Hello fellow ROLL-players!
I have been thinking about the concept of "average" in DnD and Pathfinder. There is a wide margin around the average roll (for a d20) that could mean the difference between success and failure. I understand the want for randomness in a game to spice combat and saves up. I also understand that having a set value for whether you're able to hit an enemy or not is bogus.
The goal: Use a pool of dice that when rolled result in a combined average total of 10.5 (or something close to it such as 10-11) with a min of 1 and a max of 20.
Example of a dice average total: 4d6 = 4*((1+6)/2) = 4*3.5 = 14 average. 5d4 = 5*((1+4/2) = 5*2.5 = 12.5 average.
So my question is: How would you go about rolling a set of dice together to get an average die roll for a d20 while still allowing for variation within rolls? I theorycrafted a couple different things such as 3d6 and editing saves and AC down by 1 or 2. I tried 5d4 to get a max of 20 but that meant the lowest roll was a 5. I tried 6d4-4 to get a 20 max again but the lowest roll was a 2. 4d6-4 gave a max of 20 but a minimum of 0. 3d4+2d6-4 gives a min of 1, a max of 20, but an average of 14.5.
How would you solve this problem?
EDIT: Time spent rolling may or may not be an issue because my group will be playing online where the difference in time between a d20 roll and a pool of dice rolled is negligible.
EDIT2: I should probably say another goal is to make it where the "average" is more likely to be the result than the extreme ends of the roll. When you roll a d20 you have the exact same chance of rolling a 1 as rolling a 20. I would like the die results to be the most likely at 10 or 11 and then slowly drop off like a bell curve.
2d8+d6-2.
Though I, personally, would just say 'screw it' and go straight 3d6.
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2d20 take the average, scale up the number of d20s as desired.
Dimminsy wrote:
The goal: Use a pool of dice that when rolled result in a combined average total of 10.5 (or something close to it such as 10-11) with a min of 1 and a max of 20.
How would you solve this problem?
A twenty-sided die numbered 1 - 20 looks like it would achieve that goal.
The only other way to achieve this is if one or more dice has a 0 on it, or by subtracting from the total.
Is there a reason you want to use something other than a d20 to achieve the same mathematical effect?
@Zhayne: Well, that certainly is a quick way to solve the problem. I wonder what the changes of rolling individual numbers would be. I might have to look into it.
@Hawktitan: That would be good but exact values are needed so taking the average usually won't result in a whole number. Floor and ceiling would skew the results as well.
@redward: Look at my OP EDIT2. =)
redward wrote: Dimminsy wrote:
The goal: Use a pool of dice that when rolled result in a combined average total of 10.5 (or something close to it such as 10-11) with a min of 1 and a max of 20.
How would you solve this problem?
A twenty-sided die numbered 1 - 20 looks like it would achieve that goal.
The only other way to achieve this is if one or more dice has a 0 on it, or by subtracting from the total.
Is there a reason you want to use something other than a d20 to achieve the same mathematical effect? Probability and standard deviation.
It's basically the difference between a greatsword and a greataxe.
Hitting a 12 on a Greataxe is 8.3%, hitting a 12 on a Greatsword is 2.78%.
He wants a system where you shift the probability of achieving the average roll on any particular roll towards the middle.
In such a system crits become much more rare and people preform 'more reliably' when making checks.
Exactly Hawktitan. I want crits and crit fails to be something to be unexpected rather than be accounted for 5% of the time.
redward wrote: Dimminsy wrote:
The goal: Use a pool of dice that when rolled result in a combined average total of 10.5 (or something close to it such as 10-11) with a min of 1 and a max of 20.
How would you solve this problem?
A twenty-sided die numbered 1 - 20 looks like it would achieve that goal.
The only other way to achieve this is if one or more dice has a 0 on it, or by subtracting from the total.
Is there a reason you want to use something other than a d20 to achieve the same mathematical effect? He wants a bell curve instead of a linear progression.
Dimminsy wrote: Exactly Hawktitan. I want crits and crit fails to be something to be unexpected rather than be accounted for 5% of the time. There's no such thing as a crit fail, just to mention.
Zhayne's answer is literally correct. A bit messy though, 3d6 is probably the most optimal way to approach a narrower average pool. But the real question is how often do you want failure? You could just do 3d6 + 1 or 2 if you really want to create something closer to average. You can increase dice and decrease size or add static bonuses to get a more static value. So really beyond just a certain average, the real question is how frequently do you want the value to be near the average and how much variation do you want in the value.
@Zhayne: When you're rolling an attack a 1 always results in a miss and when rolling a save a 1 always results in failing the save. That's what I mean when I said "crit fail".
@Mr. Pitt: The problem with 3d6 is that you're forcing the minimum roll higher. I still want to range of values to go from 1 to 20 so as to not alter the AC's/Saves of players/creatures but I also want the average to be close to 10.5. I obviously don't want to roll 20d20 and take the average because then there's almost 0 change for a crit success or fail, but I also don't want them to occur 5% of the time.
Okay. I was afraid you were one of those 'roll a 1, throw your sword across the room, decapitate the rest of your party' types.
You'd autofail on a 3 and autosucceed on an 18 with 3d6, obviously, or you could make it 3-4 and 17-18 if you really felt like it.
I've run games with straight 3d6. It works fine.
As soon as the game uses multiple dice to achieve a bell curve around the average, the game becomes very delicately balanced around that average.
For example, if the attack roll is on a bell curve probability distribution, small differences in AC are magnified at both ends. Just a few points lower in AC and the defender is getting hit far more often by a given attacker, whereas just a few points higher and the defender is almost untouchable by the same attacker.
A flat distribution using a single die is preferable, especially for attack rolls and saving throws, for allowing more randomness otherwise the game becomes even more broken in the hands of the even moderately efficient power gamers.
The problem is that for each new die you automatically increase the minimum value of the roll by one. You can attempt to offset it by subtracting a static bonus in the end. The 2d8 + d6 -2 proposal gives you a chance of critical failure 1 out of 384 times if I am doing the math right. If that's how often you want a 1 to occur, then it'll do exactly what you want. What you need to decide is the frequency of failure and how convenient you'd like these dice rolls to be. Averaging multiple d20s could have a similar effect; it's all about the balance of convenience and frequency, so decide roughly how often you want a 1, how steep you want the curve to be and it can probably be modeled given that there exist dice for many types of multiple. But balance it against inconvenient dice combinations for players to have.
Pink Dragon wrote:
For example, if the attack roll is on a bell curve probability distribution, small differences in AC are magnified at both ends. Just a few points lower in AC and the defender is getting hit far more often by a given attacker, whereas just a few points higher and the defender is almost untouchable by the same attacker.
So you actually have to use teamwork and tactics.
I don't see this as a bug.
2d8+1d6-2 actually looks pretty good for what you are trying to do I think (assuming my math is right):
1- 0.26
2- 0.78
3- 1.56
4- 2.60
5- 3.91
6- 5.47
7- 7.03
8- 8.59
9- 9.64
10- 10.16
11- 10.16
12- 9.64
13- 8.59
14- 7.03
15- 5.47
16- 3.91
17- 2.60
18- 1.56
19- 0.78
20- 0.26
Also realize you would need to tweak more mechanics then just die rolls. Swashbucklers for example are more or less balanced on generating panache 15% of the time before level 5 and 30% of the time afterwards.
Quote: I don't see this as a bug. It's not a 'bug' he's just trying to tinker with the core game system. It's sometimes an interesting thought experiment if nothing else, but it definitely has ripple effects.
Zhayne wrote: Pink Dragon wrote:
For example, if the attack roll is on a bell curve probability distribution, small differences in AC are magnified at both ends. Just a few points lower in AC and the defender is getting hit far more often by a given attacker, whereas just a few points higher and the defender is almost untouchable by the same attacker.
So you actually have to use teamwork and tactics.
I don't see this as a bug. Teamwork and tactics are fine. Unfortunately it doesn't take a lot of character building ingeniousness to move a character's defenses into an area where even teamwork and tactics won't easily get the job done.
I think that much of DnD's and Pathfinder's success stems from the d20 paradigm, whereas 3d6-based games, for example, are not nearly as popular.
The "roll X d20s and average them" is the most sensible, IMO. I am pretty sure people have come up with alternate Pathfinder rules for a 3d6 system, though (such as, normal crit range is a 19-20.)
For those asking "Why?" there are different distributions depending on how many dice are rolled. 1dX is a "flat" or "uniform" distribution, 2dX is a "triangular" distribution, and as you get more dice it gets more complicated but approaches a normal distribution. If you were to roll infinite dice, it would be a true normal (or "Gaussian") distribution.
This picture shows the distribution for 1d6, 2d6, 3d6, and 4d6.
I saw someone suggest 2d10 once, and I find it a very interesting compromise between the flat d20 and the 3d6, while being still mechanically simple.
By the way, if you want to quickly compare the graphs and standard deviations for your dice pools, you have the most excellent anydice.
RumpinRufus wrote: I am pretty sure people have come up with alternate Pathfinder rules for a 3d6 system, though (such as, normal crit range is a 19-20.) The 3d6 variant was already discussed in the old 3.5 Unearthed Arcana book. It is OGL, so you can still find all the adjusted rules here.
Hahah, also why did I say "normal crit range is 19-20" when both 19 and 20 are impossible using 3d6.
Looking at the anydice link, I'm really liking the 2d8+1d6-2 model. My goal of this was to not change the power level of characters but to make things a bit more realistic. Characters that "rely" on crit threats such as a Swashbuckler, a Magus, or a crit focused Fighter shouldn't become non-existant or nerfed hard, so a comparable crit chance should be held up. Looking at the 3d6 rule variant Valfen posted but using the model Zhayne posted results in a crit table conversion being:
Normal | Old % | Modified | New %
---------+-------+----------+--------
-- 20 ---|-- 05 -|- 17-20 --|- 5.2
-- 19 ---|-- 10 -|- 16-20 --|- 9.11
-- 18 ---|-- 15 -|- 15-20 --|- 14.58
-- 17 ---|-- 20 -|- 14-20 --|- 21.61
-- 15 ---|-- 30 -|- 13-20 --|- 30.2
I think that's a pretty good conversion rate. What do you guys think?
Also, when looking at the distribution, you have a 56.78% chance of rolling 8-13 (within 3 whole numbers of the average 10.5) which feels much better to me than the 30% chance of rolling those numbers on a d20.
I was mostly looking for a way to curb the "at high level you have a 5% chance every roll when facing a wizard of auto-dying no matter how high your save is and how bad the wizard is" and similar situations.
EDIT: I tried out 1d10+2d6-2 and got another curve that fit the criteria. Editing in a moment again.
EDIT2: Using 1d10+2d6-2 I got this change:
Normal | Old % | Modified | New %
---------+-------+----------+--------
-- 20 ---|-- 05 -|- 17-20 --|- 5.56
-- 19 ---|-- 10 -|- 16-20 --|- 9.73
-- 18 ---|-- 15 -|- 15-20 --|- 15.56
-- 17 ---|-- 20 -|- 14-20 --|- 22.78
-- 15 ---|-- 30 -|- 13-20 --|- 31.11
So it would actually increase the crit threat chance. Mmmmm...
I just thought I should mention that my group will be gaming on roll20.net since we live in different states. This allows us to use things like d5's and d3's if that would help fine tune the distribution.
Pink Dragon wrote: Zhayne wrote: Pink Dragon wrote:
For example, if the attack roll is on a bell curve probability distribution, small differences in AC are magnified at both ends. Just a few points lower in AC and the defender is getting hit far more often by a given attacker, whereas just a few points higher and the defender is almost untouchable by the same attacker.
So you actually have to use teamwork and tactics.
I don't see this as a bug. Teamwork and tactics are fine. Unfortunately it doesn't take a lot of character building ingeniousness to move a character's defenses into an area where even teamwork and tactics won't easily get the job done.
I think that much of DnD's and Pathfinder's success stems from the d20 paradigm, whereas 3d6-based games, for example, are not nearly as popular. I seriously doubt that matters one teeny tiny bit.
5D5-5, treat a 0 as the failure instead of the 1.
There really is no good answer to this question unless you can be more specific about how often you want the extreme values to pop up. For example, 1d20 is fine if you are okay with uniform results, while 19d2-18 gives as consistent results as possible while still allowing for results from 1 - 20. 19d2-18 gives only a 1 in 500,000 chance of getting a one. Obviously, the optimal is somewhere in the middle, but that is something you have to judge for yourself. My vote is for the 2d8+1d6-2 that's been mentioned before, but again, it's up to personal taste.
Ok, an added restriction is I also want there to be a want to convert the crit ranges over to the new system and still have %'s that are close enough to the old values. I want 1's and 20's to happen, but I don't want someone to feel like they were cheated when save or dies occur and they have a 5% of just losing their character or auto-winning a BBEG fight. However, I don't want crit threats to be removed from the game either. I went through the math about crit threat chances in my previous comment if you want clarification about what I mean about crit threats.
2d10 makes the conversion easier than using either 3d6 or the 2d8+1d6-2 distribution that will probably piss off your players for being too annoying.
Dimminsy wrote: Ok, an added restriction is I also want there to be a want to convert the crit ranges over to the new system and still have %'s that are close enough to the old values. I want 1's and 20's to happen, but I don't want someone to feel like they were cheated when save or dies occur and they have a 5% of just losing their character or auto-winning a BBEG fight. However, I don't want crit threats to be removed from the game either. I went through the math about crit threat chances in my previous comment if you want clarification about what I mean about crit threats. Honestly... it seems like you're missing the forest for the trees.
Your reasoning thus far has largely come down to "save-or-dies suck because nobody likes a 5% chance of auto-death". So why not just... remove the 'crit failure' on the 1? If you roll a 1 on your save but your save is still high enough to get over the DC, congrats you shrug off the Baleful Polymorph. Go punch the Wizard's face in for trying that.
Would that solve your core complaint, or do you have deeper issues with the d20 setup?
Dimminsy wrote: Ok, an added restriction is I also want there to be a want to convert the crit ranges over to the new system and still have %'s that are close enough to the old values. I want 1's and 20's to happen, but I don't want someone to feel like they were cheated when save or dies occur and they have a 5% of just losing their character or auto-winning a BBEG fight. However, I don't want crit threats to be removed from the game either. I went through the math about crit threat chances in my previous comment if you want clarification about what I mean about crit threats. Sorry! I didn't see your second post for some reason. It looks like the 2d8+1d6-2 works out for you after all. As long as you're doing it online, it shouldn't be too much of a hassle. Getting a one with this method is 1 in 384, so considerably less likely than a flat 5 percent, but still possible.
Adventure Path Charter Subscriber; Pathfinder Starfinder Adventure Path Subscriber
A d20 produces a set of numbers that are randomly distributed. Switching to any core mechanic where you're rolling multiple dice in place of the d20 is really going to mess with the underpinnings of the game. Multiple dice, like 3d6, are going to produce a normal distribution (despite the fact that an individual die obeys the uniform distribution, multiple dice are normally distributed due to something called the central limit theorm). That means that all those feats and class abilities that rely on criticals (or "natural 20's") are going to be worth less since those events are going to be more rare. Also, static bonuses are going to be much more important to characters because they will be needed to reliably driven up the "average" result, since you've made high rolls more rare.
If you're determined to go the multiple dice route, check out Green Ronin's AGE system. It uses 3d6 and is the core mechanic of their DragonAge RPG system.
-Skeld
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I did the math on a 3d6 variant of pathfinder a few weeks ago, and it's on this forum somewhere.
I think it's a bad idea, because it turns Challenge Rating into an iron cage. A CR+2 is almost unbeatable, and a CR-2 can't even hurt you. Teamwork and tactics won't save you when you have only a 5% chance of hitting.
Dimminsy wrote: Ok, an added restriction is I also want there to be a want to convert the crit ranges over to the new system and still have %'s that are close enough to the old values. I want 1's and 20's to happen, but I don't want someone to feel like they were cheated when save or dies occur and they have a 5% of just losing their character or auto-winning a BBEG fight. However, I don't want crit threats to be removed from the game either. I went through the math about crit threat chances in my previous comment if you want clarification about what I mean about crit threats. Instead of altering the dice, it might be easier to just houserule this type of situation. For example, to address auto-killing players, just replace all SoD-type abilities with an equivalent level SoS for the NPCs you are using. For BBEGs, houserule, and inform your players, that key enemies will have an ability that lets them roll their save twice for SoDs, or what are effectively SoDs for NPCs(i.e. hold spells). A bit more work is to turn those spells into "critical spells" like phantasmal killer. Fail two saves for the full effect, but the spell still does something with 1 failed save. Another, easier option, is to put HP percentage thresholds on SoDs for BBEGs, and maybe even PCs, making them invulnerable to SoDs above 33% health or 50% health. Make the presence or absence of vulnerability transparent to the PCs though.
You are encountering one of the major issues with Pathfinder, the fact that certain spells can trivialize encounters, especially at higher levels. What you don't want to do is take it too far. I would go for the critical spells or thresholds first, as they can add to the game emotionally even while nerfing the spells. The spells move away from trivializing encounters or doing nothing to something like martial crits. There is a certain satisfaction to seeing, for example, the barbarian finish off the dragon with a huge crit, and narrating it with a decapitation, and these alterations can give the same opportunity to the wizards. There is an amazing gap in the feel of the wizard getting Hold Monster off after you've beaten down the enemy some, and it happening round 1.
Well, I do 2 methods, both of which go up to 24.
You already mentioned 4d6, but there is a method which evens it out a tad.
4-20 are as rolled, so if you roll a 15, it is a 15.
However, if you roll a 21 = 1, a 22 = 2, a 23 =3, and a 24 = 4.
This changes the parameters a little, though the average will still be higher than 10.5.
Another variation on this is 2d12. This actually gets much closer to your intended average.
The same as with 4d6 applies to 2d12 (though the 2-20 are as rolled, the numbers higher than 20 are as the equivalents to the 21-24 for the 4d6 method).
As for crits...that is a much tougher thing to get.
kestral287 wrote: Dimminsy wrote: Ok, an added restriction is I also want there to be a want to convert the crit ranges over to the new system and still have %'s that are close enough to the old values. I want 1's and 20's to happen, but I don't want someone to feel like they were cheated when save or dies occur and they have a 5% of just losing their character or auto-winning a BBEG fight. However, I don't want crit threats to be removed from the game either. I went through the math about crit threat chances in my previous comment if you want clarification about what I mean about crit threats. Honestly... it seems like you're missing the forest for the trees.
Your reasoning thus far has largely come down to "save-or-dies suck because nobody likes a 5% chance of auto-death". So why not just... remove the 'crit failure' on the 1? If you roll a 1 on your save but your save is still high enough to get over the DC, congrats you shrug off the Baleful Polymorph. Go punch the Wizard's face in for trying that.
Would that solve your core complaint, or do you have deeper issues with the d20 setup? My issue is not the principle of failing on a 1 or succeeding on a 20. My issue is I do not think 5% of the time is the " correct" or "appropriate" chance of either of those results happening. When a 1 and a 20 are occuring multiple times in the same combat it ceases to be special. If you watch a a match on TV like MMA or boxing, usually the blows take out a "set" amount of energy from the opponent. The high light videos are of underdogs landing a knockout punch against all odds. I know it's not the best analogy and this isn't real life, but it's to give a little reason for the motivation or want for a more average die roll.
@Skeld: Ya, the somewhat normal distribution is what I was going for. My group already knows that static bonuses to weapons and spells already are the best option so they wouldn't change their tactics much. Crit threat ranges could be converted over to keep a similar enough chance to crit threat so any abilities tied to a crit success not just a natual 20 would be relatively unchanged. Thank you for your suggestion. I'll look into it!
@Orfamay: You mind linking that in here? A side goal of this is to change the fewest number of mechanics as possible because I try to play the game as close to the rules as possible unless someone's abusing the latitude they have or the party is just unbalanced too much by a problem character.
@Calth: As I said, I want to change as little as possible about the game and still make this work. However, I do like the idea of max damage threasholds to keep things from getting crazy. Maybe something like "Finger of Death deals either leveld12 damage or 50% of their max health as damage, whichever is smaller." Or an effect of "Immune to death effects when above 40% health." applied to boss-types.
@GreyWolf: The wrap-around methods you described sound like they could hold some promise. Could result in some interesting "Aww that 21 was almost a 20!" but it would make the 20 result more likely than the 1 result thus skewing the average more. I'll think about it a bit more and see if some benefit can be found.
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For simplicity of math, maybe '3d20, drop highest and lowest'? That should make 1s and 20s much rarer.
Arbane the Terrible wrote: For simplicity of math, maybe '3d20, drop highest and lowest'? That should make 1s and 20s much rarer. wow... alarmingly elegant.
here is the curve for anyone who cares.
Pathfinder Adventure Path, Lost Omens, Rulebook, Starfinder Roleplaying Game Subscriber
Cardz5000 wrote: Arbane the Terrible wrote: For simplicity of math, maybe '3d20, drop highest and lowest'? That should make 1s and 20s much rarer. wow... alarmingly elegant.
here is the curve for anyone who cares. Just took a look at this thread and was going to propose "3d20, take the median". Good to know I'm not the only one.
I think averaging multiple d20's (to flat numbers) or the above mentioned 3d20, take the middle will workl best in that case. Makes conversion really easy and gives a soft curve that doesnt mess up too bad. Still, in the end it will have a huge impact on the game, especially the challenge rating.
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