The last Pathfinder game I ran, only one roll in four that I made was actually ten or more.   Made for an interesting, if short lived, game.

20:14,  rolled 190 using 20d20 ((2,9,5,8,8,7,14,14,2,19, 1,11,7,11,14,12,1,20,17,8)).

This sequence is a probable as any other (as 20 20s). Just a point of interest. But RPOLers know things like this, which is why we all seldom buy lottery tickets.

Chaos theory kinda works against that. Research shows that probabilities only really hold up over long periods, and that generally good luck and bad luck occur in streaks.

What does chaos theory have to do with randomness? Chaos is the study of dynamic systems and their feedback mechanisms.

I'm not trying to be an apple, I honestly want to know more. Do you have any reference to this?

In reply to mole75 (msg # 10):

Chaos, by definition is Randomness.

Chaos in the everyday meaning might be just that. But chaos theory is the study of dynamic systems - often with coupled differential equations. It might be unpredictable on the short ther but it's not random.

Dice, whether physical or electronic simulations, are dynamic systems, so chaos theory does have some bearing on their outcome.

It would be stretching it to call a rolling die a dynamic system. At least in the way it's used in chaos theory. Normally you'd need to have several differential equations that influence each other. So if you rolled the die on a trampoline you might get a chaotic system but otherwise you wouldn't.

The way that electronic dice works is by using an algorithm and often use the time on the computer as the variable. If that was a dynamic system then the outcome of the algorithm would change the time. Since we don't see that many time traveling computers it's a safe bet that it doesn't.

OK to be fair that is a bit of an oversimplification. You could easily program a RNG to produce a chaotic behavior. But that would be  a really bad RNG.

Devil's advocate:

Physical dice could technically edge into the arena of a dynamic system if you consider the effects of physical wear over many thousands upon thousands of rolls.  Nearly all mathematical calculations performed for probability assume a "fair die", i.e. one that's mechanically sound/perfect.

I don't know how you could form the equation but theoretically there should be some equations which consider the effect off all past rolls on the current probability.

Some really old school roleplayers have d20s that are so worn they are no longer fair dice and will regularly favor a handful of possible values, depending on the wear pattern.  That makes sense if you think about it, it's basically a plastic orb to begin with and the sides are usually small so it takes relatively little wear to mess with them.

Casinos replace their dice pretty often for that reason.

You are right that wear and tear or even a badly made die can favour certain values. But that's not what is understood as chaotic behaviour (at least not when talking about the scientific field of chaos theory.) Such a die would still have a very simple set of equations that govern it's motions.

Of course taken over a long stretch of time the previous wear on the die would influence the rolls in the future. But that would still not be considered dynamic in the sense of chaos theory (at least not how I understand it).

There are wonderful examples of chaos theory in play with weather patterns, fluctuation of populations of animals and such. The big difference between random events and chaotic events is that you have a chance of predicting the later whereas the former is by nature random. That's why you can predict how a population of animals grows or declines but you'll never have any way of predicting when an atom decays (other than their statistic probabilities).

As I understand it, applying chaos theory to dice rolling would be more about constantly shifting variables like the particular speed and direction of spin a die gets as it's released from your hand, variations in the surface you're rolling on (a hard tabletop doesn't have many, but carpet can throw different angles into a bounce, and if you're rolling into a box top or such held on your lap, the slope of the surface can change by a few degrees from roll to roll, or even during the roll), whether or not you're having the dice rebound off a surface after the initial 'toss', etc...  They're pretty minimal variables, practically insignificant...but enough to affect the dice results.  And the possible results with most dice are such a small range that, statistically, there's little or no change in the degree of randomness you get from rolling under 'chaotic' circumstances versus the random results generated by a computer.

In reply to Genghis the Hutt (msg # 1):

Getting back on track. I had character that recently died. He was level 1, and hit once in his career. He was critically hit, from  hull HP to dying. My other character (first of two in solo) tried to heal him with the heal skill. Couldn't do it. Needed a 10, a 55% on each roll. Couldn't do it. So poor guy who was critically hit died, just wasted away.

I put meaning into it. The GM gave outs and I wanted the dice to mean something.

As for the "Did I do that?" probably not. If you want realism, no, it was your opponent's defense. If you want narrative, again, probably not. Many video game and movies show blocks and dodges, a good hit is often the only one that turns the tide.

I know dodging and armor can be repetitive, but that's the whole point. If a kobold has a good dex, or is wearing armor, that's what's doing it. Sadly, it's probably just that.

But in D&D the numbers can be construed however you want them to be. If the group wants defensive narrative, then yeah, that's probably it. If they want offensive narrative, then yeah, go for it. If they want circumstantial narrative, that can work too.

I tend to think of 1st level characters like junior year high school students. They suck, and by suck, I mean they are the equivalent of putting a junior varsity wrestler on the mat, or a junior in a band on the stage. Even the gifted ones aren't much to look on.

I had a character in one of my games like that. Sorcerer who stood in front of the group's monk, took his first hit (a crit), and insta-died.

That group was plagued by bad luck, though. An Ogre sneaked up on the rogue during the night. The rogue had something stupid like +9 to Perception. After that, the group kept their eyes out for more ninja Ogres.

I was rather referring to what has been found in studying the world with chaos theory. The universe is one big chaotic system after all.

If you consider the probabilities of a d6, then over X number of rolls, you should get about 1/6th of the rolls landing on each number. For a million rolls this is actually quite close, but as X gets smaller, particularly below a dozen, then it doesn't hold true very well.

Take a look at the line of d20 results posted above my last remark (msg #8). Not very evenly distributed even though probability would suggest a mostly even distribution. Despite only 20 rolls you actually have two results that each came up trice. The first 6 results were all below 10 and most of the results clustered around 8 with 14 and 11 bringing the majority. Of the remaining results, half were 1-2 while the others were scattered and only 3 of the 20 rolls were 15 or more even though in theory five rolls should have been 15 or more.

This effect is what I was referring to.

Within this aspect of results drifting so far from probability for any short streak of results, is where really strange things happen that are easily attributed to things unexplained by science. Whether it be chance, fate, divine intervention, or something else entirely, strange patterns appear that probability suggests as very unlikely, yet happen all the time.

For example, in my very first campaign, I had a sorcerer and when rolling for magic spells, I always used my sparkling d4s, because they always rolled well for magic, but always rolled poorly for anything else, and none of my other d4s rolled well for magic damage.

Probability says this is possible but very unlikely. Think about it, over a few hundred rolls, the only high rolls had a very strong correlation to something that could not physically impact the results.

The chances are astronomical that it would work out such that from a pool of dice only specific ones should roll high and only when the narrative met certain conditions, yet such patterns are common and so far unexplainable (except by religion).

Double post for some reason. Sorry.
This message was last edited by the user at 15:04, Tue 26 June 2018.

Because a bad string of rolls can come at any time, I try to focus on games that are fun even if the PCs are losing. Combat usually isn't such a situation, because fun itself is often at stake, in the form of the characters themselves. That doesn't have to be the case, though.

Also, some games have things for characters to do that don't require them to hit. For instance, leaders and defenders in 4th Edition D&D always have a baseline amount of effectiveness, even if they never hit any targets. And almost every character has at least one heavy hitting power that does something even on a miss.

Also, I try to play games in which things like hitting and missing and damaging are more abstract. A roll that's a miss can be described as heroic, rather than foolish. There's often little reason why a miss on the dice can't be described as a hit in the game. If it doesn't actually change or make progress toward any new state, well, so what? The target shrugs off that hit, but clearly can't keep that up forever.

Nope. Sorry but this is a tiny, tiny sample. Run the dice roller a 1000 times or 10000 times. The results won't be perfectly even but they will tend towards an even distribution. At various times there might be runs of certain numbers or clusters but it shouldn't mean anything in the long term.

Depending upon the peculiarities of random number generation software and hardware on the RPOL server the result of any previous die roll should have zero effect upon any subsequent die roll. It might look like there is a pattern but this is because humans are good at seeing cause and effect... too good in fact and so our brains keep on seeing it when it isn't there. Our brains make up a reality to suit us.

Also remember that you are sharing this die roll mechanism with people in your own game and in fact every other person on this server so there are often many other die rolls occurring in between your last die roll and your next.

As for Chaos theory, if we were talking about a perfectly random dice roller then Chaos theory has zero effect. Where Chaos Theory would have an impact would be in considering other factors, as discussed above, where you were rolling dice on a table. Things like wear and tear on the dice, the way the dice were being thrown, which face of the die was facing up when the dice were thrown, the friction of the surface onto which the dice were being thrown and so on. Other than that there is no feedback that derives purely from the previous result of a dice onto the next result that will occur when the dice is rolled again.

As for role-playing, as GM I tend to allow for a little fudging in order to make the story interesting. I dislike having the players know what they need to hit and can allow for some partial effects appropriate to the combat.

Did you read my post? The fact that it is a tiny sample and not a large sample, is a massive part of it.

Also, there is no such thing as truly random, it is always a result of a chaotic system. It just seems random because we can't even know all the exact inputs much less calculate the result.

As for the site's rng, I don't know for sure what Jase uses, but if it is a common one, or worse, the default for java/c++/etc, then it is well known for having skewed results in the first handful of results. Regardless, all rngs are not truly random.

Besides, if you reread my post, you'll realize that this,

is exactly a point I addressed. Of course, I didn't make assumptions about the source of those patterns. And taking the "scientific" view (that isn't actually scientific) is still an assumption.

Proceed with caution when telling someone that something they believe about random number generation is due to small sample size, confirmation bias, or anything else mundane. Belief in supernatural influence on random results may seem funny or quirky but I've seen it taken very seriously.

Hmm... the discussion has sparked a possibly interesting long-term experiment in probability.

As some have already pointed out, there are nuanced definitions of Chaos (as opposed to chaos), some philosophical, some mythological, and some mathematical.

With that, I've said all I intend to until after the thousandth roll is done and the numbers are crunched.  (When will I find the time...)

This might take a while, folks.  See ya!

I'd be interested in reading details about this, if someone has a source. Searching seems to just bring up questions about how to skew results deliberately for whatever reason.

If it's a well-known issue, I imagine there are well-known ways to address it, and I'd like to understand those.

The problem with probabilities is that they're only good over large sample sets.  Individual runs of data can be very good or bad with the dice.

For instance, I made a two-weapon ranger for a 4e Darksun game (which used a "weapons break on a 1" rule of some description - I don't recall if you rolled a second time to confirm it or not).  I proceeded to roll terribly in the first combat, broke both weapons, and then died.  According to probability, that was a very unlikely chain of events, but it definitely happened and left me a bit annoyed.

In another (less personal) example, Red Markets uses 2d10 to generate results.  Results of 11, 33, 55, 77, and 99 are critical failures.  During the playtesting of the game, there was a session where the players rolled so many critical failures that the creator declared they "broke math" and started to doubt the dice mechanic entirely.

So... probability is useful.  Probability is what you design characters to.  Heck, probability is something the GM should be well aware of when calling for rolls.  However, it's not necessarily what you're going to experience in a given session.

Which is one reason I like systems that let you barter something for success, regardless of the dice.  Fate/karma/moxie/benny points are an obvious example.  Other games that let you "succeed at a cost" are another.  From an objective point of view, such systems are just better because dice sometimes decide to take the story completely off the rails (beyond what's acceptable to the group, anyway).

There are two optional rules. For one of them, if you roll a 1, the weapon breaks. For the other, if you roll a 1, you may choose to re-roll the attack; after the re-roll the weapon breaks (a metal weapon only breaks on a natural roll of 1-5).


Yes, just about anything is better than "you miss; nothing happens." Even D&D gets this a little with how it makes certain things (major spells in just about every edition, and all daily powers in 4th Edition) do something on a miss. They get that some misses are just too painful.

People definitely need to know what they're putting at stake with dice rolls, though. If a particular roll or run of rolls could "take the story completely off the rails," then there's probably a better way to arrange that story, assuming the table doesn't want to use a completely different system, or just reconsider what's necessary to roll for.

Well, to just grab an example, imagine the big battle at the end of the campaign.  It's succeed or the world ends.  Those are the stakes the group has been playing toward the entire campaign and then... no one can roll above a 3 the entire fight.  It isn't a big heroic struggle where they fall just short... it's just pathetic.  No one leaves the table feeling good about the session and it probably sours perceptions of the entire campaign.  Even if the GM steps in with some sort of fiat and allows for a "heroic sacrifice" at the end to put a decent ending on the story, it only sort of mitigates the disaster.

I felt that way about that ranger, though my next character had a much longer career.  I don't feel that way about a number of other deaths and TPKs I've been through, though.  For instance, a 9 month long Ravenloft game I was playing face to face just met a TPK due to bad player choices (not die rolls) and I'm perfectly fine with that.

It's not a big heroic struggle, until it is. If that is put entirely in the hands of the dice, then it very well might not be a big heroic struggle, and deciding a priori that it will be is asking for trouble. It might go the other way too: the characters roll well, and the enemy rolls poorly, making the fight a complete pushover.

The problem is not the dice system, but the presupposition incompatible with the dice system.


I can well imagine. None of that should be staked on dice rolls.


Fortunately, there are other options than that, even without changing systems (and even under another system some of those options should probably be considered).

Basically, one has to understand what they're getting into, and not presuppose that any particular random generation system (or really any set of rules, but particularly ones with random outcomes) is going to deliver a desired outcome over something as short as a single scene or situation or evening. One simply has to be able to accept an extremely unlikely cluster of rolls. If they can't, they have no business rolling the dice.


Okay, though choosing not to take into account the possibility of bad dice rolls is also bad player choice.