Concepts → Elven Accuracy

Elven Accuracy — what does `3d20kh1` actually look like?

Elven Accuracy lets an elf or half-elf with advantage on an attack roll keep the highest of three d20s instead of two. Closed form: it's an order statistic, not a regular d20 with a flat bonus. Worked out, it's worth between 1 and 6 points of effective to-hit depending on the AC band you're in, and the curve has the same peaked-in-the-middle shape as regular advantage — just steeper.

The mechanic

Elven Accuracy (DEX/INT/WIS/CHA variant) is a half-feat that gives +1 to one of those abilities and the bonus effect: when you have advantage on an attack roll using one of those abilities, you can reroll one of the dice once. In effect: you keep the highest of three d20s.

Diceplots' notation: 3d20kh1 — roll three d20, keep the highest one. Compare to 2d20kh1 (regular advantage) and 1d20 (no advantage).

The three distributions side-by-side

Same engine, three configurations. Each click on a percentage shows the exact rational. Note how the high-end probability mass piles up dramatically as you stack rolls.

1d20

min 1 max 20

1 5.00%
2 5.00%
3 5.00%
4 5.00%
5 5.00%
6 5.00%
7 5.00%
8 5.00%
9 5.00%
10 5.00%
11 5.00%
12 5.00%
13 5.00%
14 5.00%
15 5.00%
16 5.00%
17 5.00%
18 5.00%
19 5.00%
20 5.00%

2d20kh1

min 1 max 20

1 0.25%
2 0.75%
3 1.25%
4 1.75%
5 2.25%
6 2.75%
7 3.25%
8 3.75%
9 4.25%
10 4.75%
11 5.25%
12 5.75%
13 6.25%
14 6.75%
15 7.25%
16 7.75%
17 8.25%
18 8.75%
19 9.25%
20 9.75%

3d20kh1

min 1 max 20

1 0.01%
2 0.09%
3 0.24%
4 0.46%
5 0.76%
6 1.14%
7 1.59%
8 2.11%
9 2.71%
10 3.39%
11 4.14%
12 4.96%
13 5.86%
14 6.84%
15 7.89%
16 9.01%
17 10.21%
18 11.49%
19 12.84%
20 14.26%

Means:

E[1d20] = 21/2 = 10.5
E[2d20kh1] = 553/40 ≈ 13.825
E[3d20kh1] = 1981/120 ≈ 16.51

The mean jump from no-advantage to advantage is +3.325. The mean jump from advantage to Elven Accuracy is another +2.68 — smaller, because the curve is hitting diminishing returns at the high end. Each additional die you keep adds less than the previous one.

The hit-chance curve

What we actually care about: against a target with hit-DC D (i.e., you need to roll at least D on the d20), what's the hit probability under each option?

Closed forms for keep-highest-of-N d20:

P(1d20 ≥ D) = (21 − D) / 20
P(2d20kh1 ≥ D) = 1 − ((D − 1)/20)²
P(3d20kh1 ≥ D) = 1 − ((D − 1)/20)³

Worked out for a few common AC bands:

Need-to-roll `D`	`1d20`	`2d20kh1` (advantage)	`3d20kh1` (Elven Accuracy)	EA gain over advantage
`5`	80%	96%	99.2%	+3.2 pp
`10`	55%	79.75%	90.89%	+11.14 pp
`14`	35%	57.75%	72.54%	+14.79 pp
`17`	20%	36%	48.8%	+12.8 pp
`19`	10%	19%	27.1%	+8.1 pp

Peak gain is in the middle of the AC range — roughly when you need to roll a 12-15 to hit. That's also where regular advantage peaks, so Elven Accuracy preserves the same sweet-spot intuition. At the extremes (you almost always hit or almost always miss), Elven Accuracy adds less because there isn't much room for the third die to matter.

The "is it worth giving up the level-4 ASI?" answer

The real question players ask. Comparing the half-feat (+1 to a stat + Elven Accuracy) against the full ASI (+2 to a stat):

+2 ASI: +1 to-hit and +1 damage. Worth ~5pp hit chance flat, plus +1 damage on every hit.
Elven Accuracy half-feat: +1 to-hit and +1 damage (from the +1 stat) AND the third-die effect on advantage rounds.

The half-feat trades half a point of attack-mod for a third die on advantage rounds. If you're building toward something that gets advantage frequently — Pact of the Blade Hexblade with Darkness/Devil's Sight, an Assassin Rogue, a Battlemaster using the Trip / Disarming attacks for free advantage — Elven Accuracy comes out clearly ahead in DPR. If your build gets advantage rarely, the +2 ASI's flat +1 to-hit on every attack wins.

Rule of thumb: Elven Accuracy is ahead when you're at advantage on more than ~30% of your attacks, against typical mid-band ACs. Below that, take the +2 ASI.

Try it yourself

↦ /strike/3d20kh1 — Elven Accuracy distribution ↦ /strike/2d20kh1 — regular advantage ↦ /vs/3d20kh1/2d20kh1 — Elven Accuracy head-to-head with advantage