I have Elven Accuracy so with advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can reroll one of the dice once.

So what are my crit chance with a crit range of 18/20 with three rolls also what would be the crit chance with a crit range of 17/20 with three rolls.

For "at least one" probability problems, it's usually easier to start by calculating the chance that none of the dice crit, as that saves you the hassle of combining the probabilities of getting 1/2/3 crits.

Best of three rolls with 18-20 crit range: ~39% chance to crit

Chance that a single die will not crit: 17/20 = 0.85

Chance that all three dice will not crit: (17/20) x (17/20) x (17/20) = 0.614125

Chance that at least one die will crit: 1 - (17/20)³ = 0.385875

Best of three rolls with 17-20 crit range: ~49% chance to crit

Chance that a single die will not crit: 16/20 = 0.8

Chance that all three dice will not crit: (16/20) x (16/20) x (16/20) = 0.512

Chance that at least one die will crit: 1 - (16/20)³ = 0.488

The other answers do a good job of answering the question, but I'll point out how you can answer questions like this in the future:

https://anydice.com/ is a very powerful (if slightly complicated) calculator for these sorts of questions. In your case, you'd enter the query:

output [highest 1 of 3d20]

And then select "At Least" from options below to get this table, which shows the odds of getting at least each number:

The result, is 38.59% for a crit range of 18, and 48.8% for a crit range of 17

If p is the probability of a crit on a single role, then 1-(1-p)^N is the probability of at least one crit on N roles.

so for N=3 and p=3/20, P=38.6%

for crit range 17-20, P=48.8% (WOW!)

It depends on how you use the Elven Accuracy Die

There's two ways that players are legally allowed to use the Elven Accuracy Die:

• Replace the lower of the two advantage dice (Type A)


• Replace the higher of the two advantage dice (Type B)

In the former case, this roll is mathematically equivalent to rolling 3 dice and taking the highest. In the latter case, it's more like rolling two dice, taking the lower, and then taking the higher of that result and a third die.

begin{array}{r|l|l}
text{Outcomes} & text{18-20 A} & text{18-20 B}
\ hline
text{Non-Crit} & text{61.413%} & text{83.088%} \
text{Crit} & text{38.588%} & text{16.913%} \
end{array}
begin{array}{r|l|l}
& text{17-20 A} & text{17-20 B} \ hline
text{Non-Crit} & text{51.200%} & text{76.800%} \
text{Crit} & text{48.800%} & text{23.200%} \
end{array}

Note: as far as I'm aware, in 5th Edition D&D, it is not possible to get a Critical hit range that includes 17. It's possible I'm unaware of a specific class feature or magic item that is expanding the range beyond what can be attained by a Champion Fighter at level 15. But as a result, the second table (the 17-20 range) does not have practical use in this game.