D&D 5e damage math — the recurring questions, answered exactly

The recurring questions, in one click each

The math everyone's already arguing about. Each card is a direct link to either the live comparison tool or the worked-out concept pillar.

• Greataxe (1d12+3) vs greatsword (2d6+3)?

  Same mean within half a point, very different shapes. Drag the HP slider — greatsword wins below the mean, greataxe wins above.

• Should I take Great Weapon Master?

  Closed-form rule: break-even AC ≈ attack-bonus + 8 for Greataxe-class. With +9 to-hit and a magic weapon, GWM is on against everything except plate-and-shield.

• Sharpshooter break-even AC?

  One AC point lower than GWM: attack-bonus + 7 for Longbow. And at long range, Sharpshooter is correct almost regardless of AC.

• Magic Missile or Scorching Ray at level 5?

  Crossover at AC ≈ 16 with +5 spell-attack mod. Above that, MM's auto-hit reliability beats Scorching Ray's higher mean — and force damage beats fire against a chunk of the Monster Manual.

• GWF reroll — placebo or real?

  Real, but small: ~+0.5 mean on Greataxe, ~+0.7 on Greatsword for the canonical reroll-on-1-or-2. Plus a quiet variance reduction that helps above the mean and hurts below it.

• Elven Accuracy worth the +2 ASI?

  Yes if you're at advantage on more than ~30% of attacks. Mean of 3d20kh1 is exact: 1981/120 ≈ 16.51, and crit rate jumps to ~14% on advantage rounds.

• Champion Fighter crit-fish — does it pay?

  Sometimes. Two builds with identical expected DPR can have very different per-target kill rates — the variance pillar applied to one weapon's crit profile.

• Advantage — really +5 to hit?

  Only at the middle of the AC range. Advantage is worth ~+3 to +5 in the AC 12–16 band, much less at the extremes. The full curve, worked out per AC.

• 3d4+4 vs 1d12+5 — same mean, who kills first?

  Both 11.5 mean. Reliable 3d4+4 wins below the mean; nuke 1d12+5 wins above. Crossover sits exactly at HP 12. The textbook variance paradox.

• 2d6+5 vs 3d4+4 at HP 11 — the upset

  The lower-mean roll wins kills 72.22% to 68.75%. Higher variance helps when the mean sits below the threshold. The single most counterintuitive result in dice math.

• Strahd at level 10 — how many rounds?

  Plan for 3–4 with a typical party at 50–70 aggregate DPR. The renewal-theorem floor is 144/60 = 2.4 rounds; variance pads the realistic count.

• Expected strikes to drop a boss?

  Once HP is past your single-strike maximum, mean wins linearly: E[N] ≈ HP/μ + bounded constant. Variance washes out into a half-strike correction.

5e quick-reference — what AC are we even talking about?

Diceplots' kill-probability questions all bottom out at "what AC and what attack bonus?" Use this as a calibration sheet when you're plugging numbers into the break-even pillars.

Pair these with the GWM break-even table (break-even AC ≈ attack-bonus + 8) and you can read off "is GWM on against this monster?" without doing the arithmetic. At mid-tier with +7 to-hit, GWM's break-even is AC 15 — exactly the median of the band.

Common 5e weapons, with the means computed

All means assume a +3 ability modifier (mid-game STR or DEX 16). Add 1 or 2 for higher modifiers. Click any expression to open the full distribution — including the per-outcome kill probability for any HP target.

Ranged:

Bring your own question

The grid above is what gets re-asked. The comparison tool handles anything you can write — 2d6r1+5 for Great Weapon Fighting, 2d20kh1 for advantage, 3d20kh1 for Elven Accuracy, 1d8:slashing+1d6:fire+3 for typed-damage hedges with per-type resistance via the ?r= query parameter. Full grammar at /syntax.

No accounts, no ads, no on-device tracking. The math runs client-side via a Rust engine compiled to WASM; the same engine ships in the iOS and Android apps with bit-identical results.

↦ Comparison tool — type your own expressions ↦ Concepts — the worked-out math behind every readout ↦ Expression syntax