Apologies, this is going to be shorter than I wanted.
Role-playing game systems typically use one or more geometric solid random number generators as part of their bedrock mechanics. These are usually Platonic solids, but there are others. As an aside, I’ve always wanted to have a gaming system built on the use of a truncated icosahedron (a non-uniform distribution 32-sided die).
It looks like this:
Anywho, sorry. Where was I? Oh, yes, bedrock mechanics and geometric solid random number generators.
The two most common base mechanics for gaming systems are straight-distribution systems (d20 or d100), wherein any die result has an equal probability to any other die result… and bell-curve distribution systems (typically 3d6), wherein the distribution of the results is skewed to render the outlier events disproportionately unlikely.
Both gaming systems have their advantages and drawbacks. It isn’t uncommon for some section of the remainder of the rules to either compensate or exacerbate this skew. For example, in early Advanced Dungeons and Dragons, you used a d20 to save, but you rolled for magic items on tables wherein certain items had only a 1% chance of coming up, while others would be anywhere from 2 to 50 times as likely.
However, the basic game mechanic is a fairly major part of the gameplay. In straight distribution games, a 60% chance to hit means you’ll hit 3 times in 5, generally. A penalty or an advantage to a die roll was uniform, though. A +5% is a +5%, when you’re using d100. A +1 to hit, on a d20, always gives you an additional 5% chance to succeed. In game systems like GURPS, though (which uses a 3d6 for virtually all skill checks and combat rolls), a +1 to hit means something very different to someone who has a base skill of 6 vs. a 10 vs. someone who has a base skill of 15.
Changing a 6 into a 7 changes your percentage of success from 9.3 to 16.2% Changing a 10 into an 11 changes your percentage of success from 50% to 62.5%. Changing a 15 into a 16 is a measly increase of 2.7% (thanks to this blog post for saving me the extra step of busting out a calculator. Have I mentioned I love the Internet?)
This may present one with a moment of philosophical quandary (in the gaming sense, not grand questions of the universe, here). Which more accurately reflects reality? Is a little bit of help (or a minor hindrance) more useful to people near the average, than it is to someone who is either quite good or horribly bad at something? Is the game system balanced, overall?
Do you have a preference, or is your game engine just something under the hood that lets you get around to chopping orcs into bits?
Completely unrelated… When you have to go grab your dice and make the roll, and it’s a really important roll, do you have special dice?
Percentages are more intuitively comprehensible to me than the bell curve. When I’ve sat down to try to work things out beforehand as a GM, I try and surf the bell curves in prep. If you’ve ever tried to come up with your own pen-and-paper system, this is a powerful way to maintain balance and challenge. But in the head of the moment, I’ve preferred straight percentages with modifiers because it’s easier for me to calculate what I want to see happening.
One of these days I’m going to roll out that 32-sided die system. That’ll mess with you.
Hey Pat, how are ye! What’s game theory–counting cards in casinos like those characters in that movie. 21? Yes, the MIT lads did turn Vegas on its collective head—I think they were all banned and for that matter, beaten up as well. I’d love to learn their system and if you know any teachers out there, please let me know.
Thanks. MH
Counting cards isn’t hard, you just need to practice.
Well thanks for the reply, Pat–much appreciated. Can casinos really physically rough you up if they sense any shenanigans are going on? I mean legally resort to such intimidating tactics–hey, if they’re not smart enough to thwart the Blackjack gang from MIT, that’s their problem.
Hey, how about I invest in one Patrick Cahalan spending a day in a nearby casino–I’ll give you 2/3rds I keep the rest. Sound fair?
It is not cricket to count cards in a Las Vegas casino. Typically they can tell (or will rapidly figure out) when you’re doing it, and if you’re just winning a few hundred bucks here and there they really don’t care. A few “whoos!” or “ahhs!” at a table loosen up the wallets of the suckers, after all.
But if you’re really good (I’m not, just passing) and you bet big and win lots, they will pass your photo around and they won’t let you play in the casino. They aren’t, in fact, required to let you play. This is what happened to the MIT kids. The mob doesn’t run Vegas (that way) any more.
I know a of guy who is banned from gambling at every major casino in the world; he started his company using seed money he got by counting cards at blackjack and going from casino to casino until his photo got around town. I don’t think he ever got beat up even outside the U.S. (I know he was banned in Monte Carlo).
You might get your legs broken counting cards in an illegal card club, but you don’t really need to go to those anymore if you want to gamble.
Nothing short of a super nova of our sun would convince me that AGW is real. Even then, I’d have to see the data. Probably be living on Jupiter as well.
It’s very well understood that this man-made global warming nonsense is a total complete hoax and fraud. You will find very few atmospheric scientists signing on to such transparent rubbish—the “scientists” are usually Bertrand Russell type cranks and nuts with social agendas and $$$ up their sleeves.
Remember the Mt. Kilimanjaro hoax? Just a total complete lie. Temperature sensors that were placed around this mountain recorded below freezing year round–this was for several years. Get it, gentlemen, ice can melt without warm air—drum roll please, it can also melt through EVAPORATION!! Which is precisely why glaciers are shrinking and retreating from the mountain. There has also been a substantial lack of precipation–a lack great enough that not enough precipation exists to replace the evaporating ice. And you all know from high school earth science, that sublimation turns ice into immediate water vapor.
This case is closed. Finished. If you want to be Jim Jones kool aid drinking cultists, be my guest. Hard science and scientists have and will have beaten you every step of the way. We really to stop dicking around with this subject–the flat earth warmers most decidely do not have the facts and science on their side.
Next on the Intergovernmental Panel on Climate Change is whether little, red-headed Irish men in green suits living undeground hide their pots of gold at the end of rainbows. Finally, a bit of sense on this subject!
dammit—that’s precipitation
If it’s a storytelling game, I want a bell-curve system (fudge dice!). If you’re good at telling a story and/or setting up a situation, you can get a bonus before-the-fact… and that can turn needing a +4 into needing a +2 (much more doable).
If it’s a game where max/min can come into play? I want straight percentage. Odds are, I have the bonuses to overcome the straight probability.
Bell-curve systems don’t scale well outside the bounds of the bell. GURPS worked great with “human norm” as the center of the focus, but when you tried to make this into a supers campaign, it started to get creaky.
Percentages are better if you’ve got a very long range of performance (or, of course, one can just use a wider bell curve, like using a 6d6 as the basis instead of three of the suckers).
And a truncated icosahedron looks like it’d give the best of both worlds. Give all of the numbers in the middle to the hexagrams, the numbers at the edges to the pentas.
See, you grok the possibilities immediately.
Now, imagine that the base roll for everything is two of those suckers, with the 12 smaller sides being modifiers for the other die.
I’m not sure why I want to do this, except for the whole “GM’s are masochists” thing.
I’ll note that you both dodged the lucky die question.
See, now I have to admit that I haven’t actually played for years. I have had some interest from some noobs, but am frankly intimidated by the complexity of the rules systems that once I had mastered.
But back in the day, no, I didn’t have any particular lucky dice. If players wanted to use lucky dice, I had no problem with that.
Maribou is not allowed to touch my dice.
Hm; maybe this question is too close to religion.
A supreme irony, since I saw them FIRST in the gaming store.
Embedded patriarchy. It’s pernicious.
my GM had unlucky dice. Found them blowing about on a mountain in Maine in the middle of a hurricane. After that, got stuck on an ice slick on top of the mountain (spinning around for quite a few whirls) before he finally navigated to the edge of the ice slick to safety.
… when you hear some of my “I have a friend who says/does” … it’s worth it to think of this story.
Holy cow, I love the Internet!!
I mean, seriously. The Internet is da bomb.
Hi, that was my blog post you referenced in the main post. I believe I may have created one of the tables using a spreadsheet but I’m sure I stole at least one from another web page. I also love the internet but now wonder what to do with my large personal reference library that I never use anymore…but I digress.
Very interesting article! I love learning the theory and terminology even if I don’t use it. I wanted to point out that the small improvement from 15 to 16 can be important if it is a skill that you use often and count on. That very small improvement from 95.4% to 98.1 percent means that instead of failing about once every 22 times you fail only about once every 53 times. If failure means bad things happen then it could be well worth it to pay for the difference.
All of this is interesting to think about but I never use it in actual gaming. In fact I haven’t looked at that table since I made it when we started our new game (and this blog) two years ago. I go by my gut feeling based on making many rolls at different levels.
As for the lucky dice. I don’t have that particular superstition. I don’t even use dice anymore. I use a very nice Hero System customized die rolling program. In fact, between that program, manuals in PDF and the blog which I use for game notes, I don’t use pen, paper, rulebooks or dice for my RPG anymore.
Hey, welcome to Diversions. Come and hang out, we like gamers in these parts.
The big difference in the bell distribution methods is in moderately difficult tasks (things with a -2 to -4 penalty) This is a pretty common difficulty level in GURPS, at least.
Here, of course, you can see a big difference between the more-than-competent dude with Skill-14 and the master with Skill-18.
The competent dude is down to a coin toss. The Master still has a very good chance of success.
I think some things are closer to the percentile/flat rate and some are closer to the bell curve–both in real life and in a well-designed game. It doesn’t matter if you miss an attack roll, because you’ll always get a chance next turn. But it’s silly that the expert athlete fails to jump over a five foot gap because he rolled a 1 on his check.
I’ve been thinking about a system where depending on the skill check, you either roll 1d20, 2d10, 3d6, or just add a flat 10 depending on the level of randomness inherent in the task being performed.
I play more percentile games, but not because I like that mechanic, I just like the over all games the best. It always bothers me that no matter how good I am, I always have a 5% chance to miss. Still, I have not found a system that uses a bell curve that I like better.
The other system that should be mentioned is a multi-tiered bell curve. This is mostly used in wargames, but I thought it should be mentioned. This is were one action has multiple roles of multiple dice. Warhammer 40k and a good example of this. To shoot and kill a model, the follwoing rolling steps occur:
1- roll to hit
2- roll to wound onwhat was hit
3- roll any armor saves on what was wounded
This staggered series of bell curves help flatten out the variation even more as each step help bring the rolls back into the norm range.
As for lucky dice. I have none, just unlucky dice and those are any die I roll. 🙂
Are you familiar with the dice use for Vampire 2nd edition?
A task is given a particular difficulty. Something like “driving home after work” might be given a ‘2’ while “performing CPR” might be given an ‘8’ and you get to roll a number of dice equal to your skill level.
So if you’ve got a 4 in driving, you’d roll 4 dice. A single success means that you succeeded… but more successes means that you succeeded from marginally to magnificently.
Like if the task was to “repair the car just enough to get it so you can drive home” and you get one success, it dies as you pull into the driveway. Three successes might allow you to try to repair it some more tomorrow. Five successes means that you figured out what was wrong and fixed it for good. Heck, changed the oil while you were in there.
A failure is a failure, of course… and a “botch” is something else entirely.
The Storyteller system was awesome in some ways, but the muti-d10 success/botch system was a nightmare if you or your players were the types who worried really hard about odds of success and knowing exactly how different a roll against difficulty 8 requiring 3 successes would be as opposed to difficulty 7 requiring 4 successes if you have a dice pool of 6. Not to mention that botches against high difficulty are statistically more likely if you had a 3 dice pool than a 2 dice pool.
Now, it’s entirely clear that Storyteller was designed to be about plot and character and making it hard for players to comprehend what their odds of success/failure are before a roll was an intentional feature and that was always attractive to me in my short stints as a DM.
Dice rolls are explicitly only for tasks done under duress or hurried, otherwise your attribute+talent/skill/knowledge rating was to tell whether or not you would succeed eventually, i.e. if you had strength four, we know you’ll break that door down. You only rolled if you needed to do it a certain number of tries or if someone was trying to stop you).
The nWoD has a rule that you only botch if your dice pool is 1.
Which makes sense… but there’s another house rule that I’m mulling over:
In D&D, there is a new “critical hit” rule that we’re using. Roll a Natural 20, you immediately roll again. If you roll a “hit”, that means you got a critical and get max damage. If you roll a miss, you merely hit and have to roll damage like a guy who only rolled a 19 would.
A botch would work similarly, I think. Oooh. You may have botched! Roll again and see!
This is how GURPS handled certain types of critical failures.
For example, old-timey blunderbusses might blow up if you bricked your roll and hit an 18. But a modern pistol required a verify; they’d only critically fail on a double-pump blown roll (two 18s in a row).
I did the same thing with skill levels above 20; you’d only critically fail on a verified.
… we destroyed a GM using this system. I had one good skill: “Empathy.” I used it on everyone — got some really interesting information about the ghost who was following our guide around. The GM was howling in frustration (not literally, but it was a werewolf game).
This was the GM who finally said, “The tank is immune to nuclear weapons but not fire? We’re switching systems” without consulting the rest of us.
This is where automatons come in handy. Golems and the like.
I’m not familiar with this use in RPGs, but it’s a mechanic that I’ve been exposed to before.
This is not a bad system, actually.
I’m also bothered by the small percentage of failing things that in real life just shouldn’t ever fail. That’s where the value of a good experienced GM comes in. In these kinds of situations, ours will just say that those that have the needed skill above the free “everyman” level succeed.
Generally, I don’t require rolls for things that don’t affect the narrative if you have skill in whatever it is.
If you’re making a jump, I already know if you can make it or not in many cases. Nobody needs to roll to jump over an shin-high brick wall while running across a lawn. It’s only if you’re making a jump at or near the limit of what you character can do… or you’re being pursued by/pursuing the bad guy, and it has interesting narrative consequences if you get caught vs. get away and I want to see what Random Chance dictates I need to spin as the storyline.
I don’t know about you but I see people fail things “that in real life just shouldn’t ever fail” every day.
But then, we get into the G/N/S discussion about whether it’s appropriate to have that chance in what’s meant to be escapist entertainment. When Grignr leaps up from the greasy, ale-soaked tavern table to employ his mighty thews in the service of unhanding some surly miscareant’s leering graps of a serving-wench’s shapely thigh, do I really want to have to roll to see if he gets his foot caught in the barstool?
> I don’t know about you but I see
> people fail things “that in real life
> just shouldn’t ever fail” every day.
Right on, this. But random chance can really derail a story if given too much play.
On the flip side, if someone’s getting full of themselves (or if their character is a jackass), there’s nothing wrong with throwing in the occasional egg-on-your-face moment. For narrative.
This is a good point.
While I would say that “driving home after work every day” is a 2… I would also say that I drive past at least two accidents a week.
… you can say stepping off a curb is something you can never fail.
Or, you can let it fail, and make it fun.
I step off of a curb and stumble into Aahz. Aahz is not happy. Time to deal with Aahz folks.
See? I haven’t just made your character the “guy who couldn’t walk into the street.” Just the guy who accidentally did something slightly dumb.
How do the odds on a truncated icosahedron die work out? Is the chance of landing on a particular face proportional to the surface area of that face, or is it more complicated than that?
We’d need 20,000 rolls to make sure… but the research I’ve done on the web (via googling “truncated icosahedron probability”) tells me that it’s not appropriate for a die.
Which is too danged bad.
The Internet breaks down fair dice and unfair dice. Obviously the nuclear bomb sphere is an unfair die, in the sense that the sides are not equally probable.
That doesn’t jump immediately to “not appropriate”, IMO. It just means that your representation needs to reflect the outcome you’re looking for.
If these weren’t $50 a pop, I’d buy two and run a couple thousand trials to see what the distribution is. Mebbe I can find some cheaper ones.
$50 a pop
This is *MUCH* closer to what I mean by “not appropriate” than something as silly as the concept of “fairness”.
We’re telling a story, here!
Full Point.