Advantage isn't "+5 to hit." It's a curve — and that shape changes which builds it actually helps.

The mechanic, briefly

Advantage: roll two d20s, take the higher. Disadvantage: roll two d20s, take the lower. Both cancel each other out (one of each gives a normal roll). You can't "stack" advantage — multiple sources of advantage just give one.

The flat d20 distribution looks like this — every face equally likely, mean 10.5:

How advantage reshapes the distribution

Mathematically, advantage produces the maximum of two independent d20s. The probability of rolling at least k on a normal d20 is (21-k)/20. With advantage, both rolls have to fall below k for the result to fall below k, so:

P(advantage ≥ k) = 1 − ((k−1)/20)²

The mean shifts from 10.5 (flat d20) to 553/40 = 13.825 with advantage — a +3.325 shift, the famous "advantage is about +3" result. Disadvantage symmetrically pulls the mean down to 287/40 = 7.175.

Side by side: the same d20, the same shape stretched right (advantage) and left (disadvantage). Threshold marker at 11 — the sweet-spot AC where advantage is worth the most.

The "advantage = +5 to hit" claim, dissected

Compare per-AC hit probabilities for a +0 to-hit attacker (so the AC value is the d20 roll needed):

Drag the to-hit bonus and watch the peak-gain AC slide right. The +to-hit sweet spot tracks AC ≈ to_hit + 11, which is just "the AC where you'd otherwise be at 50/50".

The "+5 to hit" claim is true in a band roughly AC 7 to AC 14. Outside that band, advantage is worth less. At the extremes (need a 2 or need a 20), advantage is barely worth a +1.

The intuition: advantage helps most when you have the most uncertainty — which is right around 50/50. When you almost always hit anyway, the second roll rarely changes the outcome. When you almost never hit, the second roll rarely lands the kill either.

Implications for builds

• Faerie Fire / Reckless Attack / Pack Tactics on a hard target (AC 18+): advantage is worth less than you'd guess from the rule of thumb. About +3 to hit, not +5.
• Same on an easy target (AC 8): also worth less. You'd hit two thirds of the time anyway; the second roll only rescues the ~22% of misses that flip to hits.
• Sweet spot: AC roughly equal to your to-hit + 11 (so you're rolling around 50% to hit). That's where Reckless Attack, Pack Tactics, Bless (separate effect), Bardic Inspiration on the attack, etc. all return their headline value.
• Critical hit interaction: advantage roughly doubles your crit rate. Two d20s, P(at least one nat 20) = 1 − (19/20)² = 39/400 ≈ 9.75% (vs 5% normal). A Champion fighter's extended 19–20 crit range with advantage hits ≈ 19% of swings. Combined with crit chance / +damage tradeoffs, this is most of what makes Reckless Attack actually good against bosses.

Disadvantage

Symmetric: P(disadvantage ≥ k) = ((21−k)/20)². Same curve, mirrored around the diagonal. Worst at AC 11 (drops a 50/50 to 25%), least damaging at the extremes (where you were probably going to hit or miss anyway).

Practical take: avoiding disadvantage is much more valuable than getting advantage because you usually have disadvantage forced on you in the AC band where it hurts most. Picking off ranged-attacker-in-melee penalty (which gives them disadvantage if they shoot you) at AC 14 vs you with +0 to-hit: their hit rate drops from 35% to 12%. That's like reducing their damage output by two-thirds.

BG3 and other 5e implementations

BG3 implements both directly. Notable interactions:

• High-ground advantage (BG3-specific, not in 5e tabletop) gives flat advantage on ranged attacks. Very strong for ranged builds because the AC range you fight is usually 13–17 — dead-centre in the band where advantage is worth its full +5.
• Reckless Attack barbarian: free advantage every turn at the cost of giving enemies advantage on you. Great offensively (your AC vs target ACs are often near 50/50), situationally bad defensively if your AC is what's keeping you alive.
• Rogue's Sneak Attack requires advantage (or an ally adjacent to the target). The advantage roll itself adds +3-ish to hit; the +Sneak Attack damage on top makes the swing worth disproportionately more than the advantage math alone suggests.

Try it yourself

↦ /strike/1d20 — flat d20 distribution ↦ /strike/2d20kh1 — advantage ↦ /strike/2d20kl1 — disadvantage ↦ /vs/2d20kh1/2d20kl1 — head-to-head ↦ Comparison tool — type your own expressions

The engine accepts NdMkh1 (keep highest) and NdMkl1 (keep lowest) — the 5e advantage / disadvantage primitive. Generic keep-K (e.g. 4d6kh3 for D&D ability scores) is parsed but not yet evaluated; that needs the order-statistic engine extension.