Comparing dice mechanics and how they affect flavor and style of gameplay

[garrowolf]

I always hated the Shadowrun dice mechanic. You roll a bucket full of dice and you have no idea if you are likely to succeed or not. It took too long to even sort out the roll and gaining or loosing a die made very little overall difference. Plus you couldn't say that something was just not possible for you because you could explode 6's.

I prefer d20 the most. It has easy to figure out chances and you can compare DCs to skill ratings and make predictions on the likelihood of making that roll. Plus you only have to care 1 dice around as opposed to a bucketfull.

 

[MacMathan]

I remember enjoying calculating out some of the odds in Shadowrun or Cyber-Yahtzee as we used to call it

It also had the statiscal anomaly of a target number 7 being as same as a 6 due to exploding dice so there would be flat spots in modifiers etc.

 

[FoxWander]

How dice mechanics of different games compare has always been an interest of mine. Fortunately I just finished (yesterday as a matter of fact) a statistics and probability class so I can finally understand it a lot better. So it's neat that I should find this thread just at the time I can most appreciate it- when all that stuff is fresh in my head.

One dice mechanic you left out is the dice pool with it's many variations- Shadowrun, WoD, WEG Star Wars/d6 system. Usually attributes and skills represent the number of dice you would roll. Some have you add the total (WEG d6) vs. a static DC. Others count each die above X number as a "success" and you count total successes vs. a target number. Usually there's some kind of exploding die system- in d6 one die in your pool is a different color, 6's on it explode, a 1 is a complication or failure of some sort. Storyteller had exploding 10s with any 1s cancelling out an equal number of successes and more 1s than successes was a "botch" (critical failure).

I remember many fun WEG Star Wars games and thinking that the game mechanics really flowed with the action IF you could add up the dice quick enough . But part of that is the ease of picturing the Star Wars setting which made it really easy to "get into" the action.

I'm not sure how the mechanics of dice pools breakdown mathematically though.

 

[Starfox]

I think that may be Feng Shui's system. Someone who's played the system care to comment?

Feng Shui uses 2 exploding dice; one positive and one negative. ("Exploding" means you roll again and add the result as long as you keep rolling sixes. The two dice explode individually.) The average result is thus zero, with a bell-curve distribution. Skill values and difficulties are thus in the same range; you have 7/12 chance to pass a skill roll at the same difficulty as your skill, with bell-curve diminishing returns as the differential between skill and DC grows. Quite extreme rolls are possible. I like this system a lot. I also find it is a lot easier to add and subtract dots than numbers; it is much easier to roll 1d6 - 1d6 if the dice have dots. That's why I find 1d10 - 1d10 much harder to use.

You are correct. I remembered what Feng Shui's system was at work today...

You forgot the exploding dice, which add quite a bit of fun IMO.

The Babylon 5 RPG used (uses) a similar system. You roll 2d6 and read only the lowest of them. If both are equal, the result is zero. This also generates a bell-distributed score of -5 to +5. If you want to add exploding dice, add 1d6 to the result if the die you did NOT use was a 6. This extra die then explodes normally. But for exploding die rolls, the Feng Shui system is probably better.


Maid uses a mechanic where you roll 1d6 and multiply this by an ability score (abilities are in the 0-10 range, with 1-4 being normal values). This works surprisingly well for opposed rolls, the chance to win or lose a particular opposed roll works out very nicely. It works less well for static difficulties. I love it for being so very simple.

 

[Ainamacar]

I dig these threads so much. They are great resources, and there are so many creative systems out there. Here's the one used in my group's homebrew system, with which I'm pretty happy.

Homebrew System (Variant Dice Pool):
Die type: d6 dice pool with variable number of dice plus a bonus to the check that is distributed among the dice, against a Target Number (TN) for each die. Dice explode on a natural 6, and their new value is 5 plus the result of a reroll. Each die may explode any number of times. If the bonus is 1 or greater it is distributed to maximize the number of successes. If it is -1 or lower it is distributed to minimize the number of successes. A natural 1 is never a success.
(Example: 4d6 + 3 vs. TN 7. The dice show 1, 3, 5, and 6. The 6 explodes and shows a 2, so its total value is 7. We add two points of the bonus to 5, making it 7, so it is also a success. The one remaining point of bonus isn't enough to make the 3 a success, and a 1 is never a success. The check has two successes.)

Probability type: Distorted binomial, such that its skewness is more negative than its nominal value when the check bonus is positive.

General Observations: The distributable bonus tends to make checks more reliable -- with a large enough bonus it is possible to get some measure of success against a high TN even if the die rolls themselves are modest. It also turns near successes into successes. We have defined three rules of thumb for TNs to guide players and DMs, given "typical" PCs with +3 training: TN 5 is easy and usually results in multiple successes, TN 8 is medium and usually results in a single success, TN 11 is hard and results in a success half the time. (For untrained average humans these TNs give expectations of about 1 success, half a success, and 1/10 a success, respectively.) In my opinion that is a defensible mapping of the terms to what the statistics say, so a DM can think about a task qualitatively and quickly interpolate a suitable TN using the rule of thumb. This aspect might even be faster than d20 in some cases, where if the DM wants a 50% chance of success on some impromptu check she might have to ask a player what his bonus is, taking time at the table.

The probabilities are non-obvious, hence the rule of thumb, which might be a turn-off for some (sorry garrowolf!), but so far everyone who has played has quickly grokked the basics. I actually enjoy not thinking about percentage chances while at the table, which I did somewhat obsessively in d20. Anyway, it gives good results with not very much calculation if the number of dice and bonus are kept modest. In our system the typical roll has about 5-6 dice, with a bonus no greater than 6. The algorithm is simple: find natural successes, then find near misses and add the bonus until you can't anymore. This is a very fast sorting process with counting and addition of small integers, and only rarely any other arithmetic. Compared to other dice pool systems it isn't that much slower, especially if those have more addition or eventually require the proverbial bucket of dice on every check. It's obviously slower than d20, but also has finer granularity of outcomes, although that's true of many dice pool systems.

Treating exploding die as 5 also smooths out the "6==7" issue from Shadowrun. (I'm kind of a math purist that way -- the exploding dice issues with Savage Worlds also bother me. In my RPG systems, if something is an upgrade of something else, I want it to be strictly non-inferior.) Anyway, on multiple explosions it should be faster to calculate for most people since, after 10s, multiples of 5 are usually easiest to use.

The system doesn't have critical successes in a d20 sense, although we have defined 1, 3, 5, and 7 successes as significant qualitative thresholds. We do define critical failures, however, which is a failed check that also has no successes at TN=original TN-3. This has a nice interpretation in terms of the rule of thumb. Plus, if most checks in everyday life are 5 or less, the only way to critically fail is usually to roll all 1s. For climbing a perilous mountain, not so much. I, at least, like this much better than a flat 5% chance of rolling a 1 on any check.

Finally, I really like the qualitative feel of how attributes and skills in the system affect the math in unique ways. The number of dice rolled is given by a primary attribute (e.g. Agility), and the bonus is determined by training in a skill. The attributes for PCs are between 3 and 6. Skills, and therefore bonuses on checks, are between 0 and 6 (untrained to legendary). Attributes define maximum potentiality, and can really be powerful, especially for easy tasks. But difficult checks can't be counted on to succeed reliably. For that you have skills, which nearly guarantee some measure of success on ever more difficult checks, and frequently turn multiple near misses into successes on easy ones. They also have a much stronger effect on reducing critical failures than extra dice.

Weaknesses of the system are that it doesn't scale very well to buckets of dice or very high bonuses, where both the number of successes and the calculation thereof gets out of hand. I envision an attribute of 11 as essentially deific. Similarly, creatures with 1-2 dice simply don't work very well in the system, especially in combat or anything where critical failure is significant. Another weakness is checks with multiple TNs, such as a fireball encompassing several creatures. In this case the system can get bogged down about the same as 3.5 did with multiple saves. Some checks are not well suited to the idea of a "least degree of success", or are so well-suited to requiring a specific number of successes that setting the TN isn't obvious. Similarly, when circumstances require a modifier on a check whether it should be a TN change or a change to the bonus is sometimes a gray area, although there are guidelines. More subjectively, the vague nature of the probabilities at the table may be a nuisance for some DMs or players. Finally, the learning curve is larger than d20 or any d100 roll under system, especially for a DM.

I still think it's awesome, but I'm totally biased!

 

[innerdude]

So here's the real question -- Which dice mechanic works best for the style/genre you're trying to emulate?

For example, it's pretty clear that most things in nature follow a normal distribution. It's just the "way things work," 67% of us fall within one standard deviation of "the mean," whatever it is we're measuring, and 95% of us fall within two.

But the real question is, how do you set a scale for success?

For example, how do you determine the DC for oh, say, a php/MySQL computer programming check? In D&D terms, supposedly if you roll a 20, it's still an automatic success, even though someone with zero skill in it is not going to have any chance of completing a DC 15 MySQL check within a week (sure, if you study the code long enough, and have any sort of reference material to guide you, you could probably figure it out eventually). Should there really even be a 5% probability that someone who's never looked at a computer in their life could complete that check?

In D20 terms, the Alexandrian has been repeatedly quoted as saying that in "calibrating" the OGL / 3.x system, even the most epic "heroes" of the books we read are probably 6th level, 8th level at most.

Einstein isn't a "20th level scientist;" he's basically a 5th level expert with an 18 intelligence, skill focus in Knowledgehysics, the standard 8 ranks available at that level, and that's about it.

Some of this question probably revolves around our own experience, or view, on how human skill and performance works. A normal distribution model basically says, "If you're good enough, you're good enough, and it's pretty rare for you to luck into something." Which, I think for most of us, is a pretty realistic assessment.

For example, I've never built a wood deck before, even though I've watched people do it. I know the basic principles of measurement, and hammering, and drilling, and creating support beams, etc., so it's not like I'd be going in blind if I tried. I could probably build a crude wooden deck that would be marginally functional, but to make something elegant, sturdy, and functional all at once? I really would have no chance at it, at least at my current skill levels.

But then again, are RPGs really supposed to model anything but the most casual realism?

I'm rambling a little bit here, but I think this is something that would be interesting to look into more.

 

[Starfox]

Heroes from the old epics are constantly doing things they don't know how to do. It's part of the nature of heroism to be boundary-breaking. In fact, heroes figure in many creation myths, where their initial attempt is now replicated and modeled trough ritual and skilled practice. If this is what we wish to model, PCs ought to have a good chance of doing even the things they don't know how to do, but generally not on the first attempt; they need to get back to the problem and attack it from a new angle (this is what epic heroes almost always have to do).

 

[amerigoV]

The focus of the threat seemed to be on the dice themselves, but I find some of the mechanics around the dice to heavily impact flavor and gameplay.

[/SIZE] Savage Worlds / Deadlands
Die Type: Uneven Dice Pool. Variable skill die + standard d6 "Wild die" for PCs. Skill checks can "explode" indefinitely. Take the best result from either die.

Probability type: Modified flat distribution (since we're not adding the two dice together, it's technically a "flat" distribution, each probability of success is counted independently for each die).

General Observations: The simplicity and elegance of the skill system for Savage Worlds is a big point in its favor. Think a particular NPC is "good" at a particular skill? Assign a d8 or d10 skill, and be done. With target numbers remaining relatively static, it makes it easy to get a quick "feel" for effectiveness, and doesn't require a lot of bookkeeping. Fast, Furious, Fun indeed.

The problem is that unlike D20, and to a lesser extent 3d6, the probabilities aren't as transparent. Just how "good" is going from a d6 skill to a d8 skill, really? To calculate the difference, you actually have to count the number times on each die a d8/d6 vs. a d6/d6 would NOT be successful, multiply each die's total, then subtract that number from the total number of possible combinations (d6/d6 = 36 total possible combinations; d8/d6 = 48 possible combos, d10/d6 = 60, etc.). Did you follow that? Yeah, it took me a few times to get it right in my head too.

To make matters more interesting, exploding dice get thrown into the mix, which upset the various probabilities in certain ways. Many people have noted that in some cases it's EASIER to hit certain target numbers by having a LOWER die number and hoping it explodes. Across the entire gamut of the game, these typically represent barely 2-3 percent of total rolls made over the course of a campaign, but for statistics purists, it's an annoying anomaly.

The other problem is that the baseline die types means there's a very shallow range of character development. If a d4 means "baseline capability," Savage Worlds only provides 4 "tiers" of capability over that baseline. The scale basically goes Competent-->Good-->Very Good-->Awesome-->Kicking Ass and Chewing Bubble Gum. And the way the dice mechanic works, there's very little "leeway" for representing nuances between each die level.

There is a further factors in Savage Worlds -
1. Bennies. The player has the option to reroll results on occasion (generally 3 times a session, but that varies wildly depending on soaking wounds and other roleplay factors). The GM has up to 1/PC plus 2 per Wild Card.

Deadlands has a variant based on the type of Bennie to roll a d6 and add to the result.

2. Being dealt a Joker during initiative gives a blanket +2 to actions (huge in Savage World) that is not generated by anything that the player does, tactical situation, etc.

The reason I bring it up is I played a ton of Savage Worlds at Origins and one game of Serenity (Cortex). These two systems look so much alike that people people lump them together, but they are completely different in play. The types of dice you roll and the Advantages/Disadvantages are very similar. The quick difference is that Cortex adds the Attribute die to the Skill Die (so not linear), no exploding dice, and their Plot points either changes the die size before you roll or adds to the result after you roll.

I really found the differences in the last two in mechanics (die explosion, how the Bennie/Plot point worked) to have a huge impact on my enjoyment of the system. I soooo wanted to roll a maxed out die or wish I could just reroll the whole thing.

I also played a quick AD&D 2e game (a quick romp through ye old Moathouse). I ran a thief and wizard. I know you lumped the d20 mechanics together, but I was rolling all sorts of dice to determine the outcome of my actions - d20 if normal old attack by the thief, a d% if I was trying to sneak or find traps, a d6 if I was looking for secret doors or if someone was surprised, or nothing at all if I was casting a spell. And depending on what I was doing, I might need to roll high (attack) or roll low (swim across the moat). In the end, basically all linear stuff but it did remind me why I drifted from those versions of the game (I had fun in that short game, but I would no play it for any length of time again). And boy did I miss Bennies from SW since we were only 3rd level - a wide Swing factor with no ability to modify it.