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

the Jester

Legend
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?
 

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overgeeked

B/X Known World
Anydice is great for this.


On 3d6 the average is 10.5. On 4d6, drop the lowest, the average is 13. So +2.5 is the difference between straight rolls. So whatever you'd need to add to make up the difference.
 

OB1

Jedi Master
Anydice is great for this.


On 3d6 the average is 10.5. On 4d6, drop the lowest, the average is 13. So +2.5 is the difference between straight rolls. So whatever you'd need to add to make up the difference.
So perhaps give a feat and a skill if you choose to roll 3d6? A feat is worth a +2 and a single skill is worth +.65
 

Lidgar

Legend
Anydice is great for this.


On 3d6 the average is 10.5. On 4d6, drop the lowest, the average is 13. So +2.5 is the difference between straight rolls. So whatever you'd need to add to make up the difference.
I was literally just writing this...so yeah. Need to generate an extra +2.5.

Options I would consider is +2 to two stats and +1 to one or +2 to one stat and +1 to three. In either case, I'd through in a skill proficiency as well (as stated above).
 

overgeeked

B/X Known World
So perhaps give a feat and a skill if you choose to roll 3d6? A feat is worth a +2 and a single skill is worth +.65
For 3d6 to compare to 4d6, drop the lowest, you'd need it to be 3d6 +2.5 per stat.

STR 10.5. DEX 10.5. CON 10.5. INT 10.5. WIS 10.5. CHA 10.5.

vs

STR 13. DEX 13. CON 13. INT 13. WIS 13. CHA 13.

That difference is more than a feat and a skill. I think.
 






Unwise

Adventurer
That +1 to everything might be similar to +1 proficiency bonus. If the OPs suggestion was because they want PCs to suck at some things, but not be worse at the things they are meant to be good at, then simply adding a +1 to proficiency could help.
 

Hriston

Dungeon Master of Middle-earth
Anydice is great for this.


On 3d6 the average is 10.5. On 4d6, drop the lowest, the average is 13. So +2.5 is the difference between straight rolls. So whatever you'd need to add to make up the difference.
The average of 4d6 drop lowest is 12.24, so the difference is 1.74 or 10.44 over six rolls.
 

Blue

Ravenous Bugblatter Beast of Traal
Looking at the difference in average can be misleading if you only look at that. Because the distribution is different as well so the mix of numebrs above and below that average is different than just 3d6+the delta. Just think - it changes the average without chanign the maximum or minimum. It doesn't accurately portray the final shape of the distribution.

But really, D&D 5e rewards specialization. So really what you are looking for is one great score, two to three good scores, and not too deep a penalty. So eight* sets of 3d6, keeping the best six, might be a better mimic of 4d6 than trying to add static numbers that could make 18s (or higher if allowed) much easier.

* for some value of eight - I haven't run the numbers.
 

DND_Reborn

Legend
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?
Since some people got this wrong... I'll set it straight for you.

Yes, 3d6 averages 10.5, but 4d6 drop lowest averages 12.24 (NOT 13! where did that come from???). [As @Hriston said.]

So, the difference between the two is less than 2 points, about 1.75.

Yes, that is for each of the six abilities, so adding those differences together is 10.5 (hey, fancy that... the average of 3d6!).

Since each +2/+1 ASI combo is 3 points, you could do three +2's, three +1's (must all be different abilities--so each ability gains a +2 or +1). That gets you 9 points, so you only need about 1.5 more, which could be the +1 for race and +1 for class.

For example, suppose your 3d6 rolls were (average 10.5): 8, 12, 12, 9, 14, 8

Adding three +2's and three +1's:

10 = 8 + 2
13 = 12 + 1 (EDIT: removed if only two +1's are allowed)
14 = 12 + 2
10 = 9 + 1
15 = 14 +1
10 = 8 + 2 (EDIT: removed if only two +2's are allowed)

Then you have two +1 floater for race and class:

10
14 = 13 +1
14
10
16 = 15 +1
10

Final array: 10, 14, 14, 10, 16, 10, average 12.333 (slightly better than 12.24 for 4d6 drop lowest).

So, there you go. Hope it helps.
 
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DND_Reborn

Legend
However.....

arguably only one of the stats is really important, one is a bit important and the rest not-so-much depending on the character class. So I would argue that 2 feats is a suitable replacement for doing 3d6 stat generation rather than 4d6 drop lowest.
That is a good point.

In my post above you could probably remove one +2/+1 pairing, so the player would only get two +2's, two +1's, and two abilities would not get a bonus. It reduces the raw numbers a bit, but is a very good point.
 

Kobold Stew

Last Guy in the Airlock
Supporter
This is more than just a math problem, though.

Some variables:
1. With 3d6, a character is much more likely to have some state below 8, and that is not easily corrected with simple numerical bonuses. The characters that get generated have limitations much less likely to be seen with 4d6dL. Are you prepared for a character to have 3 or 4 stats below 10? Will that be fun for the player? Is the player?

2. Most characters can afford to have a dump stat or two. What does a player gain by taking the 3d6 option? Bonuses that bring it to 4d6dL aren't enough, and you don't want to incentivize players to risk making a character they don't want to play (or so I presume).

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

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.
 



the Jester

Legend
1. With 3d6, a character is much more likely to have some state below 8, and that is not easily corrected with simple numerical bonuses. The characters that get generated have limitations much less likely to be seen with 4d6dL. Are you prepared for a character to have 3 or 4 stats below 10? Will that be fun for the player? Is the player?
I am, and I think that a player who willingly chose the 3d6 would be the type who would enjoy playing multiple low stats.
2. Most characters can afford to have a dump stat or two. What does a player gain by taking the 3d6 option? Bonuses that bring it to 4d6dL aren't enough, and you don't want to incentivize players to risk making a character they don't want to play (or so I presume).
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.

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

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.

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.
 

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