Nothing Adds Up & The Dice Are Loaded - part 2 of ?

Shawn Delahunty's picture

All right folks, this time I'm back to cover the second topic for this pair (group? series?) of articles. (As an aside: I have NO idea exactly how or why my stuff turns into multi-part explorations--it just does, all on it's own. Which is weird, considering I'm the guy supposedly running the keyboard when I write. So I have to ask your indulgence here.) Anyway, just to refresh your memory or in case you missed Part #1, here are the two game related topics I brought up for everyone to mull over.

  • Zero-sum games, or zero-sum outcomes
  • The danger and difficulty of "Truly Random"

Last time I wrote a good bit about the notion of Zero-Sum outcomes, and why I'm not a fan of them in gaming, business, economic planning, or Life in general. Hopefully I entertained some of you in the process, while also exploring the provable mathematical concept that, "The Universe is NOT a Zero-Sum Event!" Now it's time to put on our big, pointy "Math Hats" and explore...

The Razor-Sharp Edge of RANDOM! (*Dun, dun, daaahhhhh!*)

Ok, so there is somewhere in the neighborhood of 2.6307 squajillion articles, scientific papers, and books written on the Mathematical topic of "What is Truly Random?" Nobel Prize winners and professorial egg-heads have debated it amongst themselves for centuries; likely while they lounged about on piles of prize-money, published papers, and old, long-forgotten, grad-student applications.

What could an 'Average Joe' programmer and gamer like me possibly bring to this heady and deep discussion? Why on Earth would I think I have something to add?

The honest answer is, "I'm not sure, but that's never stopped me."

Sometimes, just sometimes, I am able to wield a mighty and fearsome superpower--defiant stubborness. I try to imagine it as the ability to forge ahead bravely, in the face of overwhelming odds. Mostly though it manifests kind of... um, sideways, and shows up as "abject stupidity" or something equally dumb. (No really, it's just like I described in my dodgeball story last time--I can be dumber than a brick. I'm a lot like Wile E. Coyote in that way. It's a delicate and delicious ironic balance: just enough BRILLIANCE to devise the most intricate of not-quite-achievable plans, just enough STUPID to think I should keep trying... even after the 3rd and 4th Earth-shattering *KABOOM*.)

So here I go, forging ahead... you might want to move a little to your left, or brace yourself for the *SPLAT!*

As before, that we may start from the same reference point, here's my loose-but-mostly-working definition of "Random":

Random: (noun)
The state or condition of having no deterministic or predictable outcome. There may be stastical or probablistic 'groupings' in a very large set or group of outcomes (like rolling a '7' on two dice in Vegas about twice as often as rolling '4') but no single outcome is predictable.

I thought I'd stick with the dice-rolling analogy, since everyone knows it, and it's simple enough for people to grasp. Plus, we're all gamers here, right? I'll get to the complex examples a bit further on.

If you've read at all about the subject of Randomness, particularly as it applies to games, game-playing, and player satisfaction, you'll have hit the hot-button topic of Random Distribution vs. "Perceived" Random Distribution. Don't roll your eyes. Once you take all the "math-y bits" out, the concept is simply grasped in the following terms:

  1. Truly Random == Anything can happen at any time, or more accurately, has an equal _chance_ of happening at any time.
  2. Humans == Bad at coping with Truly Random, just terrible.
  3. Humans like to think they are great at coping with (and even predicting) Truly Random.

That 3rd one is a doozy; it's the whole and sole reason that Las Vegas and Atlantic City consist of anything more than a gas-station, a cheezy motel, and a Kwicky Mart. There IS no other reason to visit either place. (Except maybe for the Cirque Du Soleil shows, those are awesome. But then again, those are ultimately paid for by #3, so it's kind of a toss-up.)

What do we care? How is this relevant?

Well plainly, #3 in that list is talking about the weird human urge to gamble. We all have it, even those of us (like me) who refuse to "gamble" in the classic sense. For instance, I despise casinos. Yet I still am a self-professed heavy gambler--have been since my adolescence.

Gambling. That's all RPG's are, at the most basic level, with some dragons and wizards and damsels in bikini-chain-mail thrown in. Sure, when you play D&D, there's a good time had spent sitting around a big kitchen table with friends, eating junk food and talking and rolling dice and quoting Monty Python in bad British accents. But really, at the bottom of it all, it's actually all about and driven by gambling. It's that crazy urge to double-dog-dare the odds--and either win the dragon's hoarde, or end up as crispy "Adventurer Fritters" served up on a plate-mail half-shell.

YOU: "Um, Oooooh kaaayyy... How about an example?"
ME: "No problem, let me just strap on my rocket-powered roller-skates here...."

As mentioned above, the most common analogy or demonstration given in talks on "True Random" is dice-rolling. Since we're focused on gaming of all sorts here, and since I haven't had an excuse to play with my ancient D&D dice collection for ages, let's consider the "To Hit" die: My scratched up 20-sided die.

Theoretically speaking, assuming 'perfectly made' 20-sided dice, any of the numbers could come up on any given roll. The "Math-y Bits" of it mean that in the long term, all the numbers will ultimately come up the same number of times--that's the "distribution" of the thing. Here are a couple of graphs to illustrate:

The number distrubution after 8.23 Bazillion rolls of the 20-sided dice:
20-sider Even Distribution20-sider Even Distribution
For comparison, here's a typical distribution graph after a "typical" night of D&D playing:
20-sider 'Typical' Distribution: The 20-sided rolls on a "Typical" D&D night20-sider 'Typical' Distribution:
And here is the distribution on a "bad night", when 5 measly kobolds kicked our ass repeatedly, and orcs gnawed the remains:
 When 5 measly kobolds kick your ass & orcs gnaw the remains20-sider "BAD Night" Distribution:

Again, the first graph shows the "optimal" or "eventual" number distribution. The latter two graphs show what happens on a purely human time-scale.

And that, dear readers, is "the rub" as Shakespeare put it--those pesky human time-scales. Especially the "human" part. Randomness is an ideal, a pure mathematic concept, as cold and logical as our beloved friend Spock wants to be. The crazy-train starts to belch smoke and steam and chug slowly out of the station when you add us humans into the mix--we think we want "random rolls", to "add variety" or "add unpredictability to the outcome".

This thinking can be excused up to a point--we truly don't want to roll '20' all the time, scoring perfect critical-hit/insta-death blows on our enemies, as that would be BORING. We also don't want our troll/goblin/orcish enemies to roll '1' every time--breaking their sword, their arm, and accidentally decapitating themselves all in one go. That too would be BORING; funny as hell the first time it happened, but still...

But here's where the clanking, huffing, ominously rattling crazy-train really starts picking up speed, and it all has to do with that pesky word I mentioned earlier: "Distribution". In the long term (like in geologic epoch terms) a genuine Random Distribution will end up with "all numbers equally encountered" like in Graph #1. But in the 'short term', there just isn't any way to know WHAT the heck will happen, at least not if your "random number generator" doo-hickey/machine/dice is truly RANDOM.

Now we get to the scary, horrifying, flying-off-the-bridge roar of the crazy-train as it rockets towards us spewing smoke, sparks, and fire: The "Run".

It may appear that there are "patterns", or "runs" in the sets and sequences of numbers which pop up. (And a "run" is a dangerous and addictive thing, especially at the craps tables in Vegas.) But the truth is, it's all a matter of time-scale and perceptions. The emotional 'weight' of the potential outcomes affects our internal sense of 'statistical weight'. This can manifest in 3 ways:

  • Rolling a '1' more than once in a long and dangerous battle encounter, handily shattering your magical sword "Deathtongue" AND your backup axe, feels horrible--completely unfair.
  • Rolling somewhere between '5' and '13' in every single round, missing with every single swing, while getting continually pounded on, feels horrible--again, completely unfair.
  • Rolling '19' and '20' continually, while helpful, gets boring after the first 10 rounds. (And makes everyone else sitting around the table grumpy--eventually they'll start making accusations of 'loaded dice' or 'defective dice' or 'improper "no-roll/dropping" instead of making an actual "roll" of the die'. I've seen it happen personally when someone gets on "a run" like that with high to-hit rolls--folks get excited, then jealous, then grumpy.

Any of these scenarios are possible with "Truly Random". If you've played table-top RPG's long enough, you'll have had experiences very much like those. It makes for a dreary evening sometimes, when, "the dice aren't being kind." So it would seem that what we're looking for, isn't REALLY a "true random", more of a "fair" or "interesting" quasi-random distribution, with the occasional/exceptional "True Random" event thrown in for spice.

In CRPG's, the issue gets even trickier. In the "olden days", to save precious RAM, the programmer's naturally turned to various random-number generation methods, and came up with algorithms to use those inputs. Random mazes, random encounters, random capabilities of monsters, were the initial results. As the good Dr. Matt Barton pointed out in Dungeons and Desktops, this programming and game-design methodology came to define a whole CLASS of games--Rogue-likes.

(To this day, I get the giggles when someone mis-types this as Rouge-likes. I get the immediate mental image of cross-dressing dwarves in lipstick, facepaint, and dresses, flouncing through a dungeon, spontaneously breaking into song and dance numbers during battle encounters. Yeah, I know, I'm weird.)

The ultimate extension of this "Randomly Generated World" came to fruition with the CRPG, Daggerfall. The thing BUILT AN ENTIRE FRICKIN' CONTINENT, including towns, NPCs, dungeons, the works--all randomly. EACH GAME. This game was described in goodly detail in Dr. Barton's book; I suggest reading more about it there. There are more modern examples of this though, where the random number is used to great effect in the 'creation' of the game world in which the player adventures:

  • Diablo 1 & 2. (Have not played Diablo 3, so I shouldn't comment on it.)
  • Depths of Peril (Indie CRPG game from Soldak Entertainment.)
  • Spelunky
  • Minecraft
  • Dwarf Fortress

To be fair, Minecraft and Dwarf Fortress are not "pure" in the random sense. They use random numbers to generate some initial conditions, but then use algorithms which are not random, to 'dress up' or shape the world; erosion, plant growth, river boundary movement, seasonal variation to alter the plant growth across 'ages', etc. In an interview, Derek Yu talked at length about the 'tweaks' which had to be made to Spelunky to make the purely random levels more coherent. Even Diablo certainly uses some path-finding and verification code to ensure that the random levels don't have "dead zones" or "unreachable places".

But not everyone likes these sorts of games.

There is certainly a great deal of dislike for "randomized worlds", even what I personally consider to be well-made worlds. I honestly don't know whether this is purely a matter of taste, whether it's the 'intransience' of these types of worlds which bothers people, or if there is something subtler and deeper. I've read many descriptions that state random worlds don't "feel right" to players.

In cases where the 'huge, randomly generated continents' make for pretty and realistic maps, but are entirely devoid of real NPC interactions, or have 'disconnected' adventuring areas which do not affect the main storyline, the fatal resemblence to "auto-generated grinding" IS obvious. Even to me, it feels like a cop-out by the game designer, as a shoddy way to put a catchy marketing blurb on the box, "We provide XYZ hours of re-play value!"

In other cases however, there simply seems to be a distinct separation of the player personality types which drives folks to either like the game with randomly generated content, or to really dislike it. Again, this may stem from very a deep-seated psychological place, a need for a "sense of higher order". And this may explain why such games don't "feel right" to players--they can sense the randomness. it doesn't have "an organic feel". It feels "dead" and "not alive" to them. While they can't put their finger on precisely what triggers their reaction, it is so strongly felt that it unnerves them.

This is where we could dive into the mathematical topics of FRACTALS and CHAOS, and how those are "better" than RANDOM, but I'm going to dodge that for the moment. (It quickly gets to the point where you must start introducing mathematics and specific algorithms. Maybe I'll tackle that in a future article about... well, something I'm working on.)

Taking a step back-

The discussion so far raises a good question for folks to ponder:

How much random is "Too much" in a game, particularly in a CRPG or MMO?

A whole pile of follow-on questions tumbles out and makes a big mess on the floor when trying to answer THAT precariously loaded thing. Rather than continue any further for now, let me toss up some of those questions, and let you folks ponder and debate them. If you think of other questions or related topics, PLEASE CHIME IN. I know that this is an enormous topic, but I'm curious about what people think. I'm especially interested in your previous game-play experiences; moments where you "felt the random" or "hated the random" or "loved the random"--any moment when the randomness evoked a strong emotion in you.

  1. Does the love/hate emotional factor vary depending upon how randomness affects the gameplay?
    • _Weapon swing hit/damage?
    • _Whether or not an NPC who is on the fence about the protagonist, will be helpful or clam up?
    • _Generation of NPC's?
    • _Creating quests
    • _Generation of towns?
    • _Generation of dungeons?
  2. Does randomness break your sense of immersion in a game?
  3. Do you enjoy "games of chance" outside of computer gaming?
  4. Which ones?
  5. Are there "games of chance" in which the computer version felt inferior? (Craps, poker, etc.)
  6. What did/do you like best about non-computer games that depend heavily on randomness?
  7. What CRPG games did you love, only to have them "ruined" by something obviously clunky thrown in by the RNG?
  8. If you played tabletop RPG's, were there times when the GameMaster "overrode the dice"? Did it make things better or worse?
  9. How much do you owe to your bookie? (*grin*)

OK, that's way more than enough for this time. As always, I am grateful for your attention dear readers. Please let me know what you think, and feel free to elaborate as much as you like.

"Rollin' rollin' rollin', keep them dice a' rollin'..."


Rowdy Rob
Rowdy Rob's picture
Joined: 09/04/2006
Intriguing article. My long-winded answers below...

The usual great, thought-provoking article, Shawn. I'll get right to the questionnaire this time.


Does the love/hate emotional factor vary depending upon how randomness affects the gameplay?

This is a difficult question to answer, since I came from a pen-paper-dice background into CRPGs, so the randomness of simulated dice rolls were taken for granted as part of the experience. Some smaller games, such as Rogue/Nethack or "Sword of Fargoal" seem to benefit from random dungeons, monsters, traps, and loot placement. These short-length games are designed from the ground up for replayability, so I think they benefit from randomness.

In Diablo 1 and 2, I didn't feel like I was playing a random world. Whatever random generators are powering the game, they worked very well. The seams do not show. However, I've recently been playing "Nox" from, which is a Diablo knock-off (a very good one!), and it does NOT have randomly generated levels. Personally, I don't feel the difference in these games, although the human-designed levels of Nox does not bode well for re-playability.

I haven't played "Daggerfall," so I can't comment on how well the randomly-generated worlds work in a first-person "immersive" CRPG, but I imagine the viewpoint of the player makes a big difference in how easily it is to perceive, and be distracted by, the randomness.

In combat, the old school games seemed to make combat a clearly hit/miss affair. In games like Wizardry, Bard's Tale, and so forth, your combat options were basically choices on a menu: attack, defend, run, and the results were clearly random. It was okay back then, but seems very primitive (and non-immersive) now. The modern games do a fairly good job of masking the randomness, making you feel like you're more involved than you actually are in the outcome.

I do suspect that randomly-generated NPC's are where "randomness" will fall flat, although I can't think of any examples off-hand. Even in randomly-generated worlds like "Diablo," the NPC's aren't randomly generated. I think the "human" factor can't easily be replicated by random generation, hence the hedging in the NPCs.


Does randomness break your sense of immersion in a game?

I think it depends on the game, and how well the randomness is implemented, particularly human characters. My answer to the previous question covers this.

A good example of where randomness ADDS to the experience is in the old 8-bit EA game "Seven Cities of Gold," which randomizes the "New World" for you to explore. Since it doesn't replicate the Americas in geographic accuracy, it actually increases the illusion that you are exploring the New World, replicating the feelings (to some degree) the original explorers felt.


Do you enjoy "games of chance" outside of computer gaming?

Not really, although I'd be open to a social game of cards. I think a lot of the appeal of "games of chance" is that you at least have some control over the outcome. In most CRPG's, you can utilize a battle strategy of some sort. In cards, you can pick or discard the appropriate cards.

Real gambling, as in "you're going to lose money," is just stupid in my opinion. In casinos, the odds are all stacked in favor of the "house," so yes, you might win, but the most likely outcome is that you're going to lose real money. Although the "dice" are random, the odds are heavily stacked against you, so I don't know if that's really a "random" result if the most likely outcome is that you're broke! It's no longer a game; it's a bad investment.

However, I've been known to play PC-based video poker sims, and I have "Hoyle's Casino" on my computer in case I need to remind myself how ridiculous gambling is. And, I'm embarrassed to admit that I've played "Faerie Solitaire" for countless hours. I can't tell you why these are fun, because it doesn't make much sense to enjoy something so heavily based on chance!


Are there "games of chance" in which the computer version felt inferior? (Craps, poker, etc.)

I think even the best Dungeons & Dragons-based CRPG's are inferior to the real experience overall, if you classify D&D as a game of chance (which you do in your article). Real D&D is more of a social experience. It's the nerd equivalent of partying. CRPG's can't replicate that, nor can they replicate the interactions between players and DM's who are "role playing." Conversations in CRPG's are canned, but not so in real D&D.

Videogame-based chance/gambling games are superior to the real-life experiences in the same way that violent shoot-outs in GTA is superior to being involved in a real-life shootout! In gambling games, you often see how silly they actually are when there's no real money to lose. Roulette? Seriously? How is that fun?


What did/do you like best about non-computer games that depend heavily on randomness?

I guess the sense of the unexpected, the sense of surprise, and the sense of keeping yourself on your toes. And, the feeling of being "lucky" was a prevailing factor.

I think all successful "chance" games rely on the sense of "calculated risk." Yes, gambling real money on a ball rolling around a wheel is stupid (in my opinion), but in games like poker, blackjack, and others, you have some control over the hand you're dealt, and can weigh your risk accordingly. CRPG's do this too, in the sense that you know not to take on that 20th-level dragon with your 1st-level wizard. Theoretically, I guess you have a slim chance of winning, but it's highly unlikely. I think that's the key to the fun of these "random" games -- the sense of balancing risk and reward.


What CRPG games did you love, only to have them "ruined" by something obviously clunky thrown in by the RNG?

I can't name any examples, but I recall seeing games that generated walls blocking the only exit or goal, meaning you cannot complete the level/game. Game over, and it's not your fault.


If you played tabletop RPG's, were there times when the GameMaster "overrode the dice"? Did it make things better or worse?

Since I was a "Gamemaster" back in the day (or "DM"), I can say I frequently overrode the dice (unbeknownst to my players). I had the best campaign going in my area, if I say so myself (my players did!), so I guess it made things better. My reasoning was usually that I didn't want to kill off one of my players or NPC's (yet), because D&D was so heavily a social game. My players derived great pleasure from "role playing" their characters and had become quite attached to them. And plus, we were kids (of course), so I didn't want to deal with the usual teenage pouting upon their characters' deaths. When I did kill off a character, there was usually an "out" such as a resurrection spell, ring of regeneration, or whatnot to bring the character back to life. The point was to keep the fun going, minimizing the drama.

CRPG's have similar "outs," particularly in the "save game" feature. I suspect that if "permadeath" was a predominant feature in all CRPG's, they'd be a lot less popular!


How much do you owe to your bookie? (*grin*)

Over 800 thousand dollars. :-(


Shawn Delahunty
Shawn Delahunty's picture
Joined: 08/01/2011
Cheers Rob

I greatly appreciate the feedback--thoughtful and detailed as ever sir.



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