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

#### Tazawa

##### Explorer

1. The difference between 6 x 3d6 and 6 x 4d6 drop 1 is about 10.5.

2. 10.5 is the average result for 3d6.

If people want to roll 3d6 for their attributes (in order if they are old skool), they can then roll a seventh 3d6 and apply the results of each die to three of their attributes. The only limit is attributes can’t be adjusted over 18.

It gives basically the same results as 4d6 drop 1, but eliminates the ‘one sucky attribute’ problem.

#### Laurefindel

##### Legend

1. The difference between 6 x 3d6 and 6 x 4d6 drop 1 is about 10.5.

2. 10.5 is the average result for 3d6.

If people want to roll 3d6 for their attributes (in order if they are old skool), they can then roll a seventh 3d6 and apply the results of each die to three of their attributes. The only limit is attributes can’t be adjusted over 18.

It gives basically the same results as 4d6 drop 1, but eliminates the ‘one sucky attribute’ problem.
That was my first thought after reading @DND_Reborn 's post as well

#### DND_Reborn

##### Legend
That was my first thought after reading @DND_Reborn 's post as well
LOL it was also I thought I had while writing it.

But, since the OP wanted to roll just 3d6, and then add +2/+1 ASIs, etc., I didn't bother pointing it out.

#### the Jester

##### Legend
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?
I'm okay with someone stacking those bonuses, within the context of the normal maximum. But they are not all floating bonuses. The racial ones and class ones will both be tied to their respective class and race, so only that final +2/+1 will actually float.

I don't think all my players pick their race to optimize their bonuses, but I'm sure at least some do at least some of the time. It might be an interesting experiment to playtest.

#### Mercurius

##### Legend

One set of 4d6, drop lowest
Two sets of 3d6, pick better set

I have no idea which is better, but maybe it doesn't matter.

#### Rabbitbait

I remember back in the old days you rolled 3d6 in order and then chose your class based on what you rolled. - So you didn't get to pick which attributes got the high scores. If you rolled really well in multiple stats then you could start working towards being a bard or a paladin. I think that's how it worked, it's back in the dark ages of my memory.

I completely co-incidentally rolled 18/00 in strength about half the time. Complete and total luck and not at all cheating. Honestly. (Disclaimer - I totally cheated).

#### Greenfield

1. The difference between 6 x 3d6 and 6 x 4d6 drop 1 is about 10.5.

2. 10.5 is the average result for 3d6.

If people want to roll 3d6 for their attributes (in order if they are old skool), they can then roll a seventh 3d6 and apply the results of each die to three of their attributes. The only limit is attributes can’t be adjusted over 18.

It gives basically the same results as 4d6 drop 1, but eliminates the ‘one sucky attribute’ problem.
I've suggested this before, though in my variation you used the last roll as bonus points to assign where you like. The actual average from 4D6 Drop 1 is something like 13.254. (I just a ran a 10,000 iteration random simulation.) That means that the suggested method generates results that are little less than 4D6 drop 1. (Something like 0.024 points less, but so what). The slight point difference is more than made up for in the ability to fine-tune your numbers.

No need for a +1 or +2 anywhere.

One complaint about roll v point-buy is that sometimes we just roll badly and someone else has hot dice. But the more dice you roll, the more that bell curve effect will even things out. Adding the extra 3 D6 roll helps work in that direction.

#### DND_Reborn

##### Legend
The actual average from 4D6 Drop 1 is something like 13.254
You're off by a point... it is exactly 12.2445987654321.

Hopefully that is just a type-O on your part or it is an error in your sim.

#### Greenfield

I'll re-run with a larger iteration

#### Greenfield

Confirmed. My simulator was right, I just plain fat-fingered the result.

#### Blue

##### Ravenous Bugblatter Beast of Traal
Two reminders.

1. The shape of the distribution is different. So adding a static number is a poor fit to simulate it. And it can raise the cap.

2. 5e rewards specialization. The difference between the average of 4d6K3 and 3d6 is irrelevant for this discussion. The primary point of interest is between the highest of six of each, then comparisons of the second highest of six from there, and then some minor quibbles, like how many penalty modifiers. Looking at it from the average roll will not mimic each other at all in practical terms within 5e.

#### DND_Reborn

##### Legend
Confirmed. My simulator was right, I just plain fat-fingered the result.
It happens.

#### jgsugden

##### Legend
I like my system, but it can only be used when players start a new campaign together:

• Tell your players to bring a dollar in small change, mostly pennies.
• Then, secretly roll (4d6 best 3) 8 times for each PC, with each score placed on a different index card (so you have 8 different cards for each player with a number from 3 to 18 on each).
• Now, add 5 to 20 more index cards. On each of these cards, write a fun little boon that a PC might have, like a low powered feat, an ally, a rarely used uncommon magic item, a +5 bonus to speed, a wild psionic talent, etc... You might allow an option of 2 boons to give some variability, or just put SECRET on it and let players discover the secret after they win the bid (I once did this to give a player an artifact at level one that they had to figure out how to protect, and how to activate).
• Shuffle the cards. Seat the players in a circle. Randomly pick a player to start bidding.
• Reveal a card. The player that starts the bidding must bid at least \$0.01 for the revealed card. Go in a circle and bid per normal (fail to bid and you're out for that round). If you win the bid, you must be the starting bid for the next card if you have any cash left and are eligible to bid.
• You can bid on cards only so long as you do not have 6 numbers.
• If you ever run out of \$ (and do not have 6 numbers), you get \$0.01 more.

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