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

[the Jester]

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?

 

[overgeeked]

Anydice is great for this.

AnyDice

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

anydice.com

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]

Anydice is great for this.

AnyDice

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

anydice.com

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]

Anydice is great for this.

AnyDice

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

anydice.com

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]

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.

 

[Krachek]

so 6 or 7 feats would fill the gap!

 

[the Jester]

So about a difference of 15 points total- wow, that's far more than I expected. That's five sets of +2/+1. Hm.

 

[Guest 7034872]

so 6 or 7 feats would fill the gap!

Woowwwww.....by the math, you're right. That's 7.5 feats right there.

 

[overgeeked]

so 6 or 7 feats would fill the gap!

The difference is +0 to everything in the game vs +1 to everything in the game. That's quite a jump. About +5% across the board for the entire game.

 

[MarkB]

Any limits to maximum stats? If given the choice between 4d6 drop lowest and 3d6 + 2, I could see some players taking the latter just for the chance of that 20.