A good way to analyze the differences between the two distributions is to imagine a head-to-head contest between characters.
First, suppose you have two identical characters, A
and B
, rolling off against each other with d20. They tie 5% of the time; 47.5% of the time one wins; 47.5% of the time the other wins. In contrast, if you use 3d6, ties occur 9.2% of the time and each wins 45.4% of the time. Not a huge deal. Let's discard the ties and just concentrate on who wins more, A
or B
. Now let's start giving them bonuses. Since we haven't said who is whom, we'll just declare that A
is the stronger one and B
is the weaker one.
A's bonus 3d6 d20 3d6 ratio
========= ===================== ===================== over
========= A-wins B-wins ratio A-wins B-wins ratio d20 ratio
--------- ------ ------ ----- ------ ------ ----- ---------
+0 45.36% 45.36% 1.0 47.50% 47.50% 1.0 1.0
+1 54.64% 36.31% 1.5 52.50% 42.75% 1.2 1.2
+2 63.69% 27.94% 2.3 57.25% 38.25% 1.5 1.5
+3 72.06% 20.58% 3.5 61.75% 34.00% 1.8 1.9
+4 79.42% 14.46% 5.5 66.00% 30.00% 2.2 2.5
+5 85.54% 9.65% 8.9 70.00% 26.25% 2.7 3.3
+6 90.35% 6.08% 14.9 73.75% 22.75% 3.2 4.6
+7 93.92% 3.59% 26.2 77.25% 19.50% 4.0 6.6
+8 96.41% 1.97% 49.0 80.50% 16.50% 4.9 10.0
+9 98.03% 0.99% 99.0 83.50% 13.75% 6.1 16.3
+10 99.01% 0.45% 220.0 86.25% 11.25% 7.7 28.7
+11 99.55% 0.18% 552.9 88.75% 9.00% 9.9 56.1
+12 99.82% 0.06% 1663 91.00% 7.00% 13.0 127.9
+13 99.94% 0.02% 6661 93.00% 5.25% 17.7 376.0
+14 99.98% 0.00% 46649 94.75% 3.75% 25.3 1846.3
Okay, so what does this tell us?
First, we can see that with big bonuses, A
slaughters B
head-to-head in rolls in 3d6, whereas with d20 the benefit that A
gets over B
is pretty modest (has to get all the way up to +11 before A
is tenfold more likely to win than B
!).
But, second, if you look at the ratio of ratios (that is, how much advantage A
vs B
has in 3d6 compared to A
vs B
in d20), you find that in 3d6
the bonus is pretty much squared compared to d20 (low values only--then it gets way, way more extreme later on).
So, what does this mean? Well, basically, if under 3d6 you have a +1 bonus more than someone else, it feels like a +2 difference in d20. +7 feels like +14.
So the concise explanation is: moving from d20 to 3d6 amplifies differences, making them feel about twice as large as before. (Of course, almost nothing is actually resolved as a head-to-head test, but it's a useful thought experiment.) You can cleave through hordes of lesser beings with that much more ease, and your betters become that much more fearsome. In fact, better just stay away from them. There are some kobolds that need slaying. Right? Right.
The formula is that you have to pay for an ability score the new modifier. So going from 7 to 6 gives you a price of -2, 6 to 5 and 5 to 4 each give you -3, and so on. Dropping an ability score to 3 would give you 16 points.
Score | Mod | Cost
10 | 0 | 0
9 | -1 | 1
8 | -1 | 2
7 | -2 | 4
6 | -2 | 6
5 | -3 | 9
4 | -3 | 12
3 | -4 | 16
It's uncertain whether those values would be balanced ; while they follow the pattern of ability score costs, nothing says that this pattern won't fall apart outside of the 7-18 range. Furthermore, in any case, this should never be an option available to players as discussed in the answer to this question.
Best Answer
I had experience with this kind of playstyle back in DnD 3.5. In our case the main problem was that in the first few levels, we went through an incredibly high amount of characters (one of the players had 5 in one session :) ) and this created some monsters in the end (one character had 18,17,16,16 and two stats above 12 in the end) and when you end up with something good, you will start to become increasingly wary and paranoid.
Being wary is not necessary a bad thing, though, and I enjoyed playing in a group where all of our battles were carefully planed out involving crazy traps, potions, and other limited use magic items (which we barely use in more recent systems).
Things that you should be very careful of include:
A bit later in the adventure we started to create characters with very boring and stereotypical backgrounds (as they will die soon anyway). So if you want REAL characters you might want to ask them for example to make up one interesting fact about their character and work that thing out later in the game (one character might be the son of a pirate and later in the game you can introduce some NPCs that support this statement, pirate hunters looking for his dad, other pirates looking for his treasure etc.) This is what we used eventually with limited success.
You should also keep in mind that the players of really bad characters may deliberately try to kill their character so they can roll a better one (maybe even going so far as to get themselves killed 5 times in one session). You can circumvent that with a rule that lets you reroll a character if it is COMPLETELY terrible or one that punishes character death somehow (but I would avoid things like that without the full consent of the players).
How this will affect the game and your players otherwise
With my experience I would not recommend this playstyle to anyone, but if your players are all into it, it can be fun for a time.