Advantage isn't "+5 to hit." It's a curve, and the 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 it still 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. That's 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, 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".

For a +0 attacker the "+5 to hit" claim holds roughly across AC 7 to AC 14. Outside that band, advantage is worth less. At the extremes (need a 2 or need a 20), it's barely worth a +1.

The intuition is that 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 anything. When you almost never hit, the second roll usually misses too.

What this changes for builds

The sweet spot is wherever your to-hit puts you around 50% to hit the target. For most overworld combat the AC is in that band, and the +5 rule of thumb is roughly right. The places it falls apart are at the AC edges.

Faerie Fire, Reckless Attack, or Pack Tactics on a hard target (AC 18+) gets you about +3 to hit, not +5, because you needed the high roll anyway and advantage doesn't add much on top of an already-tough roll. Same goes for advantage against an AC 8 mook: you'd hit two thirds of the time without it, so the second roll only rescues the ~22% of misses that flip. The trade is still usually worth it. The headline +5 is just oversold.

The other half of advantage's value is the crit-rate doubling, which is often more important than the to-hit boost. Two d20s give P(at least one nat 20) = 1 − (19/20)² = 39/400 ≈ 9.75%, nearly twice the flat 5%. A Champion fighter's 19–20 crit range with advantage hits ≈ 19% of swings. Combined with the crit chance vs +damage tradeoff, the doubled crit rate is most of what makes Reckless Attack actually pay against bosses, not the to-hit boost itself.

Elven Accuracy turns advantage into 3d20kh1, same peaked-in-the-middle curve but steeper, and it nearly triples your crit rate on advantage rounds. See Elven Accuracy for the worked-out distribution and the rule of thumb on whether it beats the +2 ASI.

Disadvantage

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

Avoiding disadvantage is usually more valuable than getting advantage. The reason is that disadvantage tends to be forced on you in the AC band where it hurts most. Take the ranged-attacker-in-melee penalty, which gives the shooter disadvantage on you, against a +0 to-hit attacker at AC 14: their hit rate drops from 35% to 12%. Two-thirds less damage from them that round.

BG3 and other 5e implementations

BG3 implements both advantage and disadvantage directly. The one thing it adds that the tabletop rules don't is high-ground advantage on ranged attacks. That's very strong for ranged builds because the AC range you fight in BG3 is usually 13–17, right in the band where advantage delivers its full +5.

Reckless Attack on a barbarian gives free advantage every turn at the cost of giving enemies advantage on you. Great offensively, because your attack vs the target's AC is often near 50/50 (peak advantage value); situationally bad defensively if your AC is what's keeping you alive.

Rogue Sneak Attack requires advantage (or an adjacent ally on the target). The advantage roll itself adds +3-ish to hit, but the +Sneak Attack damage stacked on top of the hit 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 NdMkh<K> / NdMkl<K> for any keep count — 2d20kh1 (advantage), 2d20kl1 (disadvantage), 3d20kh1 (Elven Accuracy), and the drop-pattern generalisation (4d6kh3 for D&D ability score generation, 4d20kh3 for the d20 analogue). The kept=1 case uses a closed-form recursion; kept>1 brute- enumerates outcomes (capped at 200K — fits 4d20 and 4d6).

Where this matters in practice

The peaked-in-the-middle advantage curve has consequences for which builds actually benefit from sources of advantage.

BG3 elven characters with shadow stealth. Shadowheart, Astarion, etc. get advantage from stealth reliably, and Elven Accuracy stacks the order statistic to 3d20kh1. The Elven Accuracy pillar shows the steeper version of this curve.

Champion Fighter advantage chains. Advantage doesn't just shift hit rate — it ~doubles crit rate (from 5% to 9.75%), which compounds with Champion's expanded crit range. The crit-chance pillar walks through where that compound effect actually pays off vs flat damage bonuses.

The "is this worth a spell slot?" question. Faerie Fire, Bless, Bardic Inspiration, Reckless Attack — every source of advantage costs something, and the +5 figure overstates the value at the AC extremes. Against AC 10 you're already hitting on a 5; advantage there is worth ~+1, not +5.