Concepts → Reliable vs nuke builds

Reliable vs nuke builds — same expected damage, opposite shapes, opposite winners

The build-guide question phrased as "should I dual-wield (lots of small swings) or two-hand (one big swing)?" is the same as the statistician's question phrased as "low-variance or high-variance for a given mean?" The answer depends entirely on where the target's HP sits relative to your average swing.

The setup

Two damage rolls with the same mean:

Reliable: 3d4+4. Range 7–16, mean 11.5, variance ≈ 3.75. Three medium dice average out, producing a tight bell-shaped distribution centred at 11–12.
Nuke: 1d12+5. Range 6–17, mean 11.5, variance ≈ 11.92. One fat die: every face 1–12 equally likely, so the distribution is uniform across the full 6–17 range.

Identical expected damage. Triple the variance on the nuke. Below, both panels show the kill probability against a 13 HP target — that choice of HP is deliberate; you'll see why.

3d4+4

min 7 max 16

6 0.00%
7 1.56%
8 4.69%
9 9.38%
10 15.63%
11 18.75%
12 18.75%
13 15.63%
14 9.38%
15 4.69%
16 1.56%
17 0.00%

1d12+5

min 6 max 17

6 8.33%
7 8.33%
8 8.33%
9 8.33%
10 8.33%
11 8.33%
12 8.33%
13 8.33%
14 8.33%
15 8.33%
16 8.33%
17 8.33%

The threshold table

Walk through several plausible target HPs:

Target HP	Reliable (3d4+4)	Nuke (1d12+5)	Winner
9 (chip)	15/16 = 93.75%	9/12 = 75.00%	Reliable
11	11/16 = 68.75%	7/12 ≈ 58.33%	Reliable
12 (the mean)	1/2 = 50.00%	6/12 = 50.00%	Tie
13	5/16 = 31.25%	5/12 ≈ 41.67%	Nuke
15	1/16 = 6.25%	3/12 = 25.00%	Nuke
16	1/64 ≈ 1.56%	2/12 ≈ 16.67%	Nuke
17 (only nuke can land it)	0	1/12 ≈ 8.33%	Nuke

The crossover is exactly at the mean (HP 12). Below the mean, reliable wins. Above the mean, nuke wins — and at HP 17, only nuke can land the kill at all because that's outside reliable's range.

Why this happens — the mass-redistribution argument

Imagine the distributions as a fixed amount of "probability mass" you're spreading across damage outcomes. Both have 100% total mass and the same average position (the mean, 11.5).

The reliable distribution piles its mass tightly around the mean — most rolls land between 10 and 13. The nuke distribution spreads its mass uniformly from 6 to 17 — equally likely to roll the floor or the ceiling.

For a kill-probability question, what matters is how much mass sits at or above the threshold. When the threshold is at or below the mean, the tightly-piled reliable distribution has more mass on the right side of the line. When the threshold is above the mean, the spread-out nuke distribution has more mass on the right side.

Stated as a rule: at the same mean, the lower-variance distribution wins below the mean; the higher-variance distribution wins above.

Where this matters in practice

D&D dual-wielding vs two-handing — two small attacks (reliable, more variance from the multi-roll structure) vs one big swing. Hit chance differences usually dominate the decision, but for damage-to-target the same lesson applies once both swings hit.
Baldur's Gate 3 Action Surge — extra attacks push you into the reliable regime. Useful against trash mobs you'd otherwise leave at 1 HP. Against a single beefy target where you need a one-round kill, a Smite-loaded greatsword swing (nuke) often outperforms.
Diablo / Path of Exile build identity — "is your damage profile bursty (nuke) or sustained (reliable)?" is exactly this dichotomy applied to per-second instead of per-swing. Bursty builds win the boss-burn race; sustained builds clear trash with fewer wasted hits.
Multi-hit cleave vs single-target — cleave spreads damage across multiple targets, making the per-target damage smaller and more reliable. Single-target focuses all of it into one fat-tailed roll.

Try it yourself

↦ /vs/3d4+4/1d12+5 — drag the HP slider, watch the winner flip ↦ /strike/3d4+4 — full reliable distribution ↦ /strike/1d12+5 — full nuke distribution