System design discussion/theory: dice pool vs TN

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?