# Looking for math: Halfling Lucky vs. Elven accuracy

#### Blue

##### Ravenous Bugblatter Beast of Traal
My anydice-fu isn't up to this task, I was wondering if I can get some help.

I'd like to compare "X or better" rolls so I can see if attacks would hit for:

This would represent basically tier 2, when the ability score has not been maxed yet so a dex increase is directly comparable.

My plan after that is to multiply the elven option by 10 (rapier + 3.5 dex* + dueling style) and the halfling option by 10.5 (rapier + 4 dex + dueling style) to account for the extra damage of +2 dex. (This isn't needed with a bow, since a halfling can't use a longbow without disadvantage, so the smaller damage die but the higher Dex are a wash).

EDIT: * Oh shoot, I forgot Elven Accuracy was a half feat which can add to Dex. Grr. Adjusting numbers above to give the halfling a ".5" bonus.

And works out special for crits, which elven accuracy favors.

It's a given that the halfling will do better without advantage or with disadvantage - higher dex plus Lucky still applies. I'd like to see how it stands up to Elven Accuracy when both have advantage.

To be blunt, I've seen a lot of excitement on both forums and in games for elven accuracy, and I wonder if we've had a sleeper with similar characteristics outside SS/GWM we've undervalued since 5e came out.

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#### FrogReaver

##### As long as i get to be the frog
When you have advantage and roll 2 on the first dice and 1 on the 2nd dice does the halfling reroll let you reroll that 1? Do you get to reroll and then decide which value to use? Must you decide which value to use before the reroll?

#### RogueJK

##### It's not "Rouge"... That's makeup.
When you have advantage and roll 2 on the first dice and 1 on the 2nd dice does the halfling reroll let you reroll that 1?

Yes, Halfling Lucky lets you reroll that 1. PHB p. 173:

When you have advantage or disadvantage and something in the game, such as the halfling’s Lucky trait, lets you reroll the d20, you can reroll only one of the dice. You choose which one. For example, if a halfling has advantage on an ability check and rolls a 1 and a 13, the halfling could use the Lucky trait to reroll the 1.

Do you get to reroll and then decide which value to use?

Sort of. Advantage means "take the higher of the two dice". So you'd take the higher of the two dice, after you reroll the 1.

Must you decide which value to use before the reroll?

No. See above. It will depend on what you roll on the Halfling Luck reroll. If you roll a 3 or better on the reroll, you would take that higher roll. If you roll another 1, you'd take the 2.

#### FrogReaver

##### As long as i get to be the frog
Yes, Halfling Lucky lets you reroll that 1. PHB p. 173:

When you have advantage or disadvantage and something in the game, such as the halfling’s Lucky trait, lets you reroll the d20, you can reroll only one of the dice. You choose which one. For example, if a halfling has advantage on an ability check and rolls a 1 and a 13, the halfling could use the Lucky trait to reroll the 1.

Sort of. Advantage means "take the higher of the two dice". So you'd take the higher of the two dice, after you reroll the 1.

No. See above. It will depend on what you roll on the Halfling Luck reroll. If you roll a 3 or better on the reroll, you would take that higher roll. If you roll another 1, you'd take the 2.

What if you roll two 1's and have advantage. Do you reroll them both?

#### RogueJK

##### It's not "Rouge"... That's makeup.
What if you roll two 1's and have advantage. Do you reroll them both?

No. Only one. The first sentence of that quote I posted from PHB p 173 addresses that very situation.

#### FrogReaver

##### As long as i get to be the frog
Chance to Hit with advantage with halfling lucky:

Die1Probability = BaseChanceToHit + .05*BaseChanceToHit
Die2Probability = .95*(Die1Probability) + .05*(BaseChanceToHit)

ChanceToMiss = [(1 - Die1Probability)*(1-Die2Probability)]
ChanceToHit = 1 - ChanceToMiss

I think you should be able to use this information and compute what you are wanting to find. Any Questions on this calculation?

#### FrogReaver

##### As long as i get to be the frog
@Blue

I did the calculations and it looks to me like you have 2 scenarios

1. The +1 Dex from Elven Accuracy increases your dex mod to the same bonus the +2 would
In this case elven accuracy is better against all AC values and climbs to a 21% more damage against AC 20.

2. The +1 Dex from Elven Accuracy doesn't increase your dex mod to the same bonus the +2 would.
In this case halfling's with lucky are better across all AC's. They are better against lower AC's than higher ones. The relative damage increase climbs to 9% more damage against AC 11.

(All this was without factoring in critical hits)

Elven accuracy makes critical better and the margin that the halfling is better in case 2 is so razor thin for most ac values that after the impact of the critical hit is factored in I expect Elven Accuracy to slightly lead across most AC values except the lowest.

Comparing to a build that just has advantage the halfling lucky and advantage build only increases your damage output by 1%-4% across all AC values.

*All AC values = 11AC to 20AC

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#### Blue

##### Ravenous Bugblatter Beast of Traal
@Blue

I did the calculations and it looks to me like you have 2 scenarios

1. The +1 Dex from Elven Accuracy increases your dex mod to the same bonus the +2 would
In this case elven accuracy is better against all AC values and climbs to a 21% more damage against AC 20.

2. The +1 Dex from Elven Accuracy doesn't increase your dex mod to the same bonus the +2 would.
In this case halfling's with lucky are better across all AC's. They are better against lower AC's than higher ones. The relative damage increase climbs to 9% more damage against AC 11.

(All this was without factoring in critical hits)

Elven accuracy makes critical better and the margin that the halfling is better in case 2 is so razor thin for most ac values that after the impact of the critical hit is factored in I expect Elven Accuracy to slightly lead across most AC values except the lowest.

Comparing to a build that just has advantage the halfling lucky and advantage build only increases your damage output by 1%-4% across all AC values.

*All AC values = 11AC to 20AC

Thank you, this is really cool!

Would it be fair to say this then:

In a build with reliable advantage, Elven Accuracy trumps Halfling Lucky. In a build without reliable advantage AND no critical multipliers (champion, GWM, etc.) Halfling Lucky is better.

I wonder what the ratio of advantaged attacks to regular attacks needs to be for Elven Accuracy and Halfling Lucky to be about the same. (Again, assuming no crit specials which EA is a multiplier for.)

#### FrogReaver

##### As long as i get to be the frog
Thank you, this is really cool!

Would it be fair to say this then:

In a build with reliable advantage, Elven Accuracy trumps Halfling Lucky. In a build without reliable advantage AND no critical multipliers (champion, GWM, etc.) Halfling Lucky is better.

I wonder what the ratio of advantaged attacks to regular attacks needs to be for Elven Accuracy and Halfling Lucky to be about the same. (Again, assuming no crit specials which EA is a multiplier for.)

I think that the ratio is going to change depending on what AC value you are looking at. I would consider it this way. Against Solo enemies which are more likely to have higher AC the party is more likely to have advantage on them. That makes the elven accuracy setup the go to for solo slaying IMO. Against larger groups of enemies I think the halfling is going to be better because they will have lower AC's and advantage will be less likely.

However, the most important point of diffrentation IMO is whether the +1 dex takes you to the next dex mod. If it does then i'd probably take being slightly worse against many different enemies to be very good against high ac solo type enemies. If you don't get that dex bonus bump then you are significantly better than the elven accuracy character when you don't have advantage. In that case I'd take the character with the higher dex bonus.

#### Gavin O.

##### First Post
There is one interesting case in which Lucky is better, and that's that Lucky can be used with Reckless Attack while Elven Accuracy can't. Obviously a Halfling Barbarian isn't the most optimal, you're starting with +2 Strength, but at level 4, you can take +1 Strength/+1 Dex, and you deal pretty good damage.

Assuming AC 14, you hit on a roll of at least 9, or 11/20. If you roll a 1 you get to reroll, so that's another (11/20)*(1/20). In total that's 57.75% to hit but not crit.
If you have advantage, we double that result (since we're making two attacks), but subtract the square (since both results coming positive doesn't count as two hits) 57.75% + 57.75% - (57.75%*57.75%) = 82.14%

Our odds of a critical hit on one dice are 1/20 (that we roll a 20) + 1/400 (that we roll exactly a 1 and then a 20) = 5.25% We're rolling 2 dice, so we double it, and subtract the miniscule probability of 2 20's: 5.25% + 5.25% - (5.25%*5.25%) = 10.77%

Since we can't use a heavy weapon and get a flat bonus to damage, I'll be doing the math using dual handaxes.

Hit damage: 1d6+5 = 8.5

Second hit: 1d6+2 = 5.5

Crit damage: 2d6+5 (12) or 2d6+2 (9)

Total DPR:
First attack: 8.5* 0.8214 + 12 * 0.1077 = 8.2795
Second Attack: 5.5 * 0.8214 + 9* 0.1077 = 5.487
Total: 13.7665

If we compare that to a strength race that just took a strength ASI at level 4, we find an 78.25% chance to hit, 9.75% chance to crit, and +1 to damage on their first weapon attack
First attack: 9.5 * 0.78 + 13 * 0.0975 = 8.7013
Second Attack: 5.5* 0.78 + 9* 0.0925 = 5.1362
Total: 13.8376

So a lucky halfling Barbarian can almost keep up with another barb who has one more point of strength. Halfling would actually be slightly better for a Zealot, since their bonus damage benefits more from better crit chance and a higher chance to hit. Once you hit level 12 and can get 20 Strength, I think Halfling could outdamage most other Barb races for dual wielding.

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#### FrogReaver

##### As long as i get to be the frog
[MENTION=6941440]Gavin O.[/MENTION]

Not that it changes the results enough to worry about but give that when both die come up as a 1 that you only get a single reroll, the calculations you are using aren't 100% accurate.

#### Gavin O.

##### First Post
[MENTION=6941440]Gavin O.[/MENTION]

Not that it changes the results enough to worry about but give that when both die come up as a 1 that you only get a single reroll, the calculations you are using aren't 100% accurate.

I'm curious as to why that's the case? If you're rolling with advantage, you are rolling 2 d20s, and from Elven Accuracy, we know that the results of those dice can change before the better one is chosen, (since we can reroll one of them). I'm pretty sure that if you roll two 1s at advantage, you would be able to reroll both of them using lucky.

#### FrogReaver

##### As long as i get to be the frog
I'm curious as to why that's the case? If you're rolling with advantage, you are rolling 2 d20s, and from Elven Accuracy, we know that the results of those dice can change before the better one is chosen, (since we can reroll one of them). I'm pretty sure that if you roll two 1s at advantage, you would be able to reroll both of them using lucky.

The bolded is incorrect. Another poster posted the relevant rules on this thread.

#### Gavin O.

##### First Post
Ahh, you're correct. Well hopefully I don't roll two 1s at advantage and reroll into another 1. If that happened, I would probably be like "welp, the god of luck has decreed it, I'm not supposed to hit this enemy"

#### FrogReaver

##### As long as i get to be the frog
Ahh, you're correct. Well hopefully I don't roll two 1s at advantage and reroll into another 1. If that happened, I would probably be like "welp, the god of luck has decreed it, I'm not supposed to hit this enemy"

Right. It’s so rare to happen that there’s very little impact on chance to hit either way.

#### Alice Mur

##### First Post
I had the same prob, but now I'm ok

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