Quote from: rytrasmi on July 20, 2022, 04:19:34 PM
I agree a lot of people don't understand probability. I don't blame them, it's not a simple topic. And I'm far from an expert, but I distinctly recall my university stats professor's rant about how probability is widely misunderstood and one of the most common misunderstandings is that you must have a significant number of samples for the whole idea of probability to have any meaning. n = 100 at a minimum...

Even people who do understand probability fail to apply it correctly more than you would expect when eyeballing a course of action.   Take a group of statistics gurus in a room and give them a modest probability decision that they'll need about 30 to 60 seconds to rough calculate a ballpark answer to.  Make them answer in 5 or 10 seconds.  On average, they'll probably do better than most people, but they'll still be wrong a lot.  Which is why statisticians are sometimes surprised by the answers they get.

Of course, this doesn't apply to the simple stuff.  No one that gets basic probability is going to keep having their character do some risky course of action that's got in the neighborhood of a 25% chance, even when their off the cuff calculations are wrong and the chance is really 30% or 18%.  They know it's low, and low chances multiplied together become practically auto fail, quick.  People that don't understand probability can learn the same lesson a little slower via experience.  And then other people never do.  Plus, you've always got a few that are staying in character, and better at judging risks through criteria other than the game math, and sometimes they do better than anyone else when it comes to deciding to do risky thing X or not.  Finally, I've observed people who are really bad at probability but try to apply it anyway, and often talk themselves into a bad course of action that their common sense was screaming the whole time was a bad idea.  It takes all kinds.

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.

Most so-called "role-play gamers" have no idea how die mechanics work, or how die percentages work. They certainly do think the d20 is more shiny than the d100, that's for sure.

Quote from: Visitor Q on July 20, 2022, 09:43:26 AM
On other occasions there isn't one stat or characteristic or skill that is appropriate to teat against but a combination. 

This isn't specific to % systems; it happens in pretty much every game system.

Probability is just probability.  How you get there is more a matter of aesthetics than functionality.  That said, some randomizer mechanics just irritate me.  Dice pools, for example.  No reason why, I just don't like them.  Percentile systems are okay, but there's a couple of reasons they're not my favorite.

1)  Adding up two digit numbers is not particularly fun.  Just because I do tensor calculus as part of my job doesn't mean I want to do a lot of arithmetic as part of my recreation.
2)  Some percentile systems use small modifiers, which IMO don't make enough difference to be worth the trouble of doing them.  It's not really worth thinking about something just to get a 1% bonus.
3)  I find roll-under to be unintuitive.  And roll-over percentile moves away from the simplicity that is the approach's primary strength.
4)  I don't actually like probabilities to by immediately apparent.  Thinking about numbers takes my head right out of the game fiction.

None of these are deal-killer for a game to me, but I think enough folks share some of these views that there is not a widespread desire to switch to percentile systems.

Swinginess is a bell-curve vs linear system issue, not specific to percentile.  And the design of the rest of the system can fix this if wanted.

At the moment, I'm leaning towards systems where randomness has a smaller role.  My current game runs on d6+skill(usually 1-20, but 30 max)+modifiers (typically up to +/- 10 total)

Quote from: HappyDaze on July 21, 2022, 12:52:16 AM

Quote from: Visitor Q on July 20, 2022, 09:43:26 AM
On other occasions there isn't one stat or characteristic or skill that is appropriate to teat against but a combination. 

This isn't specific to % systems; it happens in pretty much every game system.

That was my point. Percentile systems are intuitively good for understanding the stakes and knowing success or failures, but when that becomes more complicated perhaps there are other solutions to expressing that.

Quote from: Steven Mitchell on July 20, 2022, 04:35:13 PM
Even people who do understand probability fail to apply it correctly more than you would expect when eyeballing a course of action.   Take a group of statistics gurus in a room and give them a modest probability decision that they'll need about 30 to 60 seconds to rough calculate a ballpark answer to.  Make them answer in 5 or 10 seconds.  On average, they'll probably do better than most people, but they'll still be wrong a lot.  Which is why statisticians are sometimes surprised by the answers they get.

Or perhaps set up a range of different castle walls and run sets of trials of throwing a grapple from various distances. You could then obtain a base probability, say 63% at 10 meters range for a 5 meter wall, with modifiers for distance and height, say +/- 2% per meter.

So, you have an accurate probability. Great. But that still doesn't matter much in a campaign where you grapple onto a castle wall once or twice. Your campaign would need to have the PCs grappling walls every day left and right for the 63% to be realized in game as a trend. A single attempt, or even a few attempts, won't elicit the 63%. Or perhaps numerous players from different campaigns would compare notes and discover that the grapple chance is pretty accurate as a whole. All that is a lot of trouble, so for rare events, pick a probability that sounds reasonable and be done with it.

Quote from: Steven Mitchell on July 20, 2022, 04:35:13 PM
Plus, you've always got a few that are staying in character, and better at judging risks through criteria other than the game math, and sometimes they do better than anyone else when it comes to deciding to do risky thing X or not.

This is the best way, as far as I'm concerned. Look at the risk through the lens of your character. Bjorn the Barbarian is not going to worry about probabilities. At best, he knows that the last 5 guys who attempted this stunt all died, but rumor tells of a great man long ago who once succeeded. A good GM would award Bjorn a bonus for role play to encourage this kind of behavior at the table. A meta-carrot for the players who worry about the numbers.

No one wants to think about numbers. Think about it.

Quote from: deadDMwalking on July 20, 2022, 03:15:15 PM
I agree a lot of people don't understand probability. I don't blame them, it's not a simple topic. And I'm far from an expert, but I distinctly recall my university stats professor's rant about how probability is widely misunderstood and one of the most common misunderstandings is that you must have a significant number of samples for the whole idea of probability to have any meaning. n = 100 at a minimum.

So, for one-off events, like bashing a door down or things you might do a few times in a campaign, probability is a meaningless concept.

That's not exactly true. Mathematician, Richard von Mises, who has an award named after him, specified a distinction between Class Probability and Case Probability. You've probably heard that in a room full of 23 randomly selected people, there is > 50% chance that two will share the same birthday. That was von Mises that came up with that. What your stats professor is referring to is strictly Class Probability, and it is true that the rules of Class Probability do not generally translate to Case Probability. It is not true that Case Probability is a meaningless concept.

And I can give an example of why that matters and is not just playing word games with definitions. Consider the finitely iterated Prisoners Dilemma. Backwards induction tells us that the winning strategy is defect. It doesn't pan out in reality. Unfortunately it's common that when professors, mathematicians, and scientists, the explanation is always, "Just proves people are irrational," and there is a litany of serious problems with that dismissal. Especially when there's a fairly easy explanation. Like simply understanding that no matter what backwards induction tells us, that because the players in the prisoners dilemma are allowed to choose, it's possible they will cooperate. That is to say, there is a non-zero probability in what is essentially a one-off event (since later iterations of the game can be informed by prior ones, the various iterations do not form a class). That non-zero probability means that there is a combination of expected future iterations and expected rewards for cooperation for which there is rational indifference, and then beyond that point it's actually rational to cooperate rather than defect.

For an almost innocuous fact of p > 0 flipping a major conclusion in game theory on its head, I'd call that very meaningful. Once you get that camel's nose under the tent, it opens the field up from there. Like in an RPG, I might not know the probability of bashing down a door. But I can logically and rationally surmise that drinking a potion of strength should help matters boosting the probability by some amount greater than zero. You follow this sort of logic to its fruition, you can derive an entire system of relative probabilities--strictly ordinal, perhaps--but enough of one that for consistency's sake the DM and the game system ought to act as if the singular case of bashing in a door has percent chance attached someway somehow. It's usually just easier to give in and treat it like regular class probability.

Quote from: Mishihari on July 21, 2022, 02:57:32 AM
Dice pools, for example.  No reason why, I just don't like them.  Percentile systems are okay, but there's a couple of reasons they're not my favorite.

My central thesis here has been that arbitrary likes/dislikes are probably the only honest answers to the question posed. As soon as people start providing reasons, I have yet to see reasons that don't fall apart under scrutiny. You managed to nail the big four on this topic:

Quote1)  Adding up two digit numbers is not particularly fun.  Just because I do tensor calculus as part of my job doesn't mean I want to do a lot of arithmetic as part of my recreation.

I pointed this out in an earlier post here. If you're adding multiples of 10, that's not really two digit addition. Neither is adding a single digit number. The percentile games I actually play on a regular basis mostly use multiples of 10 as modifiers, but have a small number of modifiers that are multiples of 5, and then also single-digit modifiers. The fact is, there is a window which renders these criticisms moot, and there are percentile games that fit that window.

Quote2)  Some percentile systems use small modifiers, which IMO don't make enough difference to be worth the trouble of doing them.  It's not really worth thinking about something just to get a 1% bonus.

Small modifiers are absolutely significant when dealing with small probabilities. In actual percentile RPGs I play on a regular basis, small modifiers can often modify the die roll itself, rather than the target number, the primary effect of which is to heavily skew the probability of critical success and/or failure.

Quote3)  I find roll-under to be unintuitive.  And roll-over percentile moves away from the simplicity that is the approach's primary strength.

There are two reasons I find this point to be silly.

The first reason is, I think it lacks perspective. People who say they find roll-under counter-intuitive are perfectly happy doing something like, oh, rolling a d20 and having to add a base attack bonus each and every time to try and get a high result. If you look at normie games--non-RPGs and games that are not RPG-adjacent--you don't see this. Maybe "intuitive" isn't the reason why monopoly doesn't give the race car 2d6+4 movement on that player's turn. It's because it looks inelegant and requires an extra math step. But at the end of the day, among normie games, you're more likely to find Roll-under systems and matrix or THAC0 style systems than roll die plus base. I think that should challenge gamers notions of what is or isn't intuitive in the broader context.

But the second and more clear cut reason is, higher, lower, up, down, addition, subtraction, all of these differences can be flipped by re-framing the mechanic. In AD&D, you might have a -2 Dex bonus. Minus? Bonus? Cue mentally obese gamer saying That's Counterintuitive. And it's like, yeah, fucko. The dude is so nimble, anyone who wants to hit him has a -2. Sounds pretty fucking intuitive to me. But but... his +3 ring of protection. Surely you can't have plus and minus both make him harder to hit. Sure you can. The +3 magic bonus is added to your target number when trying to hit the guy. Now you got to roll 3 points higher.

With rollunder, instead of saying, "You gotta roll under your fuck shit up skill to hit the guy," you pin the roll on the defender saying, "You got to roll over that guy's fuck shit up skill to dodge the blow." Presto chango, now you've got a roll-over system with all the same identical statistics and even dice mechanics as ye olde roll-under system.

Quote4)  I don't actually like probabilities to by immediately apparent.  Thinking about numbers takes my head right out of the game fiction.

And this is never ever ever in any game with any GM at any table at any time anywhere ever the case. Simply because GMs are not obliged to inform players of all modifiers in play. Even if the GM regularly does, because the GM can always choose not to, there is a probability greater than zero that the GM will hold back secret modifiers. And that means you have no idea if the roll you're making right now happens to be the one in a thousand where there's something you don't know. Meaning you never actually know the probability.


None of this means you have to like percentile systems. The point is these reasons aren't the actual reasons. I mostly just want to use all the damn dice I bought and paid for.

Quote from: Lunamancer on July 21, 2022, 10:37:42 AM
That's not exactly true. Mathematician, Richard von Mises, who has an award named after him, specified a distinction between Class Probability and Case Probability. You've probably heard that in a room full of 23 randomly selected people, there is > 50% chance that two will share the same birthday. That was von Mises that came up with that. What your stats professor is referring to is strictly Class Probability, and it is true that the rules of Class Probability do not generally translate to Case Probability. It is not true that Case Probability is a meaningless concept.

And I can give an example of why that matters and is not just playing word games with definitions. Consider the finitely iterated Prisoners Dilemma. Backwards induction tells us that the winning strategy is defect. It doesn't pan out in reality. Unfortunately it's common that when professors, mathematicians, and scientists, the explanation is always, "Just proves people are irrational," and there is a litany of serious problems with that dismissal. Especially when there's a fairly easy explanation. Like simply understanding that no matter what backwards induction tells us, that because the players in the prisoners dilemma are allowed to choose, it's possible they will cooperate. That is to say, there is a non-zero probability in what is essentially a one-off event (since later iterations of the game can be informed by prior ones, the various iterations do not form a class). That non-zero probability means that there is a combination of expected future iterations and expected rewards for cooperation for which there is rational indifference, and then beyond that point it's actually rational to cooperate rather than defect.

For an almost innocuous fact of p > 0 flipping a major conclusion in game theory on its head, I'd call that very meaningful. Once you get that camel's nose under the tent, it opens the field up from there. Like in an RPG, I might not know the probability of bashing down a door. But I can logically and rationally surmise that drinking a potion of strength should help matters boosting the probability by some amount greater than zero. You follow this sort of logic to its fruition, you can derive an entire system of relative probabilities--strictly ordinal, perhaps--but enough of one that for consistency's sake the DM and the game system ought to act as if the singular case of bashing in a door has percent chance attached someway somehow. It's usually just easier to give in and treat it like regular class probability.

Interesting. (I think you were quoting me and not deadDMwalking.)

I'm struggling with the idea of Case Probability. I recall that a popular statistician was lambasted for predicting Clinton to win over Trump. Of course, he was wrong. His reply was that he only gave Clinton a 70% chance, so he wasn't actually wrong. This kind of thing is impossible to test. In other words, had he said 90% instead of 70% what difference would it have made?

It would seem that if you're building a unique Case Probability out of bits and pieces of things that have well-understood probabilities, then the ultimate Case Probability is certainty (i.e., you have total information). Or maybe I'm misunderstanding the concept.

Quote from: Lunamancer on July 21, 2022, 12:56:28 PM
With rollunder, instead of saying, "You gotta roll under your fuck shit up skill to hit the guy," you pin the roll on the defender saying, "You got to roll over that guy's fuck shit up skill to dodge the blow." Presto chango, now you've got a roll-over system with all the same identical statistics and even dice mechanics as ye olde roll-under system.

Specifically for roll-under with degrees of success (usually based on 10 under), I think people struggle. 

For example, the TN is 75, and you roll a 49.  Obvious that's a success.  But how many degrees?  59 is 1, 69 is 2, so a total of 2 'degrees'.  If it matters, you beat the TN by 26. 

I think it is easier to take your 75 skill as a base and roll/add against a TN of 100.  In the mirror image of this, rolling a 51 and adding to 75 gives you 126.  Drop the hundreds digit and you know you exceeded the TN by 26 and you can look at the 10s digit and know that it counts as 2 full degrees of success. 

Boils down to a matter of taste.

There are many pros and cons, but they also boil down to personal tastes.

A d100 has very clear chances, a dice pool is easy to add modifiers, a d20 is nice and familiar, a d6 is readily available everywhere, 3d6 has a nice bell curve, etc.

Some people prefer roll high, others roll low. Some hate the idea of "blackjack" (which is perfect for d100 IMO), etc. I find Target 20 awesome but also find descending AC counterintuitive.

I like d100 systems. CoC is great of course, Unknown Armies is cool, Mythras has interesting options, and so on.

Quote from: deadDMwalking on July 21, 2022, 03:52:28 PM

Quote from: Lunamancer on July 21, 2022, 12:56:28 PM
With rollunder, instead of saying, "You gotta roll under your fuck shit up skill to hit the guy," you pin the roll on the defender saying, "You got to roll over that guy's fuck shit up skill to dodge the blow." Presto chango, now you've got a roll-over system with all the same identical statistics and even dice mechanics as ye olde roll-under system.

Specifically for roll-under with degrees of success (usually based on 10 under), I think people struggle. 

For example, the TN is 75, and you roll a 49.  Obvious that's a success.  But how many degrees?  59 is 1, 69 is 2, so a total of 2 'degrees'.  If it matters, you beat the TN by 26. 

I think it is easier to take your 75 skill as a base and roll/add against a TN of 100.  In the mirror image of this, rolling a 51 and adding to 75 gives you 126.  Drop the hundreds digit and you know you exceeded the TN by 26 and you can look at the 10s digit and know that it counts as 2 full degrees of success.

Some games go with the blackjack method where the tens value of a successful roll-under check is the success level. In this case, if you need a 75 or lower and roll a 49, you have 4 success levels. Yes, this means you want to roll as high as possible without exceeding the target number. It's a very quick way to do it, and works especially well when degrees of failure are not relevant.

Quote from: Lunamancer on July 21, 2022, 12:56:28 PM

Quote from: Mishihari on July 21, 2022, 02:57:32 AM
Dice pools, for example.  No reason why, I just don't like them.  Percentile systems are okay, but there's a couple of reasons they're not my favorite.

My central thesis here has been that arbitrary likes/dislikes are probably the only honest answers to the question posed. As soon as people start providing reasons, I have yet to see reasons that don't fall apart under scrutiny. You managed to nail the big four on this topic:

Quote1)  Adding up two digit numbers is not particularly fun.  Just because I do tensor calculus as part of my job doesn't mean I want to do a lot of arithmetic as part of my recreation.

I pointed this out in an earlier post here. If you're adding multiples of 10, that's not really two digit addition. Neither is adding a single digit number. The percentile games I actually play on a regular basis mostly use multiples of 10 as modifiers, but have a small number of modifiers that are multiples of 5, and then also single-digit modifiers. The fact is, there is a window which renders these criticisms moot, and there are percentile games that fit that window.

Quote2)  Some percentile systems use small modifiers, which IMO don't make enough difference to be worth the trouble of doing them.  It's not really worth thinking about something just to get a 1% bonus.

Small modifiers are absolutely significant when dealing with small probabilities. In actual percentile RPGs I play on a regular basis, small modifiers can often modify the die roll itself, rather than the target number, the primary effect of which is to heavily skew the probability of critical success and/or failure.

Quote3)  I find roll-under to be unintuitive.  And roll-over percentile moves away from the simplicity that is the approach's primary strength.

There are two reasons I find this point to be silly.

The first reason is, I think it lacks perspective. People who say they find roll-under counter-intuitive are perfectly happy doing something like, oh, rolling a d20 and having to add a base attack bonus each and every time to try and get a high result. If you look at normie games--non-RPGs and games that are not RPG-adjacent--you don't see this. Maybe "intuitive" isn't the reason why monopoly doesn't give the race car 2d6+4 movement on that player's turn. It's because it looks inelegant and requires an extra math step. But at the end of the day, among normie games, you're more likely to find Roll-under systems and matrix or THAC0 style systems than roll die plus base. I think that should challenge gamers notions of what is or isn't intuitive in the broader context.

But the second and more clear cut reason is, higher, lower, up, down, addition, subtraction, all of these differences can be flipped by re-framing the mechanic. In AD&D, you might have a -2 Dex bonus. Minus? Bonus? Cue mentally obese gamer saying That's Counterintuitive. And it's like, yeah, fucko. The dude is so nimble, anyone who wants to hit him has a -2. Sounds pretty fucking intuitive to me. But but... his +3 ring of protection. Surely you can't have plus and minus both make him harder to hit. Sure you can. The +3 magic bonus is added to your target number when trying to hit the guy. Now you got to roll 3 points higher.

With rollunder, instead of saying, "You gotta roll under your fuck shit up skill to hit the guy," you pin the roll on the defender saying, "You got to roll over that guy's fuck shit up skill to dodge the blow." Presto chango, now you've got a roll-over system with all the same identical statistics and even dice mechanics as ye olde roll-under system.

Quote4)  I don't actually like probabilities to by immediately apparent.  Thinking about numbers takes my head right out of the game fiction.

And this is never ever ever in any game with any GM at any table at any time anywhere ever the case. Simply because GMs are not obliged to inform players of all modifiers in play. Even if the GM regularly does, because the GM can always choose not to, there is a probability greater than zero that the GM will hold back secret modifiers. And that means you have no idea if the roll you're making right now happens to be the one in a thousand where there's something you don't know. Meaning you never actually know the probability.


None of this means you have to like percentile systems. The point is these reasons aren't the actual reasons. I mostly just want to use all the damn dice I bought and paid for.

I'll reply to your points in order ...

(a) I don't think dice preferences are entirely irrational.  Some preferences make sense.  Quicker is better than slower.  Less work is better than more.  There are solid reasons to prefer obscuring rather than revealing probabilities or vice versa to support a preferred style of play.

(1)   It's not a big difference, but manipulating two digit numbers is verifiably more time, work, etc than 1 digit numbers.  It doesn't matter to everyone, but for those who do care it's a pretty logical reason

(2)   In a percentile pass/fail roll, a 1% modifier will change the result from fail to pass or the other way around once in every 100 rolls, on average.  That's not often enough for me to want to make the slight effort to add it in.  Admittedly, not all percentile systems use modifiers this small, but if, frex, your smallest modifier is 5%, you're better off using a d20.

(3)   I find roll over systems to be more intuitive because in so many things, more is better.  I'd rather have more money, more cars, more square footage in my house.  Higher is better on a roll is just what I expect.

(4)   Sure, sometimes there are hidden modifiers.   IME as a GM, more often there are not.  As I said, I prefer not to know precise probabilities, and that's a tiny bit harder with percentile than other single die rolls.  I prefer add up 2 or more dice for this reason

Quote from: Mishihari on July 21, 2022, 05:17:56 PM
I'll reply to your points in order ...

(a) I don't think dice preferences are entirely irrational.  Some preferences make sense.  Quicker is better than slower.  Less work is better than more.  There are solid reasons to prefer obscuring rather than revealing probabilities or vice versa to support a preferred style of play.

(1)   It's not a big difference, but manipulating two digit numbers is verifiably more time, work, etc than 1 digit numbers.  It doesn't matter to everyone, but for those who do care it's a pretty logical reason

(2)   In a percentile pass/fail roll, a 1% modifier will change the result from fail to pass or the other way around once in every 100 rolls, on average.  That's not often enough for me to want to make the slight effort to add it in.  Admittedly, not all percentile systems use modifiers this small, but if, frex, your smallest modifier is 5%, you're better off using a d20.

(3)   I find roll over systems to be more intuitive because in so many things, more is better.  I'd rather have more money, more cars, more square footage in my house.  Higher is better on a roll is just what I expect.

(4)   Sure, sometimes there are hidden modifiers.   IME as a GM, more often there are not.  As I said, I prefer not to know precise probabilities, and that's a tiny bit harder with percentile than other single die rolls.  I prefer add up 2 or more dice for this reason

Yes. Not everything expressed as "feel" is irrational.  It's not universal or even consistent across everyone, but where people place value has subtle differences that add up. Some of those differences are not so subtle with certain gamers.  Since gaming is a shared activity, it's not only about what I like but what I'm willing to put up with in others.  Explaining for the umpteenth time that for this roll you want high and that roll you want low--is well, not something that I ever enjoyed, and whatever tolerance I had for it as a necessary cost of running the game has long since evaporated.  Which is why I don't mind roll under as a player nearly so much as a GM (even though I also have a very mild irrational prejudice against roll under strictly from a feel perspective, but not so much that I can't happily play a game that uses it when it's run by someone else).

There is one concrete minor benefit to roll under that hasn't been listed yet:  If the checks are roll under and the effects are roll high (e.g. damage dice), then it discourages players using biased dice.  Works better in systems where it is all the same dice type, such as Fantasy Hero.  Of course, it's easier to simply boot the players that are deliberately using biased dice.