Elven Accuracy — what does 3d20kh1 actually look like?

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.

Means:

• E[1d20] = 21/2 = 10.5
• E[2d20kh1] = 553/40 ≈ 13.825
• E[3d20kh1] = 1239/80 = 15.4875

The mean jump from no-advantage to advantage is +3.325. The mean jump from advantage to Elven Accuracy is another +1.6625, half the size of the first jump, 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:

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. The +2 ASI gives +1 to-hit and +1 damage, worth ~5pp hit chance flat plus +1 damage on every hit. The Elven Accuracy half-feat gives +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 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.

The hidden upside: Elven Accuracy almost triples your crit rate on advantage swings. P(at least one nat 20 in 3d20) = 1 − (19/20)³ ≈ 14.26%, vs 9.75% for plain advantage and 5% for a single d20. Pair with a GWM Greataxe Fighter or any nova-on-crit build (Smite, Sneak Attack) and the third die's effective DPR contribution lands well above the to-hit-curve gain alone — see when crit chance beats base damage for the math.

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.

The per-attempt picture — what EA does to actual damage rolls

The d20 distributions above show the to-hit roll alone. Wire EA into a real attack expression and the picture sharpens — mass shifts off the 0-bar (miss) into the hit and (especially) crit branches:

Same Longbow attack (1d8+5, level-9 ranger), +9 to-hit vs AC 15. Without EA (left): P(miss) = 5/20 = 25%, P(crit) = 5%, mean per attempt = 147/20 = 7.35. With EA (right): P(miss) = (5/20)³ = 1.5625%, P(crit) = 1141/8000 ≈ 14.26%, mean per attempt ≈ 9.99. The mean jump (+2.64 per shot) is roughly half from the crit-rate amplification and half from the dropped miss probability.

The crit-fish synergy gets even louder when you stack Champion Fighter's 19-20 crit range:

P(crit) jumps to 1 − (18/20)³ ≈ 27.1% — over a quarter of EA-advantage swings crit. This is the "Elven Accuracy + Champion + nova-on-crit" build that makes EA look broken on paper.

Try it yourself

↦ /strike/3d20kh1 — Elven Accuracy d20 distribution ↦ /strike/2d20kh1 — regular advantage d20 ↦ /vs/3d20kh1/2d20kh1 — EA vs advantage, d20 only ↦ /strike/1d8+5 @ AC15 +9 elven — full per-attempt with EA ↦ /vs base vs EA per-attempt — see the mass shift ↦ /strike/… elven c19 — Champion Fighter EA crit-fish

Where this matters in practice

The third-die order statistic only pays off when you're at advantage often. Three places where that condition holds and Elven Accuracy actually shifts the math:

BG3 stealth-rogue / Astarion / shadow magic builds. Stealth gives advantage on the first attack each turn, and shadow magic / hide actions can sustain it. With advantage on 40-50% of attacks, Elven Accuracy is worth ~+3 effective to-hit and a crit rate near 14% on those rounds — see the BG3 weapon table for which weapons benefit most.

Champion 3 / Hexblade crit-fish. Elven Accuracy stacks the order statistic with Champion's expanded crit range: P(crit) ≈ 1 - (15/20)^3 = 0.578 on 19+ at advantage (a striking 58% per attack, vs 27% with regular advantage). The crit-chance pillar shows when that crit-rate inflation actually wins.

Sharpshooter / GWM with reliable advantage. The third die softens the −5 penalty enough that Sharpshooter stays on against AC bands that would normally clip it. The Sharpshooter break-even pillar shows the AC ranges where this matters — typically AC 18+ where a feat-tax flat advantage ranger otherwise gives up the trade.