System design discussion/theory: dice pool vs TN

Hi! As I'm still on the quest of finding the "Perfect* System For Me"... and still didn't manage to do so... I started to make a list of things I would like to have or find in such system. (and design my YZE hack, but it also is the subject for other time). The list will be a subject of different post, someday probably... But I found something interesting in it. Namely:

1. I love systems with TN(target number) - the have precise aim for which player have to roll, you clearly see how far or close you were to achieve the TN - if you missed or how much you have gone above it if it was really epic roll. Also - what is very important - those systems provide a nice granularity for roll. You can have many level of mods: simple +/-X to the roll sum, or adding advantage die... or even a whole die! So you can get a proper-feeling mod for each situation.

My favorite examples: Cyberpunk RED/2020, Traveller, Savage World, (OSR? Knave/Spacer? , Fabula ultima? - I don't know those well enough to be sure)

BUT.. in the same time...

2. I love system with dice pool - collecting dice to your pool as physical act - feels so good. Like collecting your thoughts, or gathering your strength. Also they usually provide fast resolution. Also you can get dice from different sources and they maybe even very different. They usually work with possibility to freely connect attributes and skills in creative way - they feel like providing more agency to players.

My favorite examples: YZE games(both step dice, and pool), Genesys, Broken Compass/Hausehold/Outgunned (D6 Systems?, FitD? CoD? - I don't know those well enough to be sure)

SO THE QUESTION IS:
Do you know any GOOD systems that appear to incorporate BOTH of those approaches? I would consider for this:
-The One Ring - my currently favorite ruleset in general, but unfortunately seems perfect for Tolkien's words and not necessary anything else
-D6 Systems - somehow I feel it should be mentioned here, but don't feel as dice poll completely. I especially like the rule for multi actions, it's somehow pool against TN... but the dice are always the same.

And thats all I know. Excluding quire a few minor/indie systems - as many of them seem to be good only for one-shots. And I want system for epic longer campaigns.

So:
- Do you know any full system with such aspects?
- Do you think that it is even a good idea to incorporate both of those in one game?
- Any other remarks? :)


*I know such thing don't exist - so the name is some kind of joking about myself... :)

Are you looking for mainly PbP play? Because that changes what works well.

When reading your initial paragraphs I wondered why you were drawing a line between the two modalities and was going to suggest combining them. :)

There are plenty of systems that use a Dice Pool and have a Target Number, like the World of Darkness (old/new/Chronicles) and such, and there are systems where have TNs as an optional rule (Cortex Prime), or set a Target Number based on an opposed roll.

Having both a varying TN and a Dice Pool can be rather slow in PbP, since that is two discussions that need to be had before the dice can be rolled, games with a static TN, of course, remove the need for a discussion about the TN.

Outside of PbP - on the table is my priority.

But isn't TN in World of Darkness for each dice separatly ? I probably should precise that those futures that I want have system when you add up your dice and then compare it against TN. World of Darkness - as far as I know it - seems as "pure" dice pool for me - you consider each die individually. So on default TN of 7 and d10 - there is not so much granulity I would like to - but maybe I don't know this system well enough.

So to put it in other worlds: you have general Target NUMBER that you work for with all your dice, not TN for each dice individually.

I am not really fluent in WoD, but isn't that 7 is for a 'Success'? I was thinking more about setting how many successes you need to complete a task as the Target Number that was being set. In YZE that TN is 1, (with some games asking for more successes, I believe).

You want to see real 'TN for each individual die'? Then a system I did not mention because it is hard in PbP is Otherkind Dice, as used by PSI*RUN. Every time you roll you have a target number for each die in your pool (maybe, if you are lucky, you have a spare die that does not need to assigned to a number).

Cortex Prime has you add together some (2?) of the dice from your pool to meet a TN that could be static or could be based on the dice pool the opposition rolled.

Cortex Prime does both at the same time. You pick a target number based on the difficulty of the task. Then you build your dice pool of at least 3 dice (can be more). Roll. Sum up two of the numbers and if it’s over the target number, you succeed. And the die type (d4, d8, d10, d12) of the last die says how well you succeeded.

Burning Wheel is probably my favorite system and has generally what you're describing except the TN is a number of dice rather than the sum of the dice. For example, you make a dice pool of d6s based on your skill, someone helping, or metacurrency and roll those. Any result on the die 4-6 is a success, and you need a number of successes to succeed. So if the TN is 3, you need 3 d6s that show 4-6. I like it because its intuitively simple that each die has about a 50% chance of success, and you can see how many dice your rolling versus how many successes you need lets you figure out the math pretty simply.

That's also the way that Paranoia does it. You calculate your dice pool (d6s) and every 5 or 6 is a success.
That game does have a few twists, like having a negative dice pool and the 'computer die'. I really enjoyed the creative way of using d6 dice pools.

I second Nezzeraj, Burning Wheel looks pretty close to what you've described. And with exploding dice and extra for Artha, even with a small dice pool, you can still theoretically hit the targets you need.

Maybe Sorceror would have something close to that, but not quite.

I'm not sure I see the distinctions you're drawing, Pedrop. There are many, many variations on these systems, and roll-under / static target systems as well. They all have their pros and cons. and can all be molded to bring in some of the other elements.

Take YZE, for example. Not a system with a Target Number, you say, it's a dice pool system at its heart? It is. But it also models difficulty, which is all systems with a TN do. And they do it in multiple ways, depending on the game. In most YZE games, difficulty is modeled by adding or removing d6 from the pool. You're still trying to get that one success, that one 6+, but your chances get better or worse. Same for T2K, which uses the step-dice version. Loads of modifiers moving the dice up and down.

But then take Bladerunner -- step dice, but no mods. Instead, you have Advantage and Disadvantage, which greatly simplifies the GM's job of making a call on the difficulty. And then look at Tales from the Loop and Things from the Flood -- where the difficulty is modeled by the number of successes needed, the number of dice coming up 6+.

Generally speaking, I would second looking into Burning Wheel and Cortex Prime or other Cortex games. I personally have a pretty strong dislike for having to arbitrarily set difficulties, so I gravitate towards games that count successes in pools, roll-under mechanics (GURPS, Black Hack, BRP, Into the Odd, Symbaroum), or systems (like, say, Shadow of the Demon Lord, Warlock! or the various Borg games) with static or at least default TNs. You might look at Modi's 2d20 games as well, as they have both TNs and a level of pool-building. And live, rolling a handful of d20s is a pretty great feeling.

Yeah. Good call Harriman, the Modi 2d20 games do it well too

You know... what you're discussing actually reminds me of Star Wars -- the old West End Games (WEG) version, before WotC got the license.

You made dice pools (including a wild die) and then had to hit a target number based on the difficulty of your action. The more proficient you were, or the better gear you had, the more likely you were to hit your TN.

It was a little more complex than that, in that there was scale issues that could add or subtract dice (if a person with a person-sized blaster was shooting a speeder, for example), and the wild die could get swingy... but that was the gist of it.

(The wild die was unique. On a 6, you reroll it... potentially many times. On a 1, you remove it AND your highest other d6.

What was interesting is, on a large enough dice pool, even a 1 on the wild dice didn't mean you failed... although if the pool of dice let you succeed, it was usually with a complication.)

As much as I like WEG's Star Wars (1e more than 2e), I don't love those wide-ranging TNs the GM has to set -- because the dice pools can get pretty sizable.

That's fair. Although, personal preferences aside, it does seem to be a pretty good match (mechanically) for what Pedrop is talking about.

Mathematically, there's not much difference between dice pool systems and roll and add (or roll under), at least not as much as people think.

A dice pool system is (generally) just a d2 system with a (usually skewed) distribution. It has a much stronger central tendency than other systems (i.e. d20) because every roll pushes the potential results closer to the total mean. Check out this AnyDice as an example. This is basically how any dice pool system where half the results are successes (i.e. BW or Mouse Guard) work. Focus on the numbers in parentheses. The first is the mean, the second is either the standard deviation or the variance (I'm pretty sure it's SD, not 100%, but they both measure similar things). You'll notice that the mean increases linearly (in 0.5 increments) while the SD does not and in fact has diminishing returns. Any system with multiple dice are going to have stronger central tendencies (relatively lower standard deviations) the more dice that are in the mix.l

The important thing with a resolution system are the implications of its distribution. For example, on one hand, a dice pool system makes it pretty easy to know where you stand for any task. For Mouse Guard, I know I need double the dice as the Obstacle (TN) to have a better than 50% chance of success. Even for systems that don't split the dice down the middle for pools (I believe Exalted only counts 5s and 6s as successes), it's still pretty easy to extrapolate what dice you need to have a fighting chance at something. On the other hand, the strong central tendency of dice pools means not much granularity. Opposed rolls in dice pool systems are almost pointless. In Mouse Guard, in an opposed roll, if one side has even one more die than the other side, then they have around a 75% chance of success. At two dice, it goes up to 95%. If dice are meant to add uncertainty to a situation, dice pools get certain really fast.

The opposite end of the spectrum is the d20 roll. A single die, linear distribution. I've often heard people call a d20 "swingy", but I would say this is a misconception. That is, most d20 based systems just have you roll to answer the question, "Did I do the thing?" You have an ability score. You roll the dice and then add the score, or try to roll under it or whatever. It doesn't matter. If I need a 14 or higher to do the thing, it doesn't matter if I roll a 2 or a 12 (i.e. the "swinginess" of the result). I fail either way. linear distributions scale better, if you need that. But, it can also make it a little hair-splitting to set TNs for tasks.

Fun fact about The One Ring, their wonky dice system doesn't hold up well under pressure and it's actually because of its strong central tendency. That is, it can be a bit of a character funnel for early characters and you need to tap into metacurrency to have a decent shot of survival. Then you hit a sweet spot where you have decent tension, but still feel like your characters are skilled, and then you get to a point where you could steamroll Sauron if you wanted. There are a few tricky features in the system to control for this, but it basically functions like rubberbanding in video games (which I find to be annoying).

To answer your original question, it seems you want to walk the line between the simplicity and tangibility of dice pools, but have the "tweaky-ness" of more linear systems. I don't really know of a system that really does that, but WEG's d6 system might be in the right neighborhood for you.

It's too bad we can't give upvotes to posts cuz I'd do it for this one.

Maybe someone already said it but I JUST learned the Conan 2d20 system and it seems like a nice mix of dice pool and DOUBLE TN! You have a system in place that lets you roll a pool of d20s under a target number with a secondary target number (or focus as they call it) for double success. The TN is derived from stat + skill with the focus being skill number only so if my Brawn is 10 and my athletics is 5 I have to roll under 15 on a base of 2d20 with results of 5 or less counting twice. Difficulty of tests is determined by number of successes needed.

I'd actually argue that, depending on the dice, there's a lot more difference than most people realize -- having to do with the number of possible outcomes and the sample size needed to be confident in the results... and have them feel fair / balanced. A d6 and a d20 can both give you a 50/50 roll easily enough -- but you have to roll the d20 hundreds of times more than the d6 to get to something like a 95% confidence level that you are seeing evenly distributed results.

What does this mean at the table? That the 'swinginess' of the d20 is real. From session to session it's very possible to see long strings of good or bad rolls. These even out in the end, but only after quite a few sessions of play.

Nice breakdown of the lovely bell curve btw, a results distribution that is near and dear to my heart. I would only add that there are now loads of d6 (and other) dice pool games on the market that go well beyond being just a bunch of d2s. Burning Wheel does this with its variable target numbers, and IMHO the Tiny D6, YZE, Forged in the Dark and Trophy-powered games can produce some statistically interesting results and are also quite fun to roll.

But, that has nothing to do with the die or even the resolution system. That's all in the adventure design, specifically how TNs are set, which is essentially independent of the resolution system. You can have an equally "good" or "bad" run in something like Mouse Guard if the Obs are generally set too low or too high. Even for dice pool systems, you're often asking, "did I do the thing?" Story games, with their often multi-tiered resolution mechanic, really aren't much different either.

In other words, the resolution method has absolutely no impact on the likelihood of a "good" or a "bad" run of rolls. It's just going to generate a random number within a range and a certain variance. Sampling only has value if you're factoring in instances of resolution. Even then, all this is going to tell you is if this series of play is "easy" or "difficult".

The "swinginess" is not real and has no intrinsic value. But the variance does matter within the larger context of the range of adjustments (skill levels, modifiers, etc.) setting TNs for the party and it's a double edged sword. Simply put, the less variance, the more polarized various tasks are going to be, and frankly, the less meaningful the die roll.

This actually ties into something else called value of effort. Let's say we were playing some d20 game, however, every check fell into one of two categories. You either could only succeed with a 20, or only fail with a 1, depending on your skill level. No in between. Put that in front of players and most of them would think this system is a waste of their time. There is a perception that if your probability of success/failure is a certain amount, then it is a "foregone conclusion". You can easily see this in effect if you look at X-Com players . How about a meme that pretty much sums up that scene?

There are a number of factors that contribute to the tension of a dice roll, but the odds of success are a big one (the other big one being the stakes, which is why an X-Com player is still white knuckling it at a 95% chance of success). When it comes to odds, it's probably no surprise that tension is highest at 50% and reduces the further you get away from that. A variance that is low relative to the range for a resolution system makes it really difficult to create tension. Mouse Guard is a good example, and actually an ironic one. Don't get me wrong, I love the game, but it's a strategy game for me. And that's the irony. It's meant to be a story game, but it actually plays pretty well if you game the system.

Now, for the sake of clarity, I'm aware one can finagle dice rolls with Fate and Persona points (and tapping traits/wises), and they are super useful when they really matter. But, you can't use them all the time. Generally speaking, I'd only use them when my dice pool is equal to double the Obs of the test (i.e. I have a 50% chance of success), or within a single die of that amount. Outside of that, odds are heavily skewed towards success/failure. If the odds are stacked for or against me, I'll impede myself with a trait or something since it's a wash anyway. Might as well get some free checks during the player's turn out of it.
I'm familiar with (most of) these systems. I've haven't real BW in forever, but by "target numbers" do you mean the threshold for success on a single die (i.e. 3+ vs. 4+ vs. 5+) or the number of successes needed to pass a test? I don't think it matters much either way. If the former, it's still a d2, just weighted. If the latter, it doesn't sound much different than MG.

And, my use of the d2 example wasn't to mean that all dice pool systems are d2 based. It's just an easy example to show the math. The truth is, a dice pool system, or roll and keep, or what have you, isn't categorically different than the old fashioned d20. They all provide a random distribution with a certain mean, range and variance. I think it's more valuable, rather than get caught up in the taxonomies of these things, is to focus on how the math of it will play out in a game. I've seen far, far, far, too many "indie games" where it claims to be a game that does one thing, but by the dice, something totally different is happening.

I think that's the big moral of the story here. Lots of people are attached to certain dice systems, not because they know the math, but because they like the "feel". However, if I had a dollar for every player I saw that was overly attached to resolution X but wanted a game that did Y (which doesn't really work with resolution X), and they were boggled by their frustration about it, I'd have a lot of dollars.

Rather than debate point-by-point here -- and we actually agree in a number of areas -- I'll just close by saying I'm aware that it all boils down to a percentage for individual rolls, but also that the way those rolls are made absolutely matters. For the player or the GM having some understanding of what the odds might be (contrast The Black Hack with Cortex here), for modeling competent / consistent PCs (d20s with modifiers vs. anything with a bell curve), and for, indeed, the feel of the mechanic. The enjoyment some get out of assembling a pool, rolling a nat 20, or hitting doubles and the like.

I absolutely agree that a lot of designers -- of both systems and adventures -- don't provide proper guidance on how often the dice should be bouncing. Games are getting better at it, but whenever I see a system that says, "don't roll too often, just when the stakes are high," and then hands you a d20 or percentile dice, I have to grin.

Love dice talk. Onward!

It matters, just not mathematically. 😁

Oh, it matters mathematically.

Look away, those who don’t dig this kind of pedantry!

Two examples.

1d20 vs. 3d6 vs 2d10
This is near and dear to my heart, because I started in the hobby with AD&D, switched hardcore to GURPS and Champions for many years, and then when I wanted to play some supers games in the 2000s I found most people preferred M&M. So I ran M&M with 2d10 instead of 1d20. ;)

These three methods produce reasonably similar ranges of results. But the distribution of the results is very different. Let’s say we’re modeling someone’s skill at something, and they hope to be able to perform at or around their skill level a good portion of the time — for sake of argument, let’s say two numbers on either side of the average rolls. How often do those come up?

For 1d20, using 10 and 11 as the average, we’ll expand the acceptable range down to 8, and up to 13. 30% of the time, a d20 roll should hit those numbers. Since the d20 has more possible outcomes than 2d10 or 3d6, perhaps we should expand further — let’s say down to 7, and up to 14. 40% of the time, the d20 is hitting in that range. Less than half the results.

Now let’s look at 3d6. 10-11 is still the mid-point / average, and if we extend down to 8 and up to 13… 3d6 land in that range 67.58% of the time. They are way more reliable.

2d10 is in-between, and that’s why I choose this mechanic for M&M — to maintain more unpredictability. The two dice mean the average is no longer 10-11, but rather just 11. Expanding down to 9, and up to 13, 2d10 should land in that range 44% of the time. Expanding one more step in each direction, down to 8 and up to 14 — now we should see 2d10 hitting that 58% of the time.

Perhaps a more straightforward way to look at this is with a roll-under system. If someone has a Strength of 13 and has to roll it or under to succeed, the results of the three dice rolls varies substantially. A d20 succeeds 65% of the time. 2d10? 72%. And 3d6 hits almost 84% of the time. 20 points difference! Obviously the delta depends on where you are in the range, but that’s the point. Some folks want more reliability and less randomness for characters that are particularly bad or good at something.

Next example, aimed at the pool Kneller was talking about before.

YZE d6 pool vs. 1d20
In classic YZE dice pool games, you roll one or more d6 dice and count sixes as successes. This means the chances for success initially go up dramatically as you add dice to the pool, then they peter out. 1d6 succeeds ~17% of the time. 2d6? 31%. Three is 42%, four is 52%, etc. But once you get up to 8d6, the success rate is 77%… and adding another die only takes you to 81%. Ten dice is 84%. So down low, adding a die to the pool is much more meaningful. And to model this using a d20, you’d have to be flexing how many +1 bonuses you were adding depending on the starting skill of the player.

This isn’t to say that any of these systems are superior to the others, but they are different, and are achieving different things — mathematically.

What you're doing here, though, is taking numbers on the dice and checking their percentages and of course, those percentages are going to be different. What you could also do is think of the percentage that you want and then check which number range that would be on your chosen dice system.
That still doesn't make the dice you choose irrelevant as they matter in which percentages can reasonably be achieved on them or make intuitive sense to use. But theoretically, you can model any of the "reliabilities" you descreibed here just by having a D100 roll-under system. You'd just need to set the right percentage values there.

Not 100% clear on your point, bowl — I’m just pointing to the fact that the mechanics do matter. You can model any dice mechanics with percentile dice, true, but percentile dice need an even larger sample size than a d20 to provide consistent results. And for dice systems that explode, that count doubles, that use different colored dice — turning that into a purely % thing isn’t practical. Or, for the large majority of people, fun. :)

I'm not sure how that is a rebuttal. My point was that the resolution mechanic is intrinsically meaningless. It only matters when you consider it in the context of the larger system (i.e. how it's used). So, if someone says they'll only play dice pool systems, it says nothing about the games they'll play. MG plays vastly different than Exalted, which plays vastly different than Shadowrun. For example, it would be easy to get me to play Mouse Guard, difficult to get me to play Exalted, and somewhere in the middle to get me on board with Shadowrun. It's virtually the same resolution mechanic for all three (I'm not sure if Exalted gets the reroll options that the other two get, though I recall Sidreals getting weird stuff like that), but the games are very different.

A lot of people have their preferences which are near and dear to their hearts and all, but it really has nothing to do with actual mathematics, just their perception of (and possibly personal tastes with) the math. Kind of like the whole verisimilitude vs. realism thing.

Even what you call the acceptable range (i.e. what I previously referred to as the "value of effort") is subjective. Whether the resolution mechanic uses 1d20 or 3d6, it's not going to change a person's value of effort threshold. So, let's say I stop giving a shit if the odds are below 10% or above 90%. In a d20 system, I will trigger not-giving-a-shit on any roll I need 2- or 19+. In a 3d6 system, the same will happen on ~7- and ~14+ rolls. But, this also varies from player to player. One player's 10% is another player's 3%.

Going further, let's say I have two games, one is d20 and the other is 3d6 for the resolution. If, all things considered, the TNs for the D20 are always between 3 and 17, and in the 3d6 system the TNs stay between 8 and 13, the end result is the same, it's just the 3d6 system provides a smaller range of possibilities.

Of course, and this gets back to the larger context of how a resolution is used, getting to a not-giving-a-shit place could be the point. This is why I like MG and don't like Exalted as much. In Exalted, I might get a bonus "stunt" die for roleplay. Big deal. I usually only need one success, which is pretty easy to get with a modicum of skill. Exalted doesn't use it's strong central tendency well in its design. However, in MG, I'm working with the team to see if we can dredge up more dice to hedge our bets with a team action. There are a lot of choices and risk vs. reward analyses happening. However, at this point we're getting out of math and into game theory. The point is that it's two similar dice rolls engaged and used in very different ways.
You basically just outlined the diminishing returns of dice pools, which is pretty well known. What I'm saying is that a dice pool system like this operates on the exact same mathematical principles as any roll and add system. Imagine you're rolling some six-sided dice, but with 0s and 1s instead. "Dice pool" dice are (usually) binary. You roll them and add them together like any other dice roll. They might not split 50/50 like MG, but your results are usually either zero or one. Roll the dice, add up all the "ones" and that's your result. Or, to put it in other terms. If I roll a d20 against a TN of 7 and roll a 10, then I have three "successes" as a result. The number of successes probably do not matter in that kind of system, but that's what happened. Exploding dice, multicolored mayhem, and so forth are going to throw some blips in the distribution, but it's still a distribution and uses the same math.
If I had a dollar for every time someone swore up in down that d% systems were superior, I'd have a lot of dollars. I don't unilaterally support them (e.g. Unknown Armies is cool, WHFRPG is meh in my book), but these systems have a staunch following. Fun is a relative thing, but it's also different from math.

I think we're just coming at the same issue from different angles. 100% agreement that the mechanics, by themselves, are just what they are. But when they are paired with elements of systems, and when they support the tropes, tone, and so on, everything can sing. Conversely, when things go the other way, it's hard to take.

Interestingly, your first post on this talked about how a game could use a d20 with only 1s and 20s being meaningful (or something like that) -- and how most folks wouldn't find that very engaging. I've run Operation White Box a couple of times recently, and it actually has exactly this mechanic (and a bunch of others). The PCs are all highly trained commandos who fight behind enemy lines, so they are trained in athletics, German weapons, how to operate radios and vehicles, parachuting, etc. In those situations, the GM simply calls for a d20 roll and says, "don't roll a 1." It is surprisingly engaging, and tension-filled. At least at the two tables I ran for.

That's a game the where the randomness of the d20 is great, btw. In one sequence, a bazooka-carrying Joe tried to take out a German tank by rushing out from cover and taking a shot. He rolled a 1 on the attack (standard White Box / OD&D mechanics for that, d20 vs. a target number) and the electric ignition failed. The panzer opened up with both an MG and the main gun -- either would have been lights out for the PC -- and both missed. He was able to duck back under cover and later take out the tank after reloading the bazooka. There was much cheering.

Anyway, point being -- the d20 in that game is a perfect fit for the nail-biting moments, because the damages are high vs. the hit points. It feels a *lot* worse to me in a supers game, at least one where the designer hasn't taken care to fuss with the odds / results.

Forgot this:
People do love their percentile systems. I've grown to just live with them, and avoid the ones where you have a hundred skills on the page and fifty points to spend. Hard to be good at much of anything with those. (I exaggerate -- my point is that having a bunch of 20-40% skills on your sheet can make for a long night.) To your initial point -- it's not the d100 that's really the problem here, it's the designer being blind to how that mechanic meshes with their skill nonsense.

If the stakes are high enough, I could totally see that kind of thing being really engaging.

This is in reply to the thread starter :

In prowlers, everything is an opposed roll, but in a sense, all rolls are against a target number (called a threshold), it's just that the threshold is determined by the result of the opposed roll. When you're rolling against "the environment", the GM will either roll or directly assign a threshold. Also, anyone can trade their dice out for automatic successes, so any roll can be directly converted to a target number.

Prowlers & Paragons, yes?