# What is the maximum possible chance to critically hit?

What is the highest possible chance to critically hit? This can include content from any official source as well as Unearthed Arcana.

For example the level 15 Champion Fighter can critically hit on a roll as low as an 18. If the character has advantage they roll two dice. The Elven Accuracy racial feat allows you to reroll 1 of the d20s essentially creating double advantage. If you also take the Lucky feat you can roll an additional d20 essentially creating triple advantage.

Note I'm looking for the highest chance for the die roll to result in a crit, NOT factoring in effects that specifically guarantee a crit (e.g. any hit on a paralyzed or unconscious enemy, or features like the rogue's Assassinate feature).

Anything that guarantees a crit including predetermined dice rolls like portent should not be considered

I'm looking for both the methods used and the overall %chance to hit. For reference, the character does not have to be viable in a game; this is pure theory-crafting.

• Would you like all effects and features that guarantee critical hits to be ignored? What about things like the Divination Wizard's Portent feature? Should we assume the target is a creature to avoid things like adamantine weapons guaranteed critical hits on objects? – Medix2 Mar 13 at 1:42
• Assume the target is a creature yes. Anything that guarantees a crit including predetermined dice rolls like portent should not be considered – Himitsu_no_Yami Mar 13 at 1:49
• I assume we're not counting arbitrary answers that depend on wish, like "I wish my next hit had a 99% chance of critting", which would meet your criteria of not being a guaranteed crit but is not a very useful answer? – Theik Mar 13 at 9:19
• Is this meant to be a one-time event or a constantly achievable critical hit chance? Can we have help from our allies (the Help action, and also spells and so forth)? – Medix2 Mar 13 at 15:56

## Once a day with a 67.94% chance, sustainably once per turn with a 38.59% chance.

Race: Elf (Any) or Half-elf (Any)
Feats: Elven Accuracy (XGE), Lucky (PHB)
Spells: Find Familiar (PHB)
Magic Items: Luck Blade (DMG)
Classes:

• Champion Fighter 15
• Divination Wizard 2
• Anything 3

From Champion Fighter, you succeed at scoring a critical hit on 3 out of 20 dice rolls (17 chances to not fail).

1. At the beginning of the day, Portent provides us with 2 banked rolls (effectively 2 rerolls).
2. Before attacking, our Familiar uses the Help Action to grant us advantage (1 reroll).
3. Elven Accuracy allows us to roll a third time any time we have advantage (1 reroll).
4. Lucky allows us to make an additional roll before an attack roll is resolved (1 reroll).
5. The Luck Blade's Luck feature grants us an additional reroll once per day (1 reroll).
6. On our attack, we roll once in the first place (1 roll).

In total, we roll a d20 seven times. If any of those rolls would be an 18 or higher, we crit. Alternatively as long as all of them aren't 17 or lower, we crit:

$$\ 1 - \left(\frac{17}{20}\right)^7 = 67.94\% \$$

This result is very similar to Dale M.'s answer, however it outlines a small improvement: Halfling Luck is conditional on a 1/20 chance of rolling a one per reroll. However often that chance of rerolling is checked, Elven Accuracy grants an additional reroll unconditionally so it is the better feature.

## Now, to consider the reliability of this build, we'll look at features that are not expended:

1. Before attacking, our Familiar uses the Help Action to grant us advantage (1 reroll).
2. Elven Accuracy allows us to roll a third time any time we have advantage (1 reroll).
3. On our attack, we roll once in the first place (1 roll).

$$\ 1 - \left(\frac{17}{20}\right)^3 = 38.59\% \$$

## How does this compare to a Halfling with Halfling Luck?

1. Before attacking, our Familiar uses the Help Action to grant us advantage (1 reroll).
2. On our attack, we roll once in the first place (1 roll).
3. If either of our rolls are a natural 1, Halfling Luck lets us reroll (conditional reroll).

$$\ \left(1 - \left(\frac{17}{20}\right)^2\right) + \left(1 - \left(\frac{19}{20}\right)^2\right)\left(\frac{17}{20}\right)= 36.04\% \$$

For reference, these are the chances depending on how many rerolls you have available for use on the attack:

$$\ \begin{array}{|c|c|} \hline \text{Rolls} & \text{Chance} \\ \hline 1 & 15.00\% \\ \hline 2 & 27.75\% \\ \hline 3 & 38.59\% \\ \hline 4 & 47.80\% \\ \hline 5 & 55.63\% \\ \hline 6 & 62.28\% \\ \hline 7 & 67.94\% \\ \hline 8 & 72.75\% \\ \hline 9 & 76.84\% \\ \hline 10 & 80.31\% \\ \hline \end{array} \$$

As you can see, with each additional reroll, you start to see diminishing returns. At the end of the day, you CAN spend a casting of Wish on your next turn to reroll the past event to get an 8th reroll, but you'd have only increased your chance of scoring a critical hit by about $$\+5\%\$$. That casting of Wish could just as easily have been used to cast Sunburst for $$\12\text{d}6\$$ damage or an 8th Level Scorching Ray for up to $$\16\text{d}6\$$ (with more chances to crit because Elven Accuracy applies).

## Chance to score a critical per turn, at least 67.94%

For this, we're going to assume that you have a source of advantage for the entire turn, which is fairly expected in high level play. Either some Faerie Fire has hit the mark or a target has been knocked prone, Flanking rules are in effect, or you just used a Scroll of Foresight. Doesn't matter where it comes from.

This means that every attack made makes three rolls minimum.

We're also going to assume that the character will be using their bonus action to Two-Weapon Fight for an extra attack per Action.

Further, we're going to assume the character is under the effects of Haste, also a fairly expected boon in high-level play.

1. At Level 15, Fighters have three main-hand attacks.
2. Action Surge grants those three attacks an additional time once per turn.
3. Two-Weapon Fighting grants an additional off-hand attack once per turn.
4. The extra action from Haste can be used to make an additional main-hand attack per turn.

In total, the character is making eight (8) attacks and each of them is being rolled at least three (3) times.

$$\ 1 - \left(\frac{17}{20}\right)^{3 \times 8} = 97.98\% \$$

Action Surge is a resource that gets consumed, so in reality, only 5 of those attacks can be expected sustainably.

$$\ 1 - \left(\frac{17}{20}\right)^{3 \times 5} = 91.26\% \$$

And lets say that you are only granted advantage on that first attack, meaning only $$\3 + 4\$$ rolls made per turn.

$$\ 1 - \left(\frac{17}{20}\right)^{3 + 4} = 67.94\% \$$

Hey now, isn't that something? That number looks pretty familiar.

• I’d deduct a couple points for sustainability from the help action, because it’s only good for a single attack and a 15th level fighter will have at least 3 of those per turn (unless they’re using a crossbow without crossbow expert for some reason). – Cubic Mar 13 at 10:04
• @Cubic Why deduct points for that? The help action can be used every turn on at least one attack. It's not being used for every attack on that turn. – Axoren Mar 13 at 10:11
• Because it reduces your average critical hit chance if you can make use of it only for 1/3 or 1/4 of your attacks. – Cubic Mar 13 at 10:12
• @Cubic That will affect maximum chance of critical per turn, not maximum chance of critical on attack. – Axoren Mar 13 at 10:13
• To quote the OP: "I don't want to factor in predetermined rolls either such as what the level two Wizard provide" and "Anything that guarantees a crit including predetermined dice rolls like portent should not be considered" – Medix2 Mar 13 at 15:55

## Using just the Player's Handbook and Dungeon Master's Guide: just over 81%

A Champion Fighter 16/Diviner Wizard 2 with the Lucky feat and a Luck Blade.

First, your Familiar will Help to give advantage, then use your action to make your attack. A combination of Superior Critical, Halfling Luck, Lucky and your Luck Blade give you about a 49% chance of a critical (or precisely $$\{1,573,143\over 3,200,000}\$$) as follows:

.

As a Diviner Wizard 2, even if you don't get your critical here, you have 2 rolls "in the bank" - the chance that at least one of these can be used to get a critical is $$\q={1-{(1-{3\over 20})}^2}={111\over 400}\$$. This raises the overall chance to almost 63% (precisely $$\{803,846,073\over 1,280,000,000})\$$.

If you still don't have your critical, you can use your Luck Blade to cast Wish using your Action Surge and reroll the whole thing again. This gets you to just over 81% (precisely $$\66,428,289,129,851\over 81,920,000,000,000\$$).

This assumes you are looking for the best chance on a single attack. Given that a 20th level fighter gets 4 attacks per round and can action surge and two-weapon fight (with 2 Luck Blades) to get a total of 9, they will have a better chance of getting a critical hit from one of those without mucking around with True Strike and Wish; particularly if they can get advantage some other way - probably over 90% although things get complicated because the Lucky Feat will run out.

• This is almost what I'm looking for but not quite. I'll update the OP tomorrow unless someone beats me to it. I don't want to factor in predetermined rolls either such as what the level two Wizard provides – Himitsu_no_Yami Mar 13 at 7:13
• True Strike only applies to the first attack made on the next turn. Replace this with using your familiar from Find Familiar to receive the Help Action. – Axoren Mar 13 at 8:32