 11:28:14 PM

Quote from: VisionStorm on July 15, 2022, 10:47:58 PM

Quote from: Jason Coplen on July 15, 2022, 09:53:37 PM
Settings is my guess. Outside CoC what cool setting do they have? None. Sure, Glorantha is neat, but definitely not everyone's cup of Joe. That and there's no really good magic systems.

D&D's magic system is crap, but it's still the market leader. Granted I'm not very familiar with any d100 based systems and haven't played any of them in decades, so I'm not sure any of them are any better.

D&D has a couple of cool settings at least, but they've never been its main selling point, and they keep changing the default setting every edition. I'm not sure that's why it and its derivatives are the best selling games.

Touche. I cannot argue against that. Maybe I'll get back to you after I pull my foot out of my mouth.

Nobody can touch D&D in name recognition. People ask me - what's RuneQuest and my default answer is - it's like D&D, only grittier. Unless some tv show that hits big makes a big todo about some other tabletop rpg D&D has no chance of being dethroned. At least currently. Pale Puppy was huge in the 1990s riding the success of vampire books and movies, including The Crow.

Good luck. This is 90s nostalgia:

Quote from: BoxCrayonTales on July 18, 2022, 11:20:59 AM

Quote from: Jason Coplen on July 15, 2022, 11:28:14 PM

Quote from: VisionStorm on July 15, 2022, 10:47:58 PM

Quote from: Jason Coplen on July 15, 2022, 09:53:37 PM
Settings is my guess. Outside CoC what cool setting do they have? None. Sure, Glorantha is neat, but definitely not everyone's cup of Joe. That and there's no really good magic systems.

D&D's magic system is crap, but it's still the market leader. Granted I'm not very familiar with any d100 based systems and haven't played any of them in decades, so I'm not sure any of them are any better.

D&D has a couple of cool settings at least, but they've never been its main selling point, and they keep changing the default setting every edition. I'm not sure that's why it and its derivatives are the best selling games.

Touche. I cannot argue against that. Maybe I'll get back to you after I pull my foot out of my mouth.

Nobody can touch D&D in name recognition. People ask me - what's RuneQuest and my default answer is - it's like D&D, only grittier. Unless some tv show that hits big makes a big todo about some other tabletop rpg D&D has no chance of being dethroned. At least currently. Pale Puppy was huge in the 1990s riding the success of vampire books and movies, including The Crow.

Good luck. This is 90s nostalgia:

Blech! You've ruined my day, you bastard!

I don't remember much of the 90s to be honest. I was chained in a basement running rpgs or sitting online in some long dead chat room.

Quote from: Lunamancer on July 16, 2022, 02:20:29 PM

Quote from: drayakir on July 16, 2022, 12:22:56 AM
Obviously it's all hypothetical. Ultimately it comes down to personal preference.

There are key variables that can turn the conclusions on their heads that hypotheticals have the luxury of excluding all "for the sake of argument" that are not excluded in reality. Sound analysis identifies those variables. And a sound hypothetical includes them. This isn't a matter of preference. It's a matter of accurate analysis versus obsession with a model.

QuoteBut the thing happens with descriptions. If you're described as a "grandmaster" at a skill, you should never fail at a basic task. I prefer looking at the Shadowrun 4e system that does it much better. An easy task requires just 1 success. A character that is considered to be a grandmaster of something is going to have something to the tune of 14 dice not counting equipment bonuses. The odds of getting at least 1 success on that many dice is 99.66%. Sure you have the statistical fluke of rolling no dice on that many, but the odds are well, less than 1%. Now if we're using CoC as an example, at character generation, someone who represents the utmost master of a skill is... 75%? I think?

I used to work with this 60 year old guy, one day he comes to work holding this big trophy. He won 2nd place national grandmaster body building competition. Sounds impressive, especially for a 60 year old. Until you find out that "grandmaster" was the name they gave to their division for older body builders who were past their prime. Kudos to the guy for competing and winning. The point is, that's a very different level of performance than coming in 2nd place in a tournament of grandmasters in chess.

I mean, I couldn't help but notice you mentioned an easy task requires just 1 success. So what does a hard task require? 3? 4? More? So you mean to tell me you could roll something that in game terms is called "success" and still fail? And yet you dare complain about how two different games might have different conceptions of a term like "grandmaster" that has no inherent or specific meaning?

It would be the easiest thing in the world to shit on everything you love picking on the stupid word choices of game designers.I prefer to take a more honest approach and look at the numbers to make sure I'm comparing apples to apples across systems.

Unless a task has an autofail range (and ones that do are not all that easy), if you have skill over 100 in LA and roll a 100, you roll a second percentile to dice against your points above 100. I don't know what "easy" means in Shadowrun. It could map to anywhere from a +20 to +60 bonus in LA. But whatever the skill plus the "easy" modifier, if it totals out to 166, then you've got a 99.66% chance to succeed. For point of reference, to achieve the highest ranks within an order (guild), the required score in the main skill has to be at least 131. So a 136 +30 easy bonus both fit's LA's idea of "grandmaster" and "easy" and yields the same probability. Apples to apples.

QuoteIt's been a while since I've looked at the system. Regardless, it doesn't even reach 90%. So, the Shadowrunner is going to have a good 20% odds of success on the bleeding edge researcher in CoC. It is also important to note that the CoC character has a flat 1% chance of failure. Then if we compare them to the poor D&D adventurer, they're just fucked. They have a flat 5% chance of failing any roll, but barring that, if we're looking at the modern edition, with it's "bounded accuracy" the character is going to have something to the tune of +5 to their primary skill at chargen (3 from stat at 17, 2 from proficiency). An easy task is a DC 10, so the starting character has a 25% chance of failure.

Two problems. What you're saying is grain-bitching. And what you're saying is also not true.

Every probability distribution approximates an S-curve just by virtue of the fact that probabilities are bounded. Yeah, even if the RPG doesn't have "bounded probability" probability is always bounded by 0 and 1. The question is what happens when you approach the bounds. Yeah, you could just say on a d20, 1 always fails, 20 always succeeds, and the curve goes horizontal at the 5% away from the bounds. A d100 system where 1 always succeeds and 100 always fails would similarly go horizontal, only at the 1% mark instead. But there could also be a tapering-out effect as I described with LA. But in all 3 of these cases, we're talking about a difference of less than 5% entirely attributable to the graininess of the mechanic. Now if I've correctly reversed engineered Shadowrun as you describe it, having only 1 die means 33% chance of succeeding as an easy task. What if you have two dice? You're going to skip straight to 55%? Sorry. You don't get to bitch about a rounding error within 5% while a rounding error in excess of 20% is fine.

And to the second point. It's just plain not true. When I play AD&D 1E, I can hit a magically held or sleeping character without any chance of failure at all. There's no whiff factor for things that are that easy. This isn't something that you will find emerging from the math. But it's how people play, and it is also there officially in the rules. Obsession over the model is going to make you blind to what is plain to see in actual play. You're simultaneously asserting that something that is noticeable and a problem, but also it won't be noticed and handled like a problem at the point of play. That's a thin line to tread.

QuoteAnd all this is because the d100 can just randomly decide to fuck you.

I have an old-school d100 I bought for $3 back in 1989. In all this time, it has never once rolled out of my dice bag under its own volition and then fornicated with anyone.

Well, your counterpoint has several flaws. First off, you're just outright dismissing the fact that the d20 and d100 system in their most popular incarnations have an auto-pass and auto-fail number. So no matter how good you are, you have a 1% or 5% chance of just failing, regardless of how good you are. That's asinine. There's no reason that someone who is a grandmaster at riding horses is going to fail mounting a horse in ideal conditions. Just not going to happen. But the d100 and d20 system say that yes, you can have the most ideal conditions imaginable, but every 100 times you will fail every 100 times or every 20 times, depending on which system we're using.

If you're complaining about nomenclature, then we'll just say that "grandmaster" refers to the top tier in skill mastery. If you're a grandmaster, this means that you're like, in the top 20 people in the planet in that skill.

And as far as Shadowrun goes, the scale is given as such: 1 is easy, 2 is average, 4 is hard, 6 is extreme. It is possible to have a target number above 6, but that's when there's an opposed check involved and someone rolled higher than 6. Then you need to match of exceed that. So, 6 successes means you can succeed at the most difficult task within the system. Which means that our human grandmaster has the following odds of success:

The probability of 6 successes or more is 31.0192476681325
The probability of 5 successes or more is 52.4499531567108
The probability of 4 successes or more is 73.8806586452891
The probability of 3 successes or more is 89.4666262733461
The probability of 2 successes or more is 97.2596100873746
The probability of 1 success or more is 99.6574512609218
The probability of no successes is 0.34254873907823
(http://www.unseelie.org/cgi-bin/shadow.cgi?number=14&target=5&cumulus=1&action=Press+once+to+send)

This makes much more sense than a flat failure/success rate of a single dice system.

Furthermore, you keep saying that 1% or 5% is just graininess. That's a great way to dismiss it, but it doesn't make sense. You said yourself that really our two numbers are 0 and 1, which I agree with. So with a dice pool system, I know that I'm going to succeed X%, but the d20 has a fuzziness rating of 10% (from the 1 and 20 face) and the d100 has a fuzziness rating of 2% (the 1 and 100 faces). Would it not be better to have something with no fuzziness?

The answer is yes. There are only disadvantages to using a single die over a dice pool.