D&D GeneralMath Question re: 3d6 vs. 4d6 drop one

the Jester

Legend
Well, point buy doesn't use either 3d6 or 4d6, so while it's a fine method of character generation if that's what you're after, it doesn't answer the question or offer anything helpful here. And while point buy will get you perfectly balanced characters every time, allowing for maximum control over your stat array, that is very much not something on offer in my game. In my game, dice, and the randomness they offer, are a large part of the experience.

A huge part of D&D for me is rolling the dice. I will never embrace a "players roll all the dice" system, not because they're bad- they're not- but because I like to roll dice too.

GreyLord

Legend
Not sure on the math, but one of my favorite methods from an older edition was to roll 3d6 12 times and choose the 6 best scores.

It seemed to reasonably give decent enough scores compared to the 4d6 drop the lowest method.

Seramus

Hero
How does 2d6+6 pan out?

Horwath

Hero
How does 2d6+6 pan out?
average is 13. higher than 4d6D1. also remove any chance of very bad rolls.

9d2 drop 2 +1 gives 8-15 range with average of 12.5

le Redoutable

I mean you no harm
One way to balance it might be to offer the 3d6 people three of the following (or all 4 if the six abilities are played in order!):
1. free feat.
3. any stat <8 after adjustments can become 10
4. uncommon magic item of choice

That's off the top of my head, but it might make it a real choice between methods then, because it gives things 4d6dL doesn't.
yess!!
( furthermore I would gladly add some stuff relative to equipment ( a stat that , when you'e proficient in, would provide you some tools/items ( a mix of Luck and Appraisal ) )

TaranTheWanderer

Hero
I am, and I think that a player who willingly chose the 3d6 would be the type who would enjoy playing multiple low stats.

Hoo boy. So let's talk about why I'm trying to come up with something- it's to accommodate players who really want those starting ASIs to be floating instead of tied to race. I know that this is controversial and I don't want to side track the thread with a big discussion about it, but in short, I don't like disconnecting ASIs from race. I'm trying to find a path where I can include both a floating +2/+1 and a fixed +2/+1, or several such sets of bonuses, and have it balance with 4d6 drop 1.

I am just now realizing that the players who I want to accommodate are probably the least likely to enjoy playing a pc with multiple low stats. Huh.

Yeah, the bonus is going to be the additional stat bumps and the added ability to customize your starting array that they offer. Now I'm wondering if I need to rethink this entirely.
So, one of the easiest ways to generate stats without causing a math headache is deciding what power you want the PCs before racial and random bonuses.

+3 total bonuses for a weaker campaign
+5 total bonuses for medium
+7 for a stronger campaign
(normally 3-5/6-7/8-9 but since you're still adding bonuses, you have to reduce it slightly. 27 point buy is around +6 or 7)

Then let the players CHOOSE their stats

The rules are as follows. Simply:
• 3 even stats
• 3 odd stats
• No stat higher than 18 (you can drop this if you don't want PCs starting with 20s)
• No stat lower than 5
• Total bonuses must be less or equal to your campaign limit

Not as fun as rolling. But everyone is happy with their stats.

Well, point buy doesn't use either 3d6 or 4d6, so while it's a fine method of character generation if that's what you're after, it doesn't answer the question or offer anything helpful here. And while point buy will get you perfectly balanced characters every time, allowing for maximum control over your stat array, that is very much not something on offer in my game. In my game, dice, and the randomness they offer, are a large part of the experience.

A huge part of D&D for me is rolling the dice. I will never embrace a "players roll all the dice" system, not because they're bad- they're not- but because I like to roll dice too.

So just ignore my suggestion

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the Jester

Legend
How does 2d6+6 pan out?
I am not open to any form of stat generation that precludes low stats.

GMMichael

Guide of Modos
Can anyone help me figure out how to balance these two options?
Don't. It will tell you who the math nerd/optimizers in the group are.

fba827

While overly complicating it how about …

1- 5d6 drop two lowest
2 - 4d6 drop lowest
3 - 3d6
Then Arrange the six as desired

thus six stats with one likely to be higher, two likely to be above average, and 3 that are likely to be average

(If it wanting to keep terminology in terms of 3d6; call them all 3d6 rolls but for one of them you can reroll any two dice, two of them you can reroll one die each.)

CleverNickName

Limit Break Dancing
Another option:
Use the 3d6 method for stats, and apply that +2/+1 modifier to stats at 1st level that you were talking about. Then, every 4 levels, allow the player the choice of a +2/+1 ASI to two stats, or a +2 ASI and a feat.

Hriston

Dungeon Master of Middle-earth
Okay, mathy people, can anyone help me figure out how to make this work?

I'd like to have two methods of stat generation that give, on average, equal results in the end.

The first is more or less what rolling for stats looks like right now: 4d6, drop one die of your choice, then add (for a typical character) +2 to one stat and +1 to another.

The second is the challenge. I want to create an option for rolling 3d6, but with several sets of +2/+1 ability score increases: one free floating, one for race, and one for class... but I don't know if that's enough to equal that extra die-drop-one. I feel like it's not.

Can anyone help me figure out how to balance these two options?
Okay, here's my answer. I had to mull this over for a bit. My assumption is that an ASI you put into an important ability is worth more than one you put into a less important ability.

You have two options:
1. Give the 3d6 option 10 points, but make a rule that you can only put two points into any one score (which isn't very interesting because the decision becomes whether a score will get no points or if you'll split your last two points between two scores), or​
2. Assume the points will be put into the two most important scores and only give 6 points. I'd probably limit this to four points in any one score.​
Either way I'd cap scores increased this way at 18.

MarkB

Legend

5d6 drop two lowest for two stats of your choice, but you must choose which stat before you roll.

Then 3d6 for each of the other four stats, arrange as you choose.

GMMichael

Guide of Modos
You could really mess with the players:

3d6+1 per score OR,

roll 1d6, DM rolls 3d6. Choose one of the DM's rolls without looking. Then, the DM reveals the lowest roll of the remaining two. You can reveal the first mystery d6 you chose, or you can switch to the one that the DM didn't show you.

CleverNickName

Limit Break Dancing
I wonder what the math would look like if you went with "roll 3d6, then reroll the lowest."

NotAYakk

Legend
4d6 in order, drop lowest
vs
3d6, arrange how you like.

Then roll 3d6. Each die swaps with the lowest 3 dice of your 6 stats (you pick). Now add these 3 dice to aby stat you didn't swap with.

---

Should give same average. Different distribution. Lets test it.
416
451
215
514
645
614

Lets make a barbarian.
Str: 654
Dex: 614
Con: 614
Int: 215
Wis: 541
Cha: 541
Bonus roll: 661

Swap 1s for 6s on Dex/Con
Add 1s to Wis, Cha and Str.

Str: 15
Dex: 16
Con: 16
Int: 8
Wis: 11
Cha: 11

Viable.

(Trick is I end up adding entire 3d6 bonus. Restricted rules prevent me from getting an automatic 18+.)

DND_Reborn

Legend
I wonder what the math would look like if you went with "roll 3d6, then reroll the lowest."
Do you have to keep the reroll if it is lower?

For example, if you rolled 3, 6, 4, and rerolled the 3 but got a 1, would you keep the 3 or must you take the 1?

Because if you can keep the 3, you have 4d6 drop lowest.

Forcing you to keep the reroll gives you an average of 11.96 (roughly)

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EzekielRaiden

Hero
One way to balance it might be to offer the 3d6 people three of the following (or all 4 if the six abilities are played in order!):
1. free feat.
3. any stat <8 after adjustments can become 10
4. uncommon magic item of choice
I'd...actually be really tempted to take that, believe it or not. It addresses the "I got one utter garbage stat" issue, it gives a potential big boost so even if you get lots of low stats, you're still reasonably likely to get at least one decent stat. And if you happen to get a pretty good roll, you can skip the 8-boost and just get the magic item.

And given how much I actually dislike rolling, ESPECIALLY 3d6 rolling, I'm genuinely shocked I can say "that's actually tempting."

Charlaquin

Goblin Queen (She/Her/Hers)
Here’s the expected results for 4d6 drop 1 graphed:

And here’s the same with 3d6:

If you round the averages you get expected arrays of
4d6 drop lowest: 16, 14, 13, 12, 10, 8
3d6: 14, 13, 11, 10, 9, 7

That’s three +2s and three +1s, so the initial suggestion of a floating +2/+1 and fixed +2/+1s from race and class could just about work, if you could somehow insure none of them ever stacked. But, of course, everyone is going to want to stack as much as possible. Maybe take a leaf out of PF2’s book and do it in a few separate, non-stackable steps?

Horwath

Hero
here is some idea for rolling(I still hate rolling for stats)

you get 6 pts:
you get 2 extra if you roll in order,

2d8+2(4-18, av 11) costs 0
2d6+6(8-18, av 13 costs 1
2d4+10(12-18, av 15) costs 2
2d3+12(14-18, av 16) costs 3

any save points can be used to raise rolled stats

stats 16-18 cannot be raised

delericho

Legend
So about a difference of 15 points total- wow, that's far more than I expected. That's five sets of +2/+1. Hm.
Bear in mind that being able to add points as desired is worth more than the same points assigned randomly, due to the ability to boost strengths and dump weaknesses. So your 3d6+bonuses would actually be more powerful than the 4d6 version.

So it's almost certainly a good idea to remove at least one of those +2/+1s, and/or replace some of them with feats.

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