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

[Hriston]

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]

How about this:

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]

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]

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

 

[NotAYakk]

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]

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)

 

[EzekielRaiden]

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.
2.+3/+2/+1 instead of +2/+1.
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]

Here’s the expected results for 4d6 drop 1 graphed:

AnyDice

AnyDice is an advanced dice probability calculator, available online. It is created with roleplaying games in mind.

anydice.com

And here’s the same with 3d6:

AnyDice

AnyDice is an advanced dice probability calculator, available online. It is created with roleplaying games in mind.

anydice.com

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]

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

point buy for roll type:
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

stat 4: add +4
stats 5-7: add +3
stats 8-12: add +2
stat 13-15: add +1
stats 16-18 cannot be raised

 

[delericho]

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.