Let's start a fight: 2d10 🎲 makes more sense than 1d20 - change my mind.
Every time I roll a d20, I am just as likely (percentage-wise) to end up with a critical failure as I am to just barely succeed, because every face on the die (theoretically) is just as likely to come up as any other.
Whereas with 2d10, the likelihood of rolling an "average" check or save (10, 11, 12) is significantly higher than getting a critical failure (double 1's) or critical success (double 10's). Not only does the 2d10 model more accurately represent a realistic potential outcome, but it also makes your skill bonuses (or penalty) more meaningful because it reliably increases (or decreases) the likely average of all your rolls, instead of just sliding the window one direction or the other.
Welcome to why almost every other TTRPG system in the entire world uses pools of dice rather than a single highly variable die to track skill outcomes. Dice pools are not only more predictable, they're more controllable and can account for factors beyond anything a d20 can manage. The highly reduced chances of criticals (either success or failure) also means those results can be made more punchy and memorable.
I'd be curious to see what a 2d10 game of D&D would look like. That might even be a better fit for the whole 'Proficiency Die' approach some folks like, rolling a d(Whatever) instead of using a flat bonus. There's a few different ways one could use a 2d10 basis to build a dice pool rather than just throwing one die and praying.
Would also make armor class matter a lot more, since highly variable swings would be significantly less common. An AC of 20 becomes a lot harder to hit when you're throwing 2d10 instead of a d20 that can spit giant numbers out at a whim. Might help some of 5e's issues with AC, which is a boon in and of itself.
There'd have to be a ton of rules rewrites, but man. The idea of rolling a pool instead of a single ****-you-20 sounds nice, doesn't it?
D&D started off with people getting a bunch of polyhedron dice and figuring out what to use for each one. The d20 is basically a relic of the early days; wither its better or worse than 2d10 doesn't really matter, because its a sacred cow. I cannot ever see them getting rid of it.
I play four games - D&D, Shadowrun, Vampire, and Mutants and Masterminds. Vampire uses d10s. Shadowrun uses d6s. M&M... uses a single d20.
2d10 stays within the game's accuracy range, though. One could theoretically drop 2d10 into any content written for 1d20, and so long as they have a way of covering advantage/disadvantage and any of the rules that specifically reference the d20, nothing else needs to be rewritten.
But what I've actually been getting into my head lately is hacking Fantasy Flight Games's Star Wars/Genesys narrative dice into D&D, which would be the best (for my tastes, of course).
2d10 only gives you 19 possible outcomes with a standard bell curve ass opposed to the 1d20’s 20 variables with the flat line.
3d6 only gives you 15 possible outcomes with a very steep curve.
2d12 gives 23 possible variables with the same bell curve as 2d10.
Why is “more possible outcomes” an inherent good?
Also, two dice isn’t enough to approximate a normal distribution, so I’m not really sure 2d10 could be said to give a “standard bell curve.” 3d6 does a better job at achieving that, if “standard bell curve” is something you’re after.
So I’m not going to argue the math, because the math argument is sound.
The fun of D&D is sitting at a table with your friends and figuring things out and then letting fate try its hand. The highest of highs and the lowest of lows, but all should be fun. Your table mates should bring you up on critical fumbles, and cheer on your successes on critical successes. By doing 2d10/2d12, a lot of the drama and high stakes goes away. Now we’re just rolling averages more often on all sides, which now truly makes this a game of math. Why make a crit heavy build when the odds of getting one are lower? What’s the point of the game if the outcome is assumed success because of the law of averages? This removes an element out of the game that is a core element, with no balancing around it.
My most memorable moments in table top revolve around critical fumbles and how the party bands together to overcome them. I’d never go to this method.
2d10 only gives you 19 possible outcomes with a standard bell curve ass opposed to the 1d20’s 20 variables with the flat line.
3d6 only gives you 15 possible outcomes with a very steep curve.
2d12 gives 23 possible variables with the same bell curve as 2d10.
2d10 (or 2d<any>) doesn't give a bell curve; it gives a simple "peak." 3d6 gives an excellent bell curve.
Also, 1d20 is range 1-20, average/median 10.5.
2d10 is range 2-20, average/median 11.
2d12 is range 2-24, average/median 13.
3d6 is range 3-18, average/median 10.5.
If you want a bell curve that centers on the same value as 1d20, you want 3d6.
Yes, you are correct about the peak.
But if you focus on the 10.5 and go with the 3d6, you can no longer hit those higher numbers, so AC, Save DCs, Check FCs, they would all need to be adjusted downward further narrowing the bounded accuracy. With 2d12 (or 3d8 if you prefer) the bounded accuracy can be spread out a little more which allows for a little more variation in pretty much absolutely everything about the game.
Remember, that 10.5 only matters because it is the midpoint between 1 and 20. If the spread is 2-24 (or 3-24), then the 13 (or 13.5) becomes the relevant number.
But if you focus on the 10.5 and go with the 3d6, you can no longer hit those higher numbers, so AC, Save DCs, Check FCs, they would all need to be adjusted downward further narrowing the bounded accuracy. With 2d12 (or 3d8 if you prefer) the bounded accuracy can be spread out a little more which allows for a little more variation in pretty much absolutely everything about the game.
Remember, that 10.5 only matters because it is the midpoint between 1 and 20. If the spread is 2-24 (or 3-24), then the 13 (or 13.5) becomes the relevant number.
The midpoint matters because it reflects the average expected roll, which a number of things are designed around. (If you adjust it up, you're essentially giving every roll a bonus.)
If you actually want a bell curve (which maybe you don't, if keeping the bounds the exact same is important), you don't care so much about the bounds. The whole point is the increased likelyhood of getting "somewhere near the middle" which makes rolls (and thus tasks) more predictable.
If you really really want both, you could so something like 3d20/3 (or 4d20/4, etc), and add math. But if you're already going with a bell curve, you probably need to adjust lots of things for game balance, anyway, including expectations about the bounds. I just think that it's easier on said design to prioritize the same average over the same bounds.
Although you are right, OP, that using pooled dice works better than a single die due to having a more normal-ish vs. uniform distribution... using a RNG with a bell curve rather than a uniform distribution would kind of not be D&D anymore. Part of what makes D&D is the fact that it is so swingy.
If you want a less swingy game, as Yurei says, almost every other RPG ever made will give you that. Champions is a good example -- it uses the 3D6 model, with "11 or less" as the base chance (slightly over 50%), and most rolls end up between 8 and 14 (which is why "low chance" is 8 or less, and "high chance" is 14 or less in Champions). Crit fail and crit success only occur on 18 and 3 (respectively), which happens 1 in 216 -- WAY less often than the 1 in 20 in D&D. WAY.
And yes, those 18s and 3s are super memorable, because they almost never happen. And the one night the unluckiest guy at the table (or at least we used to say this) rolled an 18 three times... I will never, ever, forget that.
Lots of times I've had people roll three 1s over the course of a night or three 20s... it's not super frequent but it's happened at least a few times in the last 10 months of my current bi-weekly campaign. Three 18s in a single session though? That happened once... ever. I remember who did it. I remember whose house we were playing in. I remember that I was the GM. And I remember the two guys sitting next to the player rolling, after the 3rd one, moving away from him so that he couldn't touch them, because they didn't want his bad karma to rub off on them.
However, again, much as I prefer, mathematically, the Champions way, if I wanted to play a game with 3D6 to hit, I would just play Champions (or Fantasy Hero), rather than try to hack D&D to use it.
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2d10 only gives you 19 possible outcomes with a standard bell curve ass opposed to the 1d20’s 20 variables with the flat line.
3d6 only gives you 15 possible outcomes with a very steep curve.
2d12 gives 23 possible variables with the same bell curve as 2d10.
Why is “more possible outcomes” an inherent good?
Also, two dice isn’t enough to approximate a normal distribution, so I’m not really sure 2d10 could be said to give a “standard bell curve.” 3d6 does a better job at achieving that, if “standard bell curve” is something you’re after.
I think more possible outcomes are good for some results table, which can also be placed on a curve. In just regular rolling whether for table results or a task check, wouldn't the extremes be less frequent? But this isn't my expertise, so I'm writing more to test my assumptions rather than really answer your query.
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I think more possible outcomes are good for some results table, which can also be placed on a curve. In just regular rolling whether for table results or a task check, wouldn't the extremes be less frequent? But this isn't my expertise, so I'm writing more to test my assumptions rather than really answer your query.
If you're rolling to look up a result on a table (especially a table with a set number of results expecting a flat curve), use the dice the table was designed for.
I'm not so much interested in the shape of the probability curve, as it were. I'm more interested in the fact that having a base level of competency is supposed to MEAN something. It is supposed to mean that when you try to do a thing based on your skill at other similar things, there is an expectation of your ability to perform, meaning that you are more likely to do average (ie roll a 10 or 11) than you are to fail or succeed in a spectacular fashion (ie roll a 1 or 20). The 1d20 roll puts all possible outcomes on exactly equal footing, whereas a 2d10 (or other dice pool) model means that the character is ten times more likely perform up to her expected skill level, which seems to me to be the entire point of having skill or attribute scores, bonuses and penalties in the first place.
With regard to the "more predictable=more boring" argument, I suppose it depends greatly on your intended play style. Super swingy-ness makes more sense in a lighthearted or wacky adventure where every roll can result in hilarious little tragedies that alter the storyline in fun ways. For something more gritty or hardcore, changing from 1d20 to 2d10 means that the chances of catastrophic failure is reduced from 5% per roll to 0.8% per roll, leaving room for some really emotional, gut-punch moments of unexpected failure that alter the course of a characters life and/or story arc.
Regarding the question about building around the expectation of crits, that can be easily mathed out at the table. For example, the Improved Critical skill for Champions gives you a crit on 19 or 20, which is effectively a 10% chance on 1d20. In a 2d10 system I could award a crit on a result of 17, 18, 19, or 20. This spread gives me 10 possible crit rolls on a chart of 120, or just barely over 8%. Additional perks could be tacked on to make up any perceived dip in effectiveness up to and including extra damage on crit or even an extra attack roll.
Or maybe I'm over thinking it and I should just not ask players to roll as often...
So I’m not going to argue the math, because the math argument is sound.
The fun of D&D is sitting at a table with your friends and figuring things out and then letting fate try its hand. The highest of highs and the lowest of lows, but all should be fun. Your table mates should bring you up on critical fumbles, and cheer on your successes on critical successes. By doing 2d10/2d12, a lot of the drama and high stakes goes away. Now we’re just rolling averages more often on all sides, which now truly makes this a game of math. Why make a crit heavy build when the odds of getting one are lower? What’s the point of the game if the outcome is assumed success because of the law of averages? This removes an element out of the game that is a core element, with no balancing around it.
My most memorable moments in table top revolve around critical fumbles and how the party bands together to overcome them. I’d never go to this method.
For a lot of older players, the d20 is so essentially D&D that not only is any D&D without a d20 Not D&D, but any game that doesn't use the d20 is itself so far from How A Tabletop RPG Should Be that it's not worth playing. It's one of the primary reasons Wizards remains so successful - D&D is the progenitor of the model and thus the only game people care about.
But for me, the d20 is no more essential to D&D than the d4 is. For me, the one thing D&D truly gets right is its willingness to let the players do shit. Genesys is often lauded for its Story Dice system, but having been looking into Genesys recently, the game is absolute moose piss for anything but a modern-world muggles game where no one can accomplish anything worthwhile. The one critical failure of most modern games with more advanced dice systems is criminally limiting the abilities of anyone in the game to do anything that a random New York cab driver couldn't pull off. Magic, supertechnology, psychic powers, even just people with enhanced abilities like Captain America - these games all tend to handle them extremely poorly.
The core of D&D, for me and many others, is the fact that you can be awesome. Want to be a wizard who can rain fire from the sky, summon dragons, become a dragon, teleport across planes, and do all that other Good Shit? Just level up enough and you're golden. Want to be a deadly bladesman who can slay even the mightiest of foes with a single stroke of your sword? Rogue's got you. So on and so forth.
That sense of progression is the core of D&D to me. Very few modern games allow for any sort of meaningful character progression; they focus so much on the story that they forget the characters playing in it. Genesys is absolutely terrible about it; Savage Worlds is better but not amazing. GURPS does progression well depending on the GM, but good luck convincing anyone to play GURPS.
But that's why I figure folks would hack a better dice system into D&D. Because the trappings of D&D aren't as important as its spirit, which is the collected lore of the game, its unique bestiary and history, and the fact that characters actually grow as they play. That's why implementing 2d10 into D&D is a better idea than just fluffing a Genesys game as "D&D". Because frankly, I do not have high hopes for this Genesys game I'm looking to be playing in soon X_X
i'm in yurei's boat. 2d10 makes no more sense than d20 because the rolls don't actually matter very much at all. in fact, can't actually recall a single game i've played where they actually changed the outcome.
I'm not so much interested in the shape of the probability curve, as it were. I'm more interested in the fact that having a base level of competency is supposed to MEAN something. It is supposed to mean that when you try to do a thing based on your skill at other similar things, there is an expectation of your ability to perform, meaning that you are more likely to do average (ie roll a 10 or 11) than you are to fail or succeed in a spectacular fashion (ie roll a 1 or 20). The 1d20 roll puts all possible outcomes on exactly equal footing, whereas a 2d10 (or other dice pool) model means that the character is ten times more likely perform up to her expected skill level, which seems to me to be the entire point of having skill or attribute scores, bonuses and penalties in the first place.
D&D 5E doesn't use critical successes or failures outside attack rolls. A 20 has the exact same outcome as a 15, as long as that 15 is sufficient to meet the DC. A 1 has the exact same outcome as a 5, as long as that 5 is insufficient to meet the DC. "All possible outcomes" (optional or homebrew rules notwithstanding) is two outcomes: success or failure. And unless you need to roll 11 or higher for success, they're not on exactly equal footing.
Let's start a fight:
2d10 🎲 makes more sense than 1d20 - change my mind.
Every time I roll a d20, I am just as likely (percentage-wise) to end up with a critical failure as I am to just barely succeed, because every face on the die (theoretically) is just as likely to come up as any other.
Whereas with 2d10, the likelihood of rolling an "average" check or save (10, 11, 12) is significantly higher than getting a critical failure (double 1's) or critical success (double 10's). Not only does the 2d10 model more accurately represent a realistic potential outcome, but it also makes your skill bonuses (or penalty) more meaningful because it reliably increases (or decreases) the likely average of all your rolls, instead of just sliding the window one direction or the other.
What do you think?
Welcome to why almost every other TTRPG system in the entire world uses pools of dice rather than a single highly variable die to track skill outcomes. Dice pools are not only more predictable, they're more controllable and can account for factors beyond anything a d20 can manage. The highly reduced chances of criticals (either success or failure) also means those results can be made more punchy and memorable.
I'd be curious to see what a 2d10 game of D&D would look like. That might even be a better fit for the whole 'Proficiency Die' approach some folks like, rolling a d(Whatever) instead of using a flat bonus. There's a few different ways one could use a 2d10 basis to build a dice pool rather than just throwing one die and praying.
Would also make armor class matter a lot more, since highly variable swings would be significantly less common. An AC of 20 becomes a lot harder to hit when you're throwing 2d10 instead of a d20 that can spit giant numbers out at a whim. Might help some of 5e's issues with AC, which is a boon in and of itself.
There'd have to be a ton of rules rewrites, but man. The idea of rolling a pool instead of a single ****-you-20 sounds nice, doesn't it?
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:shrug:
D&D started off with people getting a bunch of polyhedron dice and figuring out what to use for each one. The d20 is basically a relic of the early days; wither its better or worse than 2d10 doesn't really matter, because its a sacred cow. I cannot ever see them getting rid of it.
I play four games - D&D, Shadowrun, Vampire, and Mutants and Masterminds. Vampire uses d10s. Shadowrun uses d6s. M&M... uses a single d20.
I actually did a bunch of statistics for an RPG some friends of mine and I were developing, and 2d12 works just a wee bit better than 2d10 IMO.
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2d10 stays within the game's accuracy range, though. One could theoretically drop 2d10 into any content written for 1d20, and so long as they have a way of covering advantage/disadvantage and any of the rules that specifically reference the d20, nothing else needs to be rewritten.
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3d6 is even better than 2d10.
But what I've actually been getting into my head lately is hacking Fantasy Flight Games's Star Wars/Genesys narrative dice into D&D, which would be the best (for my tastes, of course).
2d10 only gives you 19 possible outcomes with a standard bell curve ass opposed to the 1d20’s 20 variables with the flat line.
3d6 only gives you 15 possible outcomes with a very steep curve.
2d12 gives 23 possible variables with the same bell curve as 2d10.
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One could use a d12 for 0 to 11, with the natural 12 counting as zero.
Then 2d12 produces 0 to 22, averaging 11, which seems somewhat comparable to 1 to 20, averaging 10.5.
he / him
2d10 (or 2d<any>) doesn't give a bell curve; it gives a simple "peak." 3d6 gives an excellent bell curve.
Also, 1d20 is range 1-20, average/median 10.5.
If you want a bell curve that centers on the same value as 1d20, you want 3d6.
Why is “more possible outcomes” an inherent good?
Also, two dice isn’t enough to approximate a normal distribution, so I’m not really sure 2d10 could be said to give a “standard bell curve.” 3d6 does a better job at achieving that, if “standard bell curve” is something you’re after.
So I’m not going to argue the math, because the math argument is sound.
The fun of D&D is sitting at a table with your friends and figuring things out and then letting fate try its hand. The highest of highs and the lowest of lows, but all should be fun. Your table mates should bring you up on critical fumbles, and cheer on your successes on critical successes. By doing 2d10/2d12, a lot of the drama and high stakes goes away. Now we’re just rolling averages more often on all sides, which now truly makes this a game of math. Why make a crit heavy build when the odds of getting one are lower? What’s the point of the game if the outcome is assumed success because of the law of averages? This removes an element out of the game that is a core element, with no balancing around it.
My most memorable moments in table top revolve around critical fumbles and how the party bands together to overcome them. I’d never go to this method.
Yes, you are correct about the peak.
But if you focus on the 10.5 and go with the 3d6, you can no longer hit those higher numbers, so AC, Save DCs, Check FCs, they would all need to be adjusted downward further narrowing the bounded accuracy. With 2d12 (or 3d8 if you prefer) the bounded accuracy can be spread out a little more which allows for a little more variation in pretty much absolutely everything about the game.
Remember, that 10.5 only matters because it is the midpoint between 1 and 20. If the spread is 2-24 (or 3-24), then the 13 (or 13.5) becomes the relevant number.
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The midpoint matters because it reflects the average expected roll, which a number of things are designed around. (If you adjust it up, you're essentially giving every roll a bonus.)
If you actually want a bell curve (which maybe you don't, if keeping the bounds the exact same is important), you don't care so much about the bounds. The whole point is the increased likelyhood of getting "somewhere near the middle" which makes rolls (and thus tasks) more predictable.
If you really really want both, you could so something like 3d20/3 (or 4d20/4, etc), and add math. But if you're already going with a bell curve, you probably need to adjust lots of things for game balance, anyway, including expectations about the bounds. I just think that it's easier on said design to prioritize the same average over the same bounds.
Although you are right, OP, that using pooled dice works better than a single die due to having a more normal-ish vs. uniform distribution... using a RNG with a bell curve rather than a uniform distribution would kind of not be D&D anymore. Part of what makes D&D is the fact that it is so swingy.
If you want a less swingy game, as Yurei says, almost every other RPG ever made will give you that. Champions is a good example -- it uses the 3D6 model, with "11 or less" as the base chance (slightly over 50%), and most rolls end up between 8 and 14 (which is why "low chance" is 8 or less, and "high chance" is 14 or less in Champions). Crit fail and crit success only occur on 18 and 3 (respectively), which happens 1 in 216 -- WAY less often than the 1 in 20 in D&D. WAY.
And yes, those 18s and 3s are super memorable, because they almost never happen. And the one night the unluckiest guy at the table (or at least we used to say this) rolled an 18 three times... I will never, ever, forget that.
Lots of times I've had people roll three 1s over the course of a night or three 20s... it's not super frequent but it's happened at least a few times in the last 10 months of my current bi-weekly campaign. Three 18s in a single session though? That happened once... ever. I remember who did it. I remember whose house we were playing in. I remember that I was the GM. And I remember the two guys sitting next to the player rolling, after the 3rd one, moving away from him so that he couldn't touch them, because they didn't want his bad karma to rub off on them.
However, again, much as I prefer, mathematically, the Champions way, if I wanted to play a game with 3D6 to hit, I would just play Champions (or Fantasy Hero), rather than try to hack D&D to use it.
WOTC lies. We know that WOTC lies. WOTC knows that we know that WOTC lies. We know that WOTC knows that we know that WOTC lies. And still they lie.
Because of the above (a paraphrase from Orwell) I no longer post to the forums -- PM me if you need help or anything.
I think more possible outcomes are good for some results table, which can also be placed on a curve. In just regular rolling whether for table results or a task check, wouldn't the extremes be less frequent? But this isn't my expertise, so I'm writing more to test my assumptions rather than really answer your query.
Jander Sunstar is the thinking person's Drizzt, fight me.
If you're rolling to look up a result on a table (especially a table with a set number of results expecting a flat curve), use the dice the table was designed for.
I'm not so much interested in the shape of the probability curve, as it were. I'm more interested in the fact that having a base level of competency is supposed to MEAN something. It is supposed to mean that when you try to do a thing based on your skill at other similar things, there is an expectation of your ability to perform, meaning that you are more likely to do average (ie roll a 10 or 11) than you are to fail or succeed in a spectacular fashion (ie roll a 1 or 20). The 1d20 roll puts all possible outcomes on exactly equal footing, whereas a 2d10 (or other dice pool) model means that the character is ten times more likely perform up to her expected skill level, which seems to me to be the entire point of having skill or attribute scores, bonuses and penalties in the first place.
With regard to the "more predictable=more boring" argument, I suppose it depends greatly on your intended play style. Super swingy-ness makes more sense in a lighthearted or wacky adventure where every roll can result in hilarious little tragedies that alter the storyline in fun ways. For something more gritty or hardcore, changing from 1d20 to 2d10 means that the chances of catastrophic failure is reduced from 5% per roll to 0.8% per roll, leaving room for some really emotional, gut-punch moments of unexpected failure that alter the course of a characters life and/or story arc.
Regarding the question about building around the expectation of crits, that can be easily mathed out at the table. For example, the Improved Critical skill for Champions gives you a crit on 19 or 20, which is effectively a 10% chance on 1d20. In a 2d10 system I could award a crit on a result of 17, 18, 19, or 20. This spread gives me 10 possible crit rolls on a chart of 120, or just barely over 8%. Additional perks could be tacked on to make up any perceived dip in effectiveness up to and including extra damage on crit or even an extra attack roll.
Or maybe I'm over thinking it and I should just not ask players to roll as often...
For a lot of older players, the d20 is so essentially D&D that not only is any D&D without a d20 Not D&D, but any game that doesn't use the d20 is itself so far from How A Tabletop RPG Should Be that it's not worth playing. It's one of the primary reasons Wizards remains so successful - D&D is the progenitor of the model and thus the only game people care about.
But for me, the d20 is no more essential to D&D than the d4 is. For me, the one thing D&D truly gets right is its willingness to let the players do shit. Genesys is often lauded for its Story Dice system, but having been looking into Genesys recently, the game is absolute moose piss for anything but a modern-world muggles game where no one can accomplish anything worthwhile. The one critical failure of most modern games with more advanced dice systems is criminally limiting the abilities of anyone in the game to do anything that a random New York cab driver couldn't pull off. Magic, supertechnology, psychic powers, even just people with enhanced abilities like Captain America - these games all tend to handle them extremely poorly.
The core of D&D, for me and many others, is the fact that you can be awesome. Want to be a wizard who can rain fire from the sky, summon dragons, become a dragon, teleport across planes, and do all that other Good Shit? Just level up enough and you're golden. Want to be a deadly bladesman who can slay even the mightiest of foes with a single stroke of your sword? Rogue's got you. So on and so forth.
That sense of progression is the core of D&D to me. Very few modern games allow for any sort of meaningful character progression; they focus so much on the story that they forget the characters playing in it. Genesys is absolutely terrible about it; Savage Worlds is better but not amazing. GURPS does progression well depending on the GM, but good luck convincing anyone to play GURPS.
But that's why I figure folks would hack a better dice system into D&D. Because the trappings of D&D aren't as important as its spirit, which is the collected lore of the game, its unique bestiary and history, and the fact that characters actually grow as they play. That's why implementing 2d10 into D&D is a better idea than just fluffing a Genesys game as "D&D". Because frankly, I do not have high hopes for this Genesys game I'm looking to be playing in soon X_X
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i'm in yurei's boat. 2d10 makes no more sense than d20 because the rolls don't actually matter very much at all. in fact, can't actually recall a single game i've played where they actually changed the outcome.
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D&D 5E doesn't use critical successes or failures outside attack rolls. A 20 has the exact same outcome as a 15, as long as that 15 is sufficient to meet the DC. A 1 has the exact same outcome as a 5, as long as that 5 is insufficient to meet the DC. "All possible outcomes" (optional or homebrew rules notwithstanding) is two outcomes: success or failure. And unless you need to roll 11 or higher for success, they're not on exactly equal footing.
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