D&D 5E Great Weapon Fighting

[GrumpyGamer]

I wrote a quick python script to take a look at greatswords vs greataxes with the Great Weapon Fighting style.

import random


def dicesim_py(n, ndice, dicetype):
    t = 0
    m = 0
    for i in range(n):        # repeat N experiments
        s = 0
        for j in range(ndice):
            r = random.randint(1, dicetype)  # roll die dicetype
            if r <= 2: # reroll 1 or 2
               r = random.randint(1, dicetype)
            t = t+r
            s = s+r
        if s == dicetype*ndice:       # successful event?
              m += 1
    a = float(t)/n  # average
    p = float(m)/n  # count of max results
    return a,p

>>> dicesim_py(100000,2,6)
(8.33177, 0.05091)
>>> dicesim_py(100000,1,12)
(7.32378, 0.09736)

From the results it looks like 2d6 does 1 more point of damage, but d12 hits for max twice as often.

I would not be shocked to find an issue with my script. Does this match expectations?

 

[fjw70]

On average the 2d6 will do 0.5 more damage (7 vs 6.5) and the d12 will hit max three times as often (1/12 vs 1/36).

 

[jodyjohnson]

It's not as good as brutal in 4e, but still a boost in damage.

 

[GrumpyGamer]

It's not as good as brutal in 4e, but still a boost in damage.

Brutal was a lot easier to model -
2d6 (Brutal 2) would be 2d4 +4 (9)
1d12 (Brutal 2) would be 1d10 +2 (7.5)

The numbers that I got are lower than 4e which is to be expected.

 

[occam]

I wrote a quick python script to take a look at greatswords vs greataxes with the Great Weapon Fighting style.

...

>>> dicesim_py(100000,2,6)
(8.33177, 0.05091)
>>> dicesim_py(100000,1,12)
(7.32378, 0.09736)

From the results it looks like 2d6 does 1 more point of damage, but d12 hits for max twice as often.

I would not be shocked to find an issue with my script. Does this match expectations?

You don't need to simulate; it's easy enough to calculate deterministic averages.

On 2d6, rolling a 1 or 2 on either die results in a replacement roll that averages 3.5. So the average damage per die is (3.5 + 3.5 + 3 + 4 + 5 + 6)/6 = 4 1/6. Average on 2d6 is 8 1/3 (matching your prediction), meaning you get a boost of 1 1/3 points of damage.

On 1d12, rolling a 1 or 2 on either die results in a replacement roll that averages 6.5. So the average damage per die is (6.5 + 6.5 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12)/12 = 88/12 = 7 1/3 (matching your prediction), meaning you get a boost of 5/6 of a point of damage.

This is ignoring crits, of course.

So using a greataxe means you'll be doing 1 point less average damage on every hit compared to using a greatsword or maul. This penalty is doubled on critical hits.

 

[GrumpyGamer]

On average the 2d6 will do 0.5 more damage (7 vs 6.5) and the d12 will hit max three times as often (1/12 vs 1/36).

1/12 without rerolling 1,2 would be .0833 so we would expect that we would get a slightly better chance with the reroll (1,2) which .0974 is. This passes a sanity check, but may still be inaccurate if my code is off.

 

[Tormyr]

On average the 2d6 will do 0.5 more damage (7 vs 6.5) and the d12 will hit max three times as often (1/12 vs 1/36).

The 2d6 chance for max would normally be 1/36, but with great weapon fighting 1s and 2s are re-rolled. That gives extra opportunities to roll a 6. Even the 1d12 is better than 1/12 because of the re-roll.

 

[fjw70]

1/12 without rerolling 1,2 would be .0833 so we would expect that we would get a slightly better chance with the reroll (1,2) which .0974 is. This passes a sanity check, but may still be inaccurate if my code is off.

Sorry, thought you were just comparing the weapons. Didn't realize you were adding the brutal 2.

 

[Savage Wombat]

What would it do to the math if you required that both sixers on the greatsword be either one or two for the reroll?

 

[jadrax]

What would it do to the math if you required that both sixers on the greatsword be either one or two for the reroll?

Must admit, I would be tempted to use that interpretation. Should favour the d12 quite a bit.