How do you deal with increasingly large dice pools?

[Drolyt]

So after doing some research I'm starting to like dice pools more and more as a resolution mechanic, but if you want a game that covers a wide range of power levels (like D&D or HERO) you will pretty quickly be rolling a ton of dice. How would you resolve this issue? I know some games let you trade in dice for a flat bonus, but this changes the probability: compare http://anydice.com/program/2313 to http://anydice.com/program/2314. They have the same expected result (10) but are otherwise very different. If you only need 10 or less the second is the better tactical choice, but if you need 11 you want the former. Is there a more elegant solution?

[Pulsewidth]

Dice rolling software.

[Lokathor]

I wrote a longer post earlier and then gave up because I couldn't get the words quite right.

Basically, more dice makes things more swingy. That's actually kinda bad. You should pick an "optimal" dice pool size for the usual case, then focus the game around people rolling about that many dice or so in terms of pool modifiers, thresholds, etc.

Dice pool games don't do well with vertical advancement because a bigger dice pool literally makes for a bigger RNG range. It's like if you leveled up in DnD and your 1d20 became a 1d22 instead of getting a +1.

[Username17]

Dice pools with fixed target numbers already are self limiting in how many dice you need. And the lower the target number, the less dice you need. Even at Fixed TN 5 (like SR4), you don't really need more than 24 dice for anything. Dicepools against a fixed TN are inherently logarithmic, which means that they scale off into crazy town with what they can represent extremely quickly.

At TN 5, 6 dice come up with hits 0.14% of the time. At 18 dice, that's the average roll and it comes up with that or better 59% of the time. The number of standard deviations you jump by adding two handfuls of dice together are so massive that it pushes the entire RNG.

That being said, things do get silly if you try to scale irresistible forces and immovable objects far enough. For that, I would suggest having needed hits and dice eliminate each other at an average rate from the tail end. Say, if you have more than fifteen dice and the success threshold is more than 5, you trade your dice for a reduction in needed success threshold at 3:1 until one of those two things isn't true anymore.

-Username17

[Drolyt]

I wrote a longer post earlier and then gave up because I couldn't get the words quite right.

Basically, more dice makes things more swingy. That's actually kinda bad. You should pick an "optimal" dice pool size for the usual case, then focus the game around people rolling about that many dice or so in terms of pool modifiers, thresholds, etc.

Dice pool games don't do well with vertical advancement because a bigger dice pool literally makes for a bigger RNG range. It's like if you leveled up in DnD and your 1d20 became a 1d22 instead of getting a +1.

I'm not sure whether you misunderstood me or I misunderstood you, but what I'm trying to do is avoid large dicepools, not because they are swingy, but because nobody wants to roll (say) 30 dice every turn. As for becoming more swingy, that is barely true. Using target number 5 like Shadowrun and rolling six dice you have a 98.22% chance of getting between 0 and 4 dice (range of five) while with 24 dice (going with what FrankTrollman said about that being the maximum you should ever need) you are rolling between 4 and 12 (range of 8) 95.17% of the time. So yeah. Three times as many dice and the deviation barely doubles.

Dice pools with fixed target numbers already are self limiting in how many dice you need. And the lower the target number, the less dice you need. Even at Fixed TN 5 (like SR4), you don't really need more than 24 dice for anything. Dicepools against a fixed TN are inherently logarithmic, which means that they scale off into crazy town with what they can represent extremely quickly.

At TN 5, 6 dice come up with hits 0.14% of the time. At 18 dice, that's the average roll and it comes up with that or better 59% of the time. The number of standard deviations you jump by adding two handfuls of dice together are so massive that it pushes the entire RNG.

That being said, things do get silly if you try to scale irresistible forces and immovable objects far enough. For that, I would suggest having needed hits and dice eliminate each other at an average rate from the tail end. Say, if you have more than fifteen dice and the success threshold is more than 5, you trade your dice for a reduction in needed success threshold at 3:1 until one of those two things isn't true anymore.

-Username17

So, for opposed rolls, would you say having dice cancel each other until both players have less than 15 (that's just a number I pulled out of my ass) dice is reasonable?
Edit: To be clear, my concern is mostly with combat. You are certainly correct that most things don't need a lot of dice, but if you want combat to scale over something like D&D's 20+ levels and have the same granularity so you improve at least a die a level then dicepools get big pretty fast.

[Lago PARANOIA]

For that, I would suggest having needed hits and dice eliminate each other at an average rate from the tail end. Say, if you have more than fifteen dice and the success threshold is more than 5, you trade your dice for a reduction in needed success threshold at 3:1 until one of those two things isn't true anymore.

I heard that there are some die-rolling schemes (like opposed rolls or margin of success) and some edge cases in which this produces funky results. Could you elaborate?

[Drolyt]

For that, I would suggest having needed hits and dice eliminate each other at an average rate from the tail end. Say, if you have more than fifteen dice and the success threshold is more than 5, you trade your dice for a reduction in needed success threshold at 3:1 until one of those two things isn't true anymore.

I heard that there are some die-rolling schemes (like opposed rolls or margin of success) and some edge cases in which this produces funky results. Could you elaborate?

This is also my concern.

[fectin]

Basically, more dice makes things more swingy. That's actually kinda bad. You should pick an "optimal" dice pool size for the usual case, then focus the game around people rolling about that many dice or so in terms of pool modifiers, thresholds, etc.

I'm not going to say you're wrong, because "swingy" can mean a lot of different things. In general usage though, more dice makes you less swingy.

[Username17]

For that, I would suggest having needed hits and dice eliminate each other at an average rate from the tail end. Say, if you have more than fifteen dice and the success threshold is more than 5, you trade your dice for a reduction in needed success threshold at 3:1 until one of those two things isn't true anymore.

I heard that there are some die-rolling schemes (like opposed rolls or margin of success) and some edge cases in which this produces funky results. Could you elaborate?

In an exploding dice scheme dice converting to average results is going to feel radically different than actually rolling them. Because the mean and the median are very different with exploding dice.

In an opposed roll, dice getting converted to their average results brings the hammer down if and only if it reduces the random factor for both players to near zero. Even the thing in Scion where the attacker rolls and the defender takes the average doesn't really get noticed. But if the attacker could take the average on enough dice that they always hit, then they'd always hit.

So if you let the dice cancel as long as both characters are rolling more than fifteen dice, that is just a high level time saver. If either character has more than fifteen dice, that's a GTFO ability that high level characters have over low level ones. Also a time saver, of course.

-Username17

[Username17]

Basically, more dice makes things more swingy. That's actually kinda bad. You should pick an "optimal" dice pool size for the usual case, then focus the game around people rolling about that many dice or so in terms of pool modifiers, thresholds, etc.

I'm not going to say you're wrong, because "swingy" can mean a lot of different things. In general usage though, more dice makes you less swingy.

Not in the context of dice pool games. In D&D, a 10 die fireball is much less swingy than a d6x10. But in Shadowrun, that isn't true at all. 5 dice rolls 0-4 95% of the time, while 10 dice rolls 1-7 95% of the time. The actual number of numbers in the likely rolling space increases by about 50% for every doubling of the physical number of dice. And that's important, because higher numbers of required hits are exponentially harder to get. So the fact that rolling one standard deviation over average on 9 dice involves rolling 2 literal hits over average while rolling one standard deviation over average on 16 dice involves rolling 3 over average means that the dicepool has gotten more swingy in a very important way when more of it is rolled.

In Shadowrun, rolled dice versus unrolled dice should not be compared to rolling a multiplied die or a pile of dice that are added together in D&D. It should be compared to rolling a pile of dice and adding the results to rolling a single die and then adding a giant bonus in D&D.

-Username17

[kzt]

So after doing some research I'm starting to like dice pools more and more as a resolution mechanic, but if you want a game that covers a wide range of power levels (like D&D or HERO) you will pretty quickly be rolling a ton of dice.

While you often do roll a ton of dice in HERO, it isn't a dice pool like in SR. You resolve all to-hit or skill rolls with one 3d6, with modifiers changing the target number, not the number of dice used. It's always 3d6. Damage is where you have the huge piles of dice.

[Josh_Kablack]

How do you deal with increasingly large dice pools?

Increasingly Large Dice

[Lago PARANOIA]

I remember awhile back we discussed my alternate idea of having a shifting TN that only shifted by character level in order to manage dicepool size. That is, rather than having the SR3 thing in which TNs shift via a variety of ways, the TN shifts are inviolate. For example, say you had implemented DND4E's tier system. Then the TNs for a 6-sided die would be:

Heroic Tier: TN 5. Summons/Minions in Heroic Tier: TN 6.
Paragon Tier: TN 4. Summons/Minions in Paragon: TN 5.
Epic Tier: TN 3. Summons/Minions in Paragon: TN4.

I know it creates some weirdness like cover or magic swords being more valuable to a high-level character than a low-level one, but honestly I kind of like that effect. Not least because it helps tamp down on the 'minions with buffs' problem but also because I tend to notice that higher-level characters tend to be more tactically careless.

So. What are the interface, mathematical, and stylistic pros and cons with this?

[Drolyt]

So after doing some research I'm starting to like dice pools more and more as a resolution mechanic, but if you want a game that covers a wide range of power levels (like D&D or HERO) you will pretty quickly be rolling a ton of dice.

While you often do roll a ton of dice in HERO, it isn't a dice pool like in SR. You resolve all to-hit or skill rolls with one 3d6, with modifiers changing the target number, not the number of dice used. It's always 3d6. Damage is where you have the huge piles of dice.

What? That was just an example of a game with a very wide range. Combat values range from 1 (standard normal) to 16 (very high powered super). So to convert that to dice pools you would need 20 or so, which isn't actually that bad but HERO keeps bonuses pretty tight. D&D covers less conceptual space (though still more than most games) but has bonuses that can easily end up in the 30s by mid to high levels. So converting D&D to a dicepool would result in fistfuls of dice. Of course one solution is just to keep bonuses tight, but that results in very coarse differentiation between characters, especially for a game like D&D with 20 levels that are supposed to be different.

How do you deal with increasingly large dice pools?

Increasingly Large Dice

You sir are awesome.

Frank, I remember awhile back we discussed my alternate idea of having a shifting TN that only shifted by character level in order to manage dicepool size. That is, rather than having the SR3 thing in which TNs shift via a variety of ways, the TN shifts are inviolate. For example, say you had implemented DND4E's tier system. Then the TNs for a 6-sided die would be:

Heroic Tier: TN 5. Summons/Minions in Heroic Tier: TN 6.
Paragon Tier: TN 4. Summons/Minions in Paragon: TN 5.
Epic Tier: TN 3. Summons/Minions in Paragon: TN4.

I know it creates some weirdness like cover or magic swords being more valuable to a high-level character than a low-level one, but honestly I kind of like that effect. Not least because it helps tamp down on the 'minions with buffs' problem but also because I tend to notice that higher-level characters tend to be more tactically careless.

I read that discussion. I like your idea, my main issue is that I favor TN 4 simply because it has a bell-curve shape making it easier for non-statisticians to understand what it is doing.

[Drolyt]

You know, it occurs to me that the decreasing target numbers pushes people off the RNG. You mention that bonuses from, say, cover are worth more at low target number, but so are all bonuses. This has the effect that the difference between someone who is somewhat good at combat and someone is really good at combat increases as you go up in level under your proposed system, which is probably a bad thing.

[tussock]

Note that D&D doesn't need as much variation as 3e gives it. AD&D had about 15 points between typical starting values and end-game caps for monsters and PCs, other than in a few places where it carried on to purposefully take some game mechanics off the RNG.

You can also cap the game at ~14th level like a sensible person.

But if you want less dice: use a low target number, used fixed successes and cancels for most bonuses and penalties (you may as well with a low TN), and split your variation up by having the defender/trap/puzzle/whatever roll half the dice (or rather less, so things can work more than half the time).

[Drolyt]

Note that D&D doesn't need as much variation as 3e gives it. AD&D had about 15 points between typical starting values and end-game caps for monsters and PCs, other than in a few places where it carried on to purposefully take some game mechanics off the RNG.

You can also cap the game at ~14th level like a sensible person.

But if you want less dice: use a low target number, used fixed successes and cancels for most bonuses and penalties (you may as well with a low TN), and split your variation up by having the defender/trap/puzzle/whatever roll half the dice (or rather less, so things can work more than half the time).

Yeah, now that I've had a chance to run more numbers I don't think it is necessary to have as many bonuses as D&D does. I think that having some bonuses work as automatic hits might also help. Anyways thanks everyone, this site has helped me a lot with understanding the statistics of dice rolling.

[Lago PARANOIA]

You mention that bonuses from, say, cover are worth more at low target number, but so are all bonuses. This has the effect that the difference between someone who is somewhat good at combat and someone is really good at combat increases as you go up in level under your proposed system, which is probably a bad thing.

1.) Make the average difference between someone who is bad at something and good at something converge as time passes.

2.) Practice bonus hygiene. In addition to ensuring that the absolute bonus number a character can get doesn't get too large, also limit (or even eliminate) specialization-specific bonuses altogether. This means that stuff like Greater Weapon Focus and Scaled Favored Enemy shouldn't exist at all in the system.

[Drolyt]

You mention that bonuses from, say, cover are worth more at low target number, but so are all bonuses. This has the effect that the difference between someone who is somewhat good at combat and someone is really good at combat increases as you go up in level under your proposed system, which is probably a bad thing.

1.) Make the average difference between someone who is bad at something and good at something converge as time passes.

Since systems usually have the opposite problem, how do you propose to do this?

2.) Practice bonus hygiene. In addition to ensuring that the absolute bonus number a character can get doesn't get too large, also limit (or even eliminate) specialization-specific bonuses altogether. This means that stuff like Greater Weapon Focus and Scaled Favored Enemy shouldn't exist at all in the system.

This is a good idea anyways. I'm pretty sure the people who decided that bonuses like favored enemy need to go up as you increase in level failed their statistics course.

[Whatever]

You mention that bonuses from, say, cover are worth more at low target number, but so are all bonuses. This has the effect that the difference between someone who is somewhat good at combat and someone is really good at combat increases as you go up in level under your proposed system, which is probably a bad thing.

1.) Make the average difference between someone who is bad at something and good at something converge as time passes.

Since systems usually have the opposite problem, how do you propose to do this?

If you wanted to have that result, you can just give people different starting values, but fixed increases. So, one player rolls level+5 and the other rolls level+3. It's a big difference when level =1, not so much when level = 5, and almost negligible when level = 15.

This assumes that you're not scaling all the opposition to level, though. If the net effect is to keep the first player ahead by 2 the whole time, then you don't converge.

[Seerow]

1.) Make the average difference between someone who is bad at something and good at something converge as time passes.

Since systems usually have the opposite problem, how do you propose to do this?

If you wanted to have that result, you can just give people different starting values, but fixed increases. So, one player rolls level+5 and the other rolls level+3. It's a big difference when level =1, not so much when level = 5, and almost negligible when level = 15.

This assumes that you're not scaling all the opposition to level, though. If the net effect is to keep the first player ahead by 2 the whole time, then you don't converge.

aka, 4e.

[Username17]

If you wanted to have that result, you can just give people different starting values, but fixed increases. So, one player rolls level+5 and the other rolls level+3. It's a big difference when level =1, not so much when level = 5, and almost negligible when level = 15.

This assumes that you're not scaling all the opposition to level, though. If the net effect is to keep the first player ahead by 2 the whole time, then you don't converge.

To expand on Seerow's observation a bit, they did in fact try that in 4e. They are doing it in D&DNext too. It doesn't actually work. Firstly, it is outright not true that a +1 is worth any less when your base bonus is +37 than it is when your base bonus is +2. It works that way for damage, and other things that accumulate action to action, but if you're rolling a d20 against a target number to see if you succeed or fail, that +1 is exactly the same 5% no matter where you are on the RNG. If that d20 is acting as a gateway towards things accumulating (such as a damage roll), that +1 is actually worth proportionately more the closer you are to the edge.

Secondly, giving out fixed bonuses by level doesn't actually even keep characters static with respect to each other. You still get abilities as you go up in level, and Swordy McSwordyface is naturally going to collect all the abilities that improve his fucking swords. And that means that while each +1 is the same 5% at every level, but level 15 he has five of the fucking things and now you're at a 25% difference.

If you want bonuses to converge over time, you gotta be super stingy with the bonuses, you gotta have things that don't stack, and you gotta force people to pick up bonuses in more things. In a system where people simply tag skills and people pick up new skills over time, the skill list of each character can be expected to overlap more and more over time.

If you really want bonuses to converge, you can give out mechanical incentives to having characters learn the skills and powers that their party members have. Say, with a discount or simply waiving the training requirements if one of their party members could be plausibly expected to show how it's done.

-Username17

[Whatever]

4e explicitly raised the DCs in lockstep with level increases, though, so characters never got better at anything. If you're still on the RNG, then your bonuses still matter. But I was talking about a fixed target number, such that higher level characters eventually succeed basically all the time.

That would look more like the old (A)D&D saving throw tables, where some characters start out with huge advantages in particular saves (although everyone is pretty likely to fail most saves they make), but eventually everyone is saving on all but their lowest rolls.

But that kind of system only converges once you move off the RNG, which is probably not a useful place for your game to go.

[Lago PARANOIA]

Since systems usually have the opposite problem, how do you propose to do this?

For a dicepool system (or really, for any system, as some degree of specialization is almost impossible to avoid) you have to make the 'poor' progression advance faster than the 'good' progression.

For example, for my tiered TN system the difference between a Marshal and a Wizard at swording or arcana knowledge is 4 die out of the gate. At the upper echelons, the difference is 1 or even zero. There's no reason why the difference can't actually be negative as time goes on. Even if the Marshal rolls 13 dice in Spellcraft to the Wizard's 11, the wizard has shit like Spell Research and Unbridled Learning to still make him the go-to- guy for Spellcraft.

But I think that too many people would psychologically rebel at the idea of someone who's 'bad' at something actually rolling more base die than someone who's good'. It's counterintuitive even though that's pretty much what needs to be done if you want to have baseline numbers + special abilities that grow over time that don't leave non-specialists in the dust.


None of this changes the fact that even if the baseline numbers are bent to work this way, you still need to do all of the shit FrankTrollman said to prevent the bonus accumulation fiasco that 3E/4E D&D had. For starters, I can totally see a design document rule (that Bruce Cordell will proceed to ignore, but whatevs) for a d6 dicepool system that says that no PC-initiated effect should give unnamed bonuses and under no circumstances should the bonus be higher than three dice. Even at epic levels. A +2 Force Shield should seriously be a campaign bending advantage that singlehandedly transforms a squishy into a front-line fighter, especially at higher levels.

Other things that you can do:

• Get rid of self-scaling effects unless the self-scaling is universal across the board. Such as for Shadowrun's Drain Overcast mechanics.
• Reduce or even eliminate bonus-die self-buffs, especially defensive self-buffs. Self-buffs are reserved for things like increasing your range increment or fixed amounts of healing.
• Eliminate No Self Buffs altogether. Of course you'd want to do this anyway.
• Implement diminishing returns. While people are okay with the paladin who never put a single point in stealth failing every single check to hide at higher levels, they're not okay with a wizard who put in an equivalent skill point investment as the rogue doing so.
• Put a time limit on so-called 'permanent' buffs. This is a controversial suggestion and I'll understand if you don't want to do it, but you should consider having theoretically permanent bonuses like that from a +3 sword not be so permanent. After 100 sword swings or 1 year after the first activation, whichever comes first, the sword becomes a normal-ass sword.
  
  This is effectively what happens in D&D anyway, but in those games you generally 'lose' permanent bonuses for them to be immediately replaced by other ones. In this system, you don't get a better replacement. You may get something totally different (like your +1 Longsword digivolving into a Cloak of the Bat) or even get bupkiss. This way you can preserve the joy of finding new things without bonus accumulation getting out of control.
• Have some sort of invisible system in place to put a 'soft' cap on bonus accumulation. Nothing as clumsy and intrusive as d20 M&M's Power Level limits, I'm thinking more Shadowrun 4E's sustain penalty. Even if the game did print up a bunch of buffing spells, the fact that you take a stacking penalty for each one (ideally) puts a soft cap on how many bonuses a person will put on. Of course the linearly stacking penalty only works because the game uses dicepools, but still.

If you do all that bojangles then you can ensure even in a game that has a lot of power scaling people will rarely roll more than 15 d6s at once and then only for campaign-climaxes made at 16th level.

[Drolyt]

To expand on what Frank says about bonuses, a (say) +6 bonus will, in most die rolling systems, always be worth roughly the same. In D&D you are 30% more likely to hit, in Shadorun 6 bonus dice would increase your expected number of hits by 2. It does not matter what that +6 bonus is adding to. Take Frank's Swordy McSwordyface, if he has a +6 bonus to swords then (using a d20) he is 30% better at swinging swords than the otherwise identical Fighter McFighty. If ten levels into the future they have both improved their fightan man skills by the same amount Swordy McSwordyface will still be 30% better at swinging swords. Except in D&D Swordy McSwordyface will have collected a bunch of bonuses like Superior Sword Swinging and some +5 Sword-chucks (yo!) and will be something like 300% better at swinging swords. Which is bad.

Switching gears, if it matters I've basically already got the answer for my OP, just don't hand out bonuses like D&D does, and if dice pools still get big trade dice in (which isn't ideal because it reduces the variance, but ah well).
Edit: Ninja'd, this post makes most since right after Frank's last post.