Nothing says “organized randomness” like a fractal image!
This one is courtesy pixabay.com/Shabinh,
cropped and color-enhanced by Mike, and looked so gorgeous that you can get a larger version by clicking on the thumbnail.

Anarchy.

Chaos.

Flexibility.

Uncertainty.

Control.

Challenge.

Unpredictability.

All of these words can be used to describe the influence of Randomness within an RPG. Every GM uses randomness in all seven of these ways, the relative significance being the primary variant. But why do RPGs contain a random element?

Randomness in RPGs derives from two sources, neither of which can by considered truly random, as you will soon see.

Player Choice

The one thing at the table that the GM has, theoretically, no control over, is the players. In practice, there is the GM’s understanding of the psychology of the players, of the characters that they are playing, of how the player plays the PC; there is knowledge to some extent of how the PC will react to a broad range of triggers and conditions, and can manipulate mood and situation to play on those factors to at least some extent. So player choice is never purely random, even though it may sometimes seem capricious (at best) to the GM.

The better the player, the more he will hone in on some “inner truth” about each character that they play, which they can use as a foundation and guiding principle, ensuring greater consistency of characterization over many sessions. Sometimes, a less-skilled player will find a character that simply “fits” their psychology like a glove, subconsciously finding that “inner truth”; such characters are very likely to become a favorite of the player in question.

And sometimes, no matter how experienced and capable they may be, an experienced player will be unable to find that “inner truth” at the core of a character, and will consequently struggle to roleplay them either effectively or to their satisfaction.

The more consistent the characterization, the more predictable it becomes to the GM, and hence the more control the GM has over this aspect of unpredictability at the game table.

Such control can never be absolute, however, because of the presence of the second source of randomness.

Die Rolls

Die rolls are employed to collapse the quantum uncertainty of an outcome into a finite resolution of uncertainty. If the game mechanics are d20 based, there are 20 possible outcomes of any given die roll; modifiers may shift those possible outcomes one way or another, but there remain just twenty possible results.

That can, of course, change if some exploding die roll mechanism is incorporated into the rules, but let’s keep this discussion simple.

Right away, the randomness of any outcome can be seen to be restricted to just those 20 discrete possibilities. For the additional flexibility and scope of randomness, some game systems are percentile based; others employ non-linear probability to achieve greater variability. I’ll get into that in a moment.

In practice, in many cases, the degree of variability actually collapses still further. Success or Failure – a binary state, almost certainly of unequal probability, but nevertheless a simple yes-or-no proposition. Some GMs add interpretations of degrees of success or failure as a rules refinement to overcome this simplicity when the situation is suggestive of more than two possible outcomes. Others subdivide a task and require appropriate checks for each subdivision.

If, for example, the character is attempting to bake a cake, you could divide this into ingredient selection, ingredient mixing, baking, and decoration. Get any one of them wrong and the end result may or may not be edible. But – unless it’s particularly important, or one of those steps presents an unusual challenge for some reason – most of the time, the same results can be achieved with a degree-of-difficulty measure.

That means that if a character succeeds by 10, their outcome will be just a little more appetizing than a character who succeeds only by 5. The only thing that a character who just barely succeeds will be confident of is that the cake won’t accidentally poison those who eat it.

Another way of handling these nuances is to ignore margin of success and instead apply modifiers to the roll. A master baker’s minimum standard of success is going to be a lot higher than that of an unskilled home baker for whom edibility is the primary objective. That is easily simulated by “raising the bar” by one every time the master baker adds X to his skill level. X could be two, or three, or perhaps four. I don’t recommend it to be more, or less, than that (out of twenty). This modifier determines success or failure according to different criteria than the simplest such meaning. You can even have a rule that, above a certain skill level, that simplest such criteria is always achieved except on a critical failure.

The psychology of the character should also factor into this discussion. A perfectionist will have a much higher standard of success than the ordinary practitioner. “It’s light, moist, delicious, and beautifully decorated.” – “Yes, but the bottoms dried out just a little too much, the baking tray was too close to the heat, so the cooking is just a little too uneven. I’m ashamed to put them forward for others to eat.”

In the non-linear probability model, the fact that some outcomes will occur with lower frequency. This can be seen when you plot the probability by outcomes of various dice rolls.



Graphs generated using AnyDice.com

The graphs to the left show the probability of outcome of 1, 2, 3, and 4d6, stretched horizontally to the same size. As you can see, 1d6 is a flat or linear probability (as you would expect), 2d6 is a straight line up and another down, peaking at the mean result of 7, 3d6 is a somewhat imperfect bell shaped curve, while 4d6 gives a very smooth bell curve by comparison. That means that with multiple dice, extremely low and extremely high results are quite improbable while outcomes close to the mean are relatively likely. The more dice you add, the greater the likelihood of a “central” result, a fact that I took advantage of with the “additional dice against a moving target number” mechanic in my Zener Gate rules.

It can take a while to intuitively grasp the impact of an nDx roll’s probability curve, whereas a flat roll can be instantly understood by almost everyone, making a linear system easier for beginners to get a handle on. Once you do, you can generally operate with reasonable ease, but you do need to shift mental “gears”.

Since nDx gives access to a limited number of low-probability outcomes, enabling a match to be made between a target number and the significance of success in achieving that number, that is more nuanced than a linear curve of similar size in terms of outcome range. The minimum percentage chance of an outcome on d20 is 5%, by definition. The minimum percentage chance of an outcome on 3d20 is 0.46% (3 or 18), and the next most improbable result is 1.39% (4 and 17), and the one after that is 2.78% (5 and 16). Only at the 6 and 15 results do the probabilities roughly match – 4.63%. The “missing” chances have to go somewhere, and the place they go is on results closer to the mean (10.5) than 6 and 15. Results of 10 or 11 account for 1/4 of the outcomes, and results of 9 and 12 are almost as likely at 23.14%.

But the collapsing into known possible outcomes mean that while the outcome in any individual case might be unknown and unknowable, in terms of the outcomes, these are very much predictable – and a good thing, too, because it enables creation of adventures that can encompass a range of outcomes.

Those are the only two mechanisms by which randomness enters the game. Everything else is under the direct control of the GM. And, as you can see, by changing definitions and difficulty settings, or by the manipulation of the players, even these are under the indirect control of the GM to at least some extent.

Which leaves out answer to the question of what purpose randomness serves within an adventure on very shaky ground. It must serve some useful purpose, or why bother having it?

So, what are the possible uses, given these new facts?

Image courtesy pixabay.com/TheDigitalArtist,
cropped and enhanced by Mike.
Once again, a larger version is available by clicking on the thumbnail!

Giving Players The Illusion Of Freedom

A cynic is sure to suggest that one possible purpose is to give players the illusion of being free to act as they see fit. Determination of success or failure is down to the die roll, an independent arbiter, and not the capricious whims of a GM. Die rolls, in other words, provide a metagame mechanism by which players can seize control of the game from the GM, or at least attempt to do so.

Empowering The Players

This posits a very adversarial relationship at the gaming table though. A less adversarial function that amounts to the same thing would be the GM willingly yielding an element of control over the game to empower the players, giving them confidence in their control over their characters.

Die Rolls For Everything?

Taken to its extreme, players might be permitted to roll dice, or be asked to roll dice, for absolutely everything that their characters want to do, down to whatever level of minutia the GM sees fit. “Make an armor roll to put on your left boot. Okay, now make another one for the right boot…”

Sounds ridiculous, doesn’t it? Yet, I’ve been in games (very briefly) that operated in exactly this manner, if not quite to this extreme. In fact, the very premise of task subdivision derives from such interpretations of the presence of die rolls within an RPG. The difference is that task division separates a complex task into multiple logical stages that can be clearly articulated and the impact of their success or failure on the ultimate outcome can be interpreted by the GM.

Derailing the Plot Train

This is one of the most important functions of die rolls in a game. By injecting a source of unpredictability as to outcome, however shaped and controlled by the GM, they enable the deliberate derailing of plot trains.

Instead of saying “no”, the GM says “It probably won’t work, but roll…”

The problem is that a failure to succeed is sometimes interpreted by a player as the GM manipulating the circumstances to ensure that the dice say ‘no’ for the GM, acting as a proxy for his will. That brings us back to that issue of “Illusion of freedom” again.

The illusion of a plot train is just as damaging to a campaign as a plot train. The only solution is to permit the dice to fall where they may at least part of the time – and make sure the players know it.

The dice, in other words, won’t do your job for you. It’s your responsibility to avoid plot trains, through your choices, through listening to the players, and occasionally risking a little anarchy slipping through the cracks.

Anarchy

This function of randomness within an RPG actually relates directly to the events that inspired the entire article. Since they’re relevant, the time has come to relate the story (in very compressed form, I assure you).

On Saturday, the adventure opened with the characters in the middle of an emergency. I started by relating to them how things got to this point – a villain, confronted in a reasonable way, tactically, with the characters doing the sort of thing that they would have predictably done anyway, but things didn’t go according to plan, resulting in the emergency.

How the players chose to deal with this emergency was up to them – I followed my usual maxim of “where there’s one solution to a problem, there will be others,” and – in fact – the solution they came up with was much better than the one I was prepared to offer if they were truly lost – and if they rolled well enough on an appropriate skill.

With the emergency resolved, they had to come up with a plan to deal with the villain responsible, which was actually the point of the whole encounter, which was part of a much larger picture that’s been building up in subplots for several adventures now. It took only seconds for me to recognize that the players were coming up blank.

I could have had someone make a die roll, but instead chose a non-random approach: an NPC offered a plan that was (a) in keeping with his personality as the players have come to see it; (b) tactically sound; and (c) within the group’s capabilities, giving everyone something to do. Accepting the plan was purely the PCs prerogative – sometimes they do, sometimes they don’t (and sometimes the plans are deliberately designed to contain unacceptable shortcomings or risks so that they will be rejected – the NPC isn’t just a mouthpiece for the GM to tell the players what to do). But, in this case, the plan sounded (and was) reasonable, if a little left-field, so they accepted it.

And then one of the players repeated a line he had used earlier, and which is a common one at my gaming tables: “tell us where the plan goes wrong.”

According to my adventure plan, it didn’t. But I saw an opportunity to inject a little anarchy and derail any perceptions of plot trains, so I had the team’s leader (chosen by the other PCs) roll on behalf of the team. If that roll had been good enough, the plan would have succeeded as described, but that wasn’t the outcome; the die roll indicated that it was about 66% successful. Since the plan had five steps, I decided that it was stage 4 that failed, chose a rational cause for that failure to have occurred, and presented the PCs (effectively) with a new problem.

If the PCs failed to solve that problem, I was prepared to let the villain escape – the anarchy factor, because I would have to come up with a new encounter with him on-the-fly – but immediately after devising the problem, I saw a solution that would enhance the credibility and viability of the main plot function of the adventure (in scenes that we have yet to play). This was only possible because one of the usual players was absent on this particular day, due to ill-health, and I happened to be wearing the “Runeweaver Hat” at the time, i.e. I was running the PC as an NPC. So he offered a solution to the problem that worsened a long-term problem being created by the villain ultimately responsible and left it to the team’s leadership and the player whose character would be directly affected to choose whether or not to accept the proposal – with no certainty on the player’s part that it would work, of course.

He did, and play proceeded.

As you can see, a little anarchy can be a good thing, prompting player engagement and permitting the occasional refinement of the “big picture” on the fly. If I had thought of it in advance, I might have scripted the entire encounter the way that it eventually played out – but I didn’t. Instead, I let the players AND myself think on our collective feet.

Challenge

Which also illustrates the challenge that randomness can provide the GM – not every random factor can be anticipated, or should be. Keeping the main plot more-or-less “on course” is the challenge, or modifying that main plot to incorporate unexpected changes in circumstance.

The players won’t always notice that you have done so, but even the occasional appreciation of such changes reinforces their perception (correctly) that the PCs, and the choices that the players make for them, do ultimately make a difference. And that makes the game more fun for them, and for the GM, both directly and vicariously.

Problem-solving is a routine challenge for the players. Permitting the occasional spur-of-the-moment bout of problem-solving by the GM brings the two roles closer together, and directly tears away at any perceived player-vs-GM adversarial relationship.

Flexibility

Deliberately incorporating a controlled level of unpredictability into a game forces the GM to be more flexible in his planning, and that gives him the scope for greater flexibility at the gaming table.

Players who read my adventure plans after the fact are astonished at three things: How much of it has been planned in advance, how much has been deliberately set up in past adventures or to feed into future situations, and how much of what some might consider “the important bits” has not been planned.

I’ve spoken of this before: if you can get contextual inference to do the “big picture work”, such as consequences of the fact that an adventure is even taking place, then you can be indifferent as to the outcome of that adventure once it is underway. Again, this neutrality affords you flexibility and gives the players license to be creative.

Control

At the same time, in most adventures, there are critical moments (which often seem to be of superficial significance at the time), beats that I need the adventure to hit in order for the big picture to continue evolving according to my larger plans.

Randomness through die rolls, controlled by the techniques described earlier, and
coupled with the manipulative techniques and triggers described, permits steering of these moments within a narrow range of possible outcomes. Setting situations up so that either outcome serves your purpose in different ways can be difficult, but smart players recognize that a die roll can fail, and are prepared with both back-up plans and with arguments that enhance their likelihood of success in the first place.

The incorporation of some genuine anarchy provides an effective camouflage for these moments. And, even if they notice at the time, most players are prepared to let such moments slide, first because they are of only superficial significance at the time, and second, because they are confident that when they do snowball into significance, the players will be given greater flexibility in how to respond.

You only get that level of trust on the part of the players by earning it. Every piece of deliberate anarchy that you court in a campaign can be thought of as money in the “credibility bank” – ‘funds’ that you then draw on when you need to.

At the same time, I put a lot of research effort into my adventures. Once again, every measure of credibility that you can incorporate adds to the willingness to let something slide, for the sake of the adventure, when you inevitably mess up. Keeping a positive balance in both “accounts” earns you brownie points for when you really need them. And that’s a form of big-picture control, too.

Predictably Unpredictable In A Controlled Way

I try to be predictably unpredictable in my adventures. Plot twists, but not all the time. Things planned only vaguely. Multiple option branches within a limited range of possibilities. Player flexibility and the occasional injection of anarchy – as much to enhance my own enjoyment of the game and the challenge of running it well, as to provide entertainment for the players. But all controlled and confined to the immediate situation or to longer-range circumstances that I can work around, to the ultimate benefit of the big picture that’s taking shape and evolving in the background.

Randomness is the tool that enables all of this to occur. And that more than justifies its presence within an RPG.

BONUS CONTENT!

This is a section that I was going to drop in wherever it seemed to belong but which, at the end of the day, didn’t seem to quite fit anywhere; it’s just a little bit off to the side of the main subject of this article, but too good to ignore, and not large enough to spin off into its own article.

D&D Combat is described not as simulating every blow exchanged, every parry and thrust, but as representing the cumulative result of many individual attempts to inflict harm upon an enemy.

That definition is at odds with the variability of linear probability die rolls. You can even argue that 3d6 provides too much variability.

A far more realistic simulation of this principle could be achieved by defining the success of a combat interaction as the % that the attack value represents over the sum of the attack value and the defender’s armor class, then multiplying that by the damage roll, or even multiplying it by the maximum damage that can be inflicted.

• Attack of 10 vs an AC of 15: 10/25 = 40%. So in a round of combat, the attacker does 40% of the damage it’s possible for him to inflict.
• Attack of 5 vs an AC of 25: 5/30 = 16.66%. So in a round of combat, the attacker does 17% of the damage it’s possible for him to inflict.
• Attack of 20 vs an AC of 10: 20/30 = 66.66%. So in a round of combat, the attacker does 67% of the damage it’s possible for him to inflict.

If you still felt it necessary to have some randomness, add the same d6 roll to the attack value:

• Attack of 10 vs an AC of 15, Attacker rolls a 4: [10+4]/25 = 56%. So in a round of combat, the attacker does 56% of the damage it’s possible for him to inflict.
• Attack of 10 vs an AC of 15: Attacker rolls a 6: [10+6]/25 = 64%. So in a round of combat, the attacker does 64% of the damage it’s possible for him to inflict.
• Attack of 10 vs an AC of 15, Attacker rolls a 1: [10+1]/25 = 44%. So in a round of combat, the attacker does 44% of the damage it’s possible for him to inflict.

If you still want to preserve the extreme results of a critical or a fumble, you could use an exploding d6. This works as follows: if you roll a 6, roll again, and add 5 to the result for every additional die rolled. If you roll a 1, roll again, and subtract 5 from the result for every additional die rolled.

• Attack of 10 vs an AC of 15: Attacker rolls a 6, then a 1 for a total of 5+1=6: [10+6]/25 = 64%. So in a round of combat, the attacker does 64% of the damage it’s possible for him to inflict, and a critical hit.
• Attack of 10 vs an AC of 15: Attacker rolls a 6, then a 3, for a total of 5+3=8: [10+8]/25 = 72%. So in a round of combat, the attacker does 72% of the damage it’s possible for him to inflict, and a critical hit.
• Attack of 10 vs an AC of 15: Attacker rolls a 6, then a 6, then a 4, for a total of 5+5+4=14: [10+14]/25 = 96%. So in a round of combat, the attacker does 96% of the damage it’s possible for him to inflict, and a critical hit.
• Attack of 10 vs an AC of 15: Attacker rolls a 6, then a 6, then a 6, then a 2, for a total of 5+5+5+2=17: [10+17]/25 = 108%. So in a round of combat, the attacker does 96% of the damage it’s possible for him to inflict, and a critical hit.
• Attack of 10 vs an AC of 15, Attacker rolls a 1, then a 4, for a total of 4-5=-1: [10-1]/25 = 36% – and a fumble.
• Attack of 10 vs an AC of 15, Attacker rolls a 1, then a 1, then a 6, for a total of 6-5-5=-4: [10-4]/25 = 24%, and a fumble.
• Attack of 10 vs an AC of 15, Attacker rolls a 1, then a 1, then a 1, then a 2, for a total of 2-5-5-5=-13: [10-13]/25 = -12%. If I were writing this game system, I would have this damage be inflicted on someone on the attacker’s side – PLUS a fumble.

If that makes fumbles and criticals too frequent for you, you could employ a d20 check as usual to confirm. But, since it minimizes the significance, you could probably achieve the same result by requiring a second exploding result before a formal critical or fumble was declared: so a 6 then a 6 gives you a critical but a 6 then a 5 just gives you a better hit; a 1 then a 1 gives you a fumble, but a 1 and then anything but a 1 simply gives you a worse hit. That makes the chances 2.78%, a little over half what they are in the d20/pathfinder system.

The effects of gaining attack levels aren’t so much in overwhelming damage, it’s in the reliability of that damage. Being able to do 35 points or whatever every – single – turn – is usually more valuable and a more reliable indicator of expertise than someone who might do 60 points if they get lucky, but might only do 10.

But the major reason I like this as a variant combat system for d20/Pathfinder is the impact on the mage/fighter game balance. Let the ever-flashy mages roll all their dice in an attack – they might get lucky, they might not. But against a fighter with lots more hit points who is repeatedly hacking away 20 or 30 HP every round, sometimes more, the fighter will win at least as often as he loses. Think about that.

Refinements are possible. Do you add any STR bonus (or DEX bonus for bows) to the damage before or after you apply the percentage shown? I can see things working either way. The latter does mean that you can literally achieve ineffectual blows with low strength.

It’s always fun to play with randomness!

As I said, not directly relevant to any of the discussions of the main article – but too interesting not to throw out there, anyway.