afreshstart wrote:I think you made a mistake.

It's definitely possible I got something wrong, so here's how I proofed it. I was going to save this for when someone said it's off, as to not clutter the original post with extra info.

If I messed up in this, the formula is almost definitely wrong.

As for the formula you gave, I'm still messing with it...

**[D×(20-T-N)+(D×T×{N×5÷100})+(D×M×T×{H×5÷100})]÷20**
**D×(20-T-N)** is the number of rolls that are normal hits.

H is the number of rolls aren't a miss.

(20-T-N) and H, are always different, to be more exact, (20-T-N)+T = H
**(D×T×{N×5÷100})+(D×M×T×{H×5÷100})** just figures out what percentage of damage is from successful vs. unsuccessful crits.

**{N×5÷100}+{H×5÷100}** always equals 1.0, or 100%.

**Proof:**
19-20 with threat rolls and 20 without threat rolls are the same IF there's a 50% chance to hit

Proof:

19-20 = 10% chance

20 = 5% chance

.10 × .50* = .05, or 5%

*the percentage of of successful crits
So I used this to say that instead of failing crits 50% of the time with a 19-20/x2, I instead have a 20/x2 with guaranteed crit. This removes threat rolls as a factor for the sake of simplicity while proofing.

Lets say you roll 20 times, and roll each roll once (which is the average outcome of 20 rolls; this is what my formula should be doing)

AB 9

AC 20

Chance to Hit: 50%

Weapon: 10damage 19-20/x2 (although using 20/x2 guaranteed crit instead, to remove threat rolls as a factor)

10×9= 90 damage from the 9 normal hits, in those 20 rolls

0×10= 0 damage from the 10 misses, in those 20 rolls

10×2×1=20 damage from the 1 guaranteed crit

9

(hits)+10

(misses)+1

(crit)=20 rolls

90+0+30 = 110

110÷20 =

**5.5**
Now if instead of calculating this manually; I use my formula and factor in threat range.

AB 9

AC 20

Chance to Hit/Miss: 50%, or 10 rolls each on the die.

Weapon: 10damage 19-20/x2

10% chance to crit

[D×(20-T-N)+(D×T×{N×5÷100})+(D×M×T×{H×5÷100})]÷20

D×(20-T-N)

10 × (20-2-10)

10 × 8 =

**80**
D×T×{N×5÷100}

10×2×{10×5÷100}

10×2×.5 =

**10**
D×M×T×{H×5÷100}

10×2×2×{10×5÷100}

10×2×2×.5

40×.5 =

**20**
(80+10+20)÷20 =

**5.5**
If you see a mistake in this, Please let me know.

Reviewing what you told me did make me realize one small error, which is that if the AB exceeds the AC, N needs to be different for the first and second segment of the formula.

1 being a miss on the attack roll, but not being an auto failure on the threat roll.

I'm not sure how to easily fix this, though.