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

[Tazawa]

Reading this thread, I came up with an idea.

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]

Reading this thread, I came up with an idea.

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]

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]

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?

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]

How about they choose between:

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]

Reading this thread, I came up with an idea.

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]

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.