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## A search for an optimal resolution mechanic

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OgreBattle
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Post by OgreBattle » Thu Oct 24, 2013 9:34 am

I'm rereading the SAME system, and y'know, a d20 with target numbers just seems completely superior to having increasingly large amounts of dice and modifiers.
Like, "hitpoints are always 10, your defense number goes up" is just way easier to comprehend and not fuck up than "hitpoints keep on going up, dice grow bigger"
Is there ANY advantage that current D&D dice rolling has over just a d20+ target numbers?
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Username17
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Post by Username17 » Thu Oct 24, 2013 10:18 am

> OgreBattle wrote:I'm rereading the SAME system, and y'know, a d20 with target numbers just seems completely superior to having increasingly large amounts of dice and modifiers.
> Like, "hitpoints are always 10, your defense number goes up" is just way easier to comprehend and not fuck up than "hitpoints keep on going up, dice grow bigger"
> Is there ANY advantage that current D&D dice rolling has over just a d20+ target numbers?

It's less operations, especially on the player's side. "Everyone take 30 points of damage" is simply less work to deal with than "everyone take a 30 strength hit, calculate damage." It has drawbacks. It doesn't scale well, it interacts really weirdly at the low and high end. And of course, if you patch it up with DR and damage thresholds and shit you're back to "calculate damage" anyway. But in its most basic state, it is less operations for the player to have to do when they are being attacked.
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Post by silva » Thu Oct 24, 2013 12:23 pm

> OgreBattle wrote:I'm rereading the SAME system, and y'know, a d20 with target numbers just seems completely superior to having increasingly large amounts of dice and modifiers.
> Like, "hitpoints are always 10, your defense number goes up" is just way easier to comprehend and not fuck up than "hitpoints keep on going up, dice grow bigger"
> Is there ANY advantage that current D&D dice rolling has over just a d20+ target numbers?

A single d20 produces no bell curve. This can be a problem, depending on the game premise. (Ie: a more realistic one where you want results to fall on the mid range of the scale to keep extraordinary outcomes to a minimum)
Its what justify a d100 roll-under in increaments of 5 (like the one seen in Runequest 2e) over, say, a single d20. In fact, Greg Stafford made that for Pendragon (adopted a single d20 instead of d100), but then realism is not one of Pendragon goals.
Last edited by silva on Thu Oct 24, 2013 12:25 pm, edited 1 time in total.
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Lago PARANOIA
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Post by Lago PARANOIA » Thu Oct 24, 2013 12:25 pm

> deaddmwalking wrote:Clearly, what he has created is not easier or more intuitive than just rolling large fistfuls of dice.

It's not supposed to be more intuitive or 'easier' (as in a new player can just hop right in) than rolling large fistfuls of dice. What it's supposed to be is faster after you do an elementary amount of memorization -- with the probability curves still being very close to rolling large fistfuls of TN3 d6s.
There's no transformation until you get to 6 dice (though I could easily shift things so that it starts at any point) at TN 3, so newbies starting off the game at low level don't treat it any differently differently than just rolling large fistfuls of dice.

> Josh Kablack wrote:Your freedom to make rulings up on the fly is in direct conflict with my freedom to interact with an internally consistent narrative. Your freedom to run/play a game without needing to understand a complex rule system is in direct conflict with my freedom to play a character whose abilities and flaws function as I intended within that ruleset. Your freedom to add and change rules in the middle of the game is in direct conflict with my ability to understand that rules system before I decided whether or not to join your game.
> In short, your entire post is dismissive of not merely my intelligence, but my agency. And I don't mean agency as a player within one of your games, I mean my agency as a person. You do not want me to be informed when I make the fundamental decisions of deciding whether to join your game or buying your rules system.

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Post by Kaelik » Thu Oct 24, 2013 2:01 pm

> silva wrote:A single d20 produces no bell curve. This can be a problem, depending on the game premise.
> Its what justify a d100 roll-under in increaments of 5 (like the one seen in Runequest 2e) over, say, a single d20.

No. Not at all. A d100 also has no bell curve, so... that cannot be it.

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Post by Red_Rob » Thu Oct 24, 2013 3:41 pm

> silva wrote:Its what justify a d100 roll-under in increaments of 5 (like the one seen in Runequest 2e) over, say, a single d20.

Did... did you just say that because a D100 has two dice it produces a bell curve?
Wow.
And for the record, nothing justifies "a d100 roll-under in increaments of 5 (like the one seen in Runequest 2e)" over a D20. Both have exactly 20 possible results with an exactly equal chance of each result. The D100 just takes more time to roll, more mental effort to process and means you can't make multiple checks at once.
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John Magnum
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Post by John Magnum » Thu Oct 24, 2013 4:07 pm

A d100 takes LESS mental effort to process, because people understand that they have a 35% chance of rolling under 35 better than they understand that they have a 7/20 chance of rolling over 13.
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Post by wotmaniac » Thu Oct 24, 2013 4:17 pm

d20 &#8801; d100 in increments of 5. That's 3rd-grade math, no matter how you slice it.
d100 simply gives bigger #s, to make people feel better.
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Post by RobbyPants » Thu Oct 24, 2013 4:36 pm

> silva wrote: Its what justify a d100 roll-under in increaments of 5 (like the one seen in Runequest 2e) over, say, a single d20. In fact, Greg Stafford made that for Pendragon (adopted a single d20 instead of d100), but then realism is not one of Pendragon goals.

As Kaelik already mentioned, d100 is not a bell curve, despite being two dice. If you added them like 2d10, then you'd have a bell curve.
Now, you could do a bell curve on a d100 by using it to seed a lookup table, but that's a lot of work for no real benefit, so you wouldn't do that.
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Post by RobbyPants » Thu Oct 24, 2013 4:38 pm

> wotmaniac wrote:d20 &#8801; d100 in increments of 5. That's 3rd-grade math, no matter how you slice it.
> d100 simply gives bigger #s, to make people feel better.

There's also the "granularity" aspect, where you can break stuff up into even more fiddly bits (in 1% increments), but it honestly doesn't really add anything. You may play for a whole night and not notice a +1 bonus on a d20 roll. You could play for a whole campaign and not see the benefit of a +1 to a d100 roll.
Of course, that doesn't stop people from fapping to "granularity".
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OgreBattle
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Post by OgreBattle » Thu Oct 24, 2013 5:19 pm

How about 2d10 vs d20?
I remember reading here that bell curves make modifiers a bit wonky, but I forgot what the pros and cons of that was.
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Post by wotmaniac » Thu Oct 24, 2013 5:52 pm

> OgreBattle wrote:How about 2d10 vs d20?
> I remember reading here that bell curves make modifiers a bit wonky, but I forgot what the pros and cons of that was.

Unearthed Arcana covered this.
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Post by PhoneLobster » Thu Oct 24, 2013 10:39 pm

> Lago PARANOIA wrote:What it's supposed to be is faster

...but but Lago! We were told repeatedly at the front end of this thread that dice pools are just as fast or FASTER than rolling one dice! That the time costs were negligible if not negative for marshalling multiple dice and resolving whatever elaborate multi dice mechanic you might want to use!
Why would you need to make them even faster still? Or do you think Frank was wrong about that?
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Post by Foxwarrior » Thu Oct 24, 2013 11:39 pm

4d4+6 gives a pretty similar bell curve to Lago's 24 dicepool replacement.
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Post by Cyberzombie » Thu Oct 24, 2013 11:41 pm

> Foxwarrior wrote:4d4+6 gives a pretty similar bell curve to Lago's 24 dicepool replacement.

I don't think anyone wants to roll a bunch of d4s ever though.
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Post by Lago PARANOIA » Fri Oct 25, 2013 12:29 am

> daenruel87 wrote:I'm sorry Lago but I just don't understand the basics of what you are posting. I understand it is a resolution mechanic but I can't make heads or tails of it. Not to mention Statement B says you have a 10 die absolute maximum and then you talk about die pools of 13, 16, and 24.
> Im lost man

> Clearly, what he has created is not easier or more intuitive than just rolling large fistfuls of dice.

Fair enough. Let's try this one more time. Less memorization and calculating extra dice and autohits are two medium-length sentences.
I'd like to reiterate, though, that it's not going to be more intuitive than just rolling the number of dice equal to a 2-digit number on your sheet. That's like the easiest thing in the world. However, the point is to make doing so is to A.) make it less clunky at the table, B.) still make the process of counting pretty quick C.) still have the broad functionality of dicepools with an easy-to-calculate probability curve rather than having some strange hodgepodge.
http://anydice.com/program/2c78

Dicepool | Base | Auto | Extra Dice
12 | 6 | 4 | 2
13 | 7 | 4 | 2
14 | 8 | 4 | 2
15 | 9 | 4 | 2
16 | 10 | 4 | 2
17 | 11 | 4 | 2
18 | 6 | 8 | 3
19 | 7 | 8 | 3
20 | 8 | 8 | 3
21 | 9 | 8 | 3
22 | 10 | 8 | 3
23 | 11 | 8 | 3
24 | 6 | 12 | 4
25 | 7 | 12 | 4
26 | 8 | 12 | 4
27 | 9 | 12 | 4
28 | 10 | 12 | 4
29 | 11 | 12 | 4
30 | 12 | 12 | 4

[*] Your modified dicepool roll now is [Hits of TN3 Base Die] + [Auto Die] + Result of Extra Die.
[*] There are no longer those weirdass 1d4 or 1d8/2 extra dice. All extra dice are d6s. To determine the value of an extra dice, if you roll a 1 or 2 you subtract a hit. 3 or 4 ignore the extra dice. 5 or 6, add to the hit. If you bought specialty dice, even better. Just add the -1, 0, or 1 per dice to the Base and Auto Die. If not, that's okay, any d6 will do.
[*] Until you have 12 or more dice, you don't worry about using a modified dicepool. So a large proportion of games won't even have to worry about them except for special occasions.
[*] Breakpoints for modifying your modified dicepool are at multiples of 6. This is so that people have less memorization to do.
[*] I'm going with the assumption that rolling more than 16 dice is uncalled for and even doing more than 12 as a matter of course is too much.
[*] The probability simulator has a top end of 30 dice and is supposed to range from D&D's inerpretation of a crap-covered peasant to a top-end deity. Since the TN is 3 this is pretty reasonable.
[*] The curves of an actual dicepool versus an unmodified dicepool starts to diverge at the 24 dice mark. I could make them fit closely again by just throwing in another extra dice, but that's a bit too much. It would make the formula too unituitive as I mentioned and I can't imagine anything short of DBZ that needs more than 30 TN3 dice, even when mapping strength from a housecat to Vecna... assuming 3 dice is the difference in strength between an average healthy human and a bodybuilder.
[*] If for some reason you need to roll more than 30 dice the formula for going past that point is simple. For every multiple of six dice in the pool, use another Extra Dice. Subtract 6x the number of extra dice you have to determine your dicepool. Extra dice minus one times four is the number of autohits you have.
Last edited by Lago PARANOIA on Fri Oct 25, 2013 12:34 am, edited 2 times in total.

> Josh Kablack wrote:Your freedom to make rulings up on the fly is in direct conflict with my freedom to interact with an internally consistent narrative. Your freedom to run/play a game without needing to understand a complex rule system is in direct conflict with my freedom to play a character whose abilities and flaws function as I intended within that ruleset. Your freedom to add and change rules in the middle of the game is in direct conflict with my ability to understand that rules system before I decided whether or not to join your game.
> In short, your entire post is dismissive of not merely my intelligence, but my agency. And I don't mean agency as a player within one of your games, I mean my agency as a person. You do not want me to be informed when I make the fundamental decisions of deciding whether to join your game or buying your rules system.

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Post by virgil » Fri Oct 25, 2013 12:34 am

> PhoneLobster wrote:

> > Lago PARANOIA wrote:What it's supposed to be is faster

> ...but but Lago! We were told repeatedly at the front end of this thread that dice pools are just as fast or FASTER than rolling one dice! That the time costs were negligible if not negative for marshalling multiple dice and resolving whatever elaborate multi dice mechanic you might want to use!
> Why would you need to make them even faster still? Or do you think Frank was wrong about that?

&#936;...we get it, you hate Frank and everything he says, like, ALL the time.
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Post by PhoneLobster » Fri Oct 25, 2013 12:44 am

> virgil wrote:&#936;...we get it, you hate Frank and everything he says, like, ALL the time.

Actually I hate dice pool mechanics and I want a fucking honest admission about the insane costs of rolling fistfuls of dice from at least one fucking dishonest dice pool adherent EVER.
I'm still waiting for Lago or ANYONE to honestly answer THIS from back in this thread...

> PhoneLobster wrote:

> > Lago PARANOIA wrote:A median time of 1-1.5 seconds?! Bitch, please. That's just how long it takes to reach over the notes and actually pick up the d20.

> Aaaand how long does it take you to reach over and pick up a variable number of d6s you've just now determined/been told from a larger pile of d6s and clear away similar d6s for the roll?
> Simple thought exercise Lago? Same amount of time or more?

Last edited by PhoneLobster on Fri Oct 25, 2013 12:46 am, edited 1 time in total.
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Post by virgil » Fri Oct 25, 2013 1:11 am

I wouldn't call myself an adherent, but I don't really hold any preference between dice pools, single dice, and bell curves; which probably makes me an adherent in your eyes.
I'll say that it takes longer to roll the 8d6 (TN 5) than it does to roll 1d20. Feel better? I will also say that it's not enough to matter. Once you make the TN variable, get much more than a dozen dice in one roll, or use something other than d6s, then I'll start feeling encumbered. All three, like in Deadlands, and I'll groan in annoyance but will still find it better than no game at all.
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Strung Nether
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Post by Strung Nether » Fri Oct 25, 2013 1:38 am

One point for rolling fistfulls of d6s is that if you get some custom dice, IE 2 white sides and 4 black sides for shadowrun, counting the successes is really fast, and you don't have to do any math.
rolling one d20 is probably faster, but then you have to do math like addition and shit...and no one likes math. You look at the dice, look at the 4 numbers you need to add to it, and feel like a fucking idiot because you spent 5 years in college learning how to be an engineer and cant add shit without making a mistake or doing it multiple times.
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Post by Foxwarrior » Fri Oct 25, 2013 1:54 am

Okay, the 4d4 thing I suggested isn't actually a pattern. This one is better than Lago's, though, as long as you're willing to use three kinds of specialty d6s:
http://anydice.com/program/2c7a
It can represent a 27 die pool with only 9 dice. The maximum roll is equal to the dicepool-equivalent size, and the chance of getting the maximum roll always decreases, it never increases. The standard deviation always increases, too, but not too quickly. It even implements that automatic hit mechanic in a non-jumpy manner.
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Post by Strung Nether » Fri Oct 25, 2013 1:58 am

> Foxwarrior wrote:things

that's actually really cool.
Last edited by Strung Nether on Fri Oct 25, 2013 2:28 am, edited 1 time in total.
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Lago PARANOIA
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Post by Lago PARANOIA » Fri Oct 25, 2013 2:00 am

Well, if speed was the only thing I cared about I'd probably go with a linear RNG. The d20 has a lot of advantages such as having easily calculated probabilities, easily calculated probability shifts, and also being fast.
However, it also has some weaknesses that I don't particularly care for.
[*] All numbers away from the average but on the RNG are equally likely. In some ways this is a good thing because it makes combats more exciting. I talk about it a bit more later, but, it does create stupidity like your muscleman barbarian losing an arm-wrestling competition to a wizard in 3 out of 10 matches.
[*] d20 doesn't lock out until numbers start to get unmanagably high. You need a 18 point shift to get a 90% lockout. If you repeat this process a couple of times, you start throwing around +54s and such.
[*] If you're teetering between an 'almost but not quite locked out' and a 'unfavorable but fighting chance' position on the RNG then dicepools are less resilient to RNG shifts. For example, making orcs or skeletons threatening to mid-level adventurers is very hard. Giving them masterwork equipment and the high ground helps but doesn't quite make them much more of a threat.
[*] Dicepool circumstantial bonuses are easier to keep track of. If you wanted to simulate the above effect on a d20, you'd have to do stuff like remember high ground is +1, masterwork equipment is another +1, flanking is +2, etc.. The vast majority of TN3 dicepool bonuses are +1, so you just need to list the circumstances rather than list the circumstances AND the bonuses.
[*] Dicepools, or rather those with low TNs, generate fewer black swan events near the average range. This may or may not be desirable. In a 4-color superhero game with mild consequences for losing or setbacks, generating a lot of black swan events is great. In a game like D&D they can be memorable but can also cause a lot of frustration. People will remember the time that the 9th-level party cleric got decapitated by two lucky ogre greataxe criticals more than them doing the same to a CR+2 storm giant.
Last edited by Lago PARANOIA on Fri Oct 25, 2013 2:02 am, edited 1 time in total.

> Josh Kablack wrote:Your freedom to make rulings up on the fly is in direct conflict with my freedom to interact with an internally consistent narrative. Your freedom to run/play a game without needing to understand a complex rule system is in direct conflict with my freedom to play a character whose abilities and flaws function as I intended within that ruleset. Your freedom to add and change rules in the middle of the game is in direct conflict with my ability to understand that rules system before I decided whether or not to join your game.
> In short, your entire post is dismissive of not merely my intelligence, but my agency. And I don't mean agency as a player within one of your games, I mean my agency as a person. You do not want me to be informed when I make the fundamental decisions of deciding whether to join your game or buying your rules system.

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Post by Lago PARANOIA » Fri Oct 25, 2013 2:14 am

http://anydice.com/program/2c7b
Alternatively: If there's a really pressing need to traverse the entire top RNG, the extra dice can have a set of {-2,-1,0,0,1,2} which maps to {1,2,3,4,5,6} on the d6 -- you will have to reduce each of the extra dice in the chart.
That makes the curves fit pretty closely. Moreover, it's also one fewer die to keep track of. And fewer dice are go. However, I chose not to do that because while I'm pretty sure humans can subtract 1 just as quickly as they can add 1, I don't know about some random sequence of -2s and 1s and 2s and such. It's not that many extra dice what with being from 2-4 but I'm worried about there being a dip in resolution time.
You still won't be able to plumb the bottom of the RNG, but considering that you have less than 1/100,000th of a chance even in a regular d6 dicepool of size 18, TN3 to get a 3 or lower I don't see that as a big deal.
http://anydice.com/program/2c7d

> Foxwarrior wrote:It can represent a 27 die pool with only 9 dice. The maximum roll is equal to the dicepool-equivalent size, and the chance of getting the maximum roll always decreases, it never increases. The standard deviation always increases, too, but not too quickly. It even implements that automatic hit mechanic in a non-jumpy manner.

I'm amazed at how smooth that shit is, but, I'm honestly not a fan. There's no way most people will be able to use your formula without having to look at a table for every dice roll, because sometimes the amount of a particular kind of dice goes up and sometimes it goes down.
What's more, your setup is pretty much impossible to place without specialty dice. People are going to get dice mixed up and shit. If you had just two separate groups it'd be easy enough to keep them separate just by throwing them in different spots, but not with three.
Still, I recognize your criticism about a smooth curve and offer a counter-proposal:
http://anydice.com/program/2c7d
It uses the same basic setup I outlined with the chart, except:
[*] Despite a noticeable jump in autohits per multiple of 6, it's still a pretty smooth transition.
[*] Subtract one from the extra dice chart in all cases. So 12-18, you use one Extra Die. 19-23, you use two Extra Die. 24-30, you use three. The maximum number of dice you'll ever be rolling is 15 and that's like for Zeus locked in mortal combat with Odin.
[*] The Extra dice set is {-2,-1,0,0,1,2} instead of {-1,-1,0,0,1,1}. I'm hoping that people won't find subtracting 2 repeatedly harder than subtracting 1. However, it's only 3 Extra Dice at the top quintile of the range.
Last edited by Lago PARANOIA on Fri Oct 25, 2013 3:00 am, edited 3 times in total.

> Josh Kablack wrote:Your freedom to make rulings up on the fly is in direct conflict with my freedom to interact with an internally consistent narrative. Your freedom to run/play a game without needing to understand a complex rule system is in direct conflict with my freedom to play a character whose abilities and flaws function as I intended within that ruleset. Your freedom to add and change rules in the middle of the game is in direct conflict with my ability to understand that rules system before I decided whether or not to join your game.
> In short, your entire post is dismissive of not merely my intelligence, but my agency. And I don't mean agency as a player within one of your games, I mean my agency as a person. You do not want me to be informed when I make the fundamental decisions of deciding whether to join your game or buying your rules system.

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PhoneLobster
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Post by PhoneLobster » Fri Oct 25, 2013 2:33 am

> Lago PARANOIA wrote:[*] All numbers away from the average but on the RNG are equally likely. In some ways this is a good thing because it makes combats more exciting. I talk about it a bit more later, but, it does create stupidity like your muscleman barbarian losing an arm-wrestling competition to a wizard in 3 out of 10 matches.

That seems like a highly contrived example that no one cares about. And all the more reason to run with the "and for highly contrived examples no one cares about maybe you shouldn't even be rolling at all" type of approach recently discussed.

> [*] d20 doesn't lock out until numbers start to get unmanagably high. You need a 18 point shift to get a 90% lockout. If you repeat this process a couple of times, you start throwing around +54s and such.

And if you care about that so much you just use a smaller linear RNG. Those +18s are only required when they are productively achieving something. If they aren't you're using the wrong size of dice.

> [*] If you're teetering between an 'almost but not quite locked out' and a 'unfavorable but fighting chance' position on the RNG then dicepools are less resilient to RNG shifts. For example, making orcs or skeletons threatening to mid-level adventurers is very hard. Giving them masterwork equipment and the high ground helps but doesn't quite make them much more of a threat.

That is just insanity. It doesn't even parse well enough to make clear what you think your advantage here exactly is.

> [*] Dicepool circumstantial bonuses are easier to keep track of. If you wanted to simulate the above effect on a d20, you'd have to do stuff like remember high ground is +1, masterwork equipment is another +1, flanking is +2, etc.. The vast majority of TN3 dicepool bonuses are +1, so you just need to list the circumstances rather than list the circumstances AND the bonuses.

The bonuses are actually about the same to keep track of. Their EFFECT in a dice pool system is really rather hard to keep track of. That is a net loss. A major one. Even THE major one. On it's own it kills dice pools as a viable base mechanic for most RPGs and for D&D in particular.

> [*] Dicepools, or rather those with low TNs, generate fewer black swan events near the average range. This may or may not be desirable.

It simply isn't desirable at all. It is flat out horrible. If you are using a rolling mechanic with a vanishingly small chance in the mere 0.01's of a percent chance range of some result it undermines ANY ability to design a sensible mechanical output for that result.
On the one hand you flat out may as well not even roll once you have anything close to a large number of dice. The results are going to be so close to a quick average that your largely wasting your time hoping for a rare outlier.
But if a rare outlier DOES happen, if the actual results are weighted remotely according to the value of it's rarity, holy crap does that break games. I mean you took the time of writing in a 0.01% chance of a particular result, so what IS an appropriate 0.01% likelihood of being stabbed with a blunt shiv by a level 0 street urchin for your 10th level barbarian?
Go ahead WHAT justifies those odds in that circumstance? It's not "he just succeeds in dealing minor damage" because that's just not fucking enough to justify the mechanic needed to generate that low a chance. And it's not "he kills the barbarian instantly" because that's fucking insanely stupidly bad for the game (but actually worth the mechanical cost). SO WHAT THE FUCK IS IT?
Last edited by PhoneLobster on Fri Oct 25, 2013 2:35 am, edited 2 times in total.
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