5E Making the most of a Halfling's Lucky feature

Blue

Ravenous Bugblatter Beast of Traal
I'm in the mood to roleplay a martial halfling. I was looking at Lucky and thinking about how I can make the most use of it. More as a fun exercise for what I could do with the character, not because I expect to come up with a DPR-king or anything like that. Lucky doesn't move the needle enough to optimize around it - unless you're doing it for the joy of playing around. Which I am.

For my actual played character I'll be going with whatever will be fun to run, but I had a bunch of thoughts about Lucky and I wanted to have a theoretical discussion with folks. Get your ideas so we can really make a halfling shine regardless if it's the exact one I play.

The follows is me sharing a bit of my journey of discovery, and I hope your comments lead me to unexplored territory I hadn't considered.

So, let's set a foundation: Point buy, official books only, can't rely of getting specific magic items, played levels 1-12. We can talk up to 20 but who knows if a campaign will really reach there.

That last part is a bit telling. You see, my original thought was that the best way to make use of lucky was the most attack roles. Both fighter and warlock's Eldritch Blast can manage 4 without a bonus action. But ... at the levels likely to be played the best they can do is get 3 attacks (without a bonus action) and even there most other martial classes keep up with them until 11th, which is the last 10%-ish of play. So maybe that's not as big of a deal if it's only for a bit of play.

Halfling +2 DEX talks toward finesse or ranged weapons, though +1 CHR for Lightfoot can make warlock for EB (or Hexblade I guess) reasonable.

Bonus action attacks: two weapon fighting with the fighting style is pretty accessible, and damage drop compared to finesse weapons isn't a big deal. Monk also gives a bonus action attack, with the chance to get a second for a Ki. Monk is pretty MAD though, which might take up feat space. Would have to play with it. Polearm Master gives a bigger weapon die and some other goodies, but none of the weapons (even the errata'd in Spear) are finesse, so it would have to go STR.

And really, it seems like chance to hit is big for making the most of Halfling's Lucky. The smaller the die results that miss, the bigger the boolean hit/miss effect on rerolling one of them. If you hit on a 2 you normally have a 1/20 chance to miss. But if you reroll 1s, even if you need to keep it if it's another 1, it reduces that failure to 1/400. Now hitting on a 2+ isn't likely with bounded accuracy, but it's why moving to STR would dilute the talent a noticeable amount.

Advantage is helped by lucky in a different way. It's two rolls, so two chances of Lucky coming into play. But ignoring the double 1 case, the chance that the reroll is the best roll is a little less than half (since we already know the other roll is above a 1). So it triggers twice as much but is only meaningful half as much - not that it's bad, but it's not as huge a help as it might seem on first blush.

The more I think of it though Halfling's Lucky seems to give the most bang for the buck with the smallest chance to miss - that's a big impact vs. without Lucky. Compared to that, the chance of a "standard" 65% chance to hit increasing to 68% or something seems like not that huge of a change even with four attacks a round. Though as the saying goes, Quantity has it own Quality.

If reducing chance to hit is the best case, going ranged with the Archery fighting style is attractive. Sharpshooter with its -5 dilutes Lucky even if normally it's a great feat. Crossbow Expert on the other hand adds more of that quantity. But is the opportunity cost for that worth delaying +2 DEX (which increases chance to hit and damage), or is it only worth it once DEX 20 has been achieved?

And still, could Monk be the way to go? Does two-weapon come on early enough that it's the superior choice over levels 1-12 even if it doesn't finish quite as strong? EB Warlock with Devil's Sight and Darkness? Or, more excitingly, something I haven't thought about at all?

What's your thoughts?
 

Fenris-77

Explorer
If you want to maximize the number of ones you reroll, you need to maximize the number of dice you roll. Seems like some Captain Obvious stuff, but that's the place to start. The best way to roll the maximum number of d20s in combat is to maximize attacks and maximize the potential for advantage.

If you want to (mostly) cap the discussion around 12th level you have a lot of room when it comes to base attacks. Only the fighter gets more than one extra, and then only at 11th level, so not a lot of room to dip for synergy. There are lots of options for the base second attack though, so lots of room to play.

One solid option is to dip Ranger 3 and go Gloomstalker for the extra attack in each first round of combat (with the extra d8 damage). If you combine that with Monk and go way of the Shadow you are going to end up with a halfling ninja, which would be friggin' awesome. One the first round of combat you're rocking three monk weapon attacks and three unarmed strikes (Flurry of Blows). Shadow Step lets you manufacture advantage on your first attack, which you use for Stunning Stike, which, if it works, gets you advantage on all your other attacks that turn. Fun.

If you were going to go GloomStalker 3/Monk 9 you might still want to consider archery style, as you can throw monk weapons so long as they have that key word. So daggers mostly, but it's still not useless (call 'em ninja stars if it makes you feel better). Going SS for a feat can still be pretty deadly with thrown weapons, so that's an option.The other option that works ok there for this MC is Dueling Style to get +2 dmg on all your monk weapon attacks.

You will also be making a ton of Stealth rolls with this character, which gives you yet more opportunities for Lucky to kick in.

Another version of the same idea is to go Assassin 3/Monk X for the first round advantage and crits. I find the Gloomstalker build a little more reliable encounter to encounter, but the Assassin build is better nova if you're building that way. Ideally, at that point, you're looking at Fighter 2/Assassin 3/Monk 6-7 and you're playing with a ton of attacks and crits.
 

krustyy

Visitor
Bountiful Luck is on pg 73 of XGE, so no need for unearthed arcana.

The UA version is better, though probably because it's imbalanced. XGtE is once per round. UA is whenever.

edit: correction: It uses a reaction so both are only once per round, but the UA version lets you also​ use the lucky feature on yourself during that same duration.
 
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Fenris-77

Explorer
I think once per round still sounds pretty good. That said, if you can talk the DM into the UA version, more power to you.

*edit* Mostly I'm not going to spend a feat on it. I'd rather take the actual feat called Lucky and double on my luck. If I wanted all y'all to be lucky too I'd use the help action.:cool:

Having just said that, a Halfling Inquisitive with the Lucky feat is starting to have a real Dirk Gently vibe, which could be a very cool character if build right. Now I need to go play with lucky halflings too, damn you eyes.
 
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Esker

Explorer
Advantage is helped by lucky in a different way. It's two rolls, so two chances of Lucky coming into play. But ignoring the double 1 case, the chance that the reroll is the best roll is a little less than half (since we already know the other roll is above a 1). So it triggers twice as much but is only meaningful half as much - not that it's bad, but it's not as huge a help as it might seem on first blush.
I think your conclusion -- that Lucky helps about as much when you have advantage as when it doesn't, on average -- is more or less right, but I think the reasoning is missing some pieces. On most rolls the number you get doesn't particularly matter, only whether you meet the DC or not (or, in the case of an attack, whether you crit). So rerolling a 1 and getting a 2 technically increased your roll, but isn't going to make any difference outside the easiest of easy rolls.

On a straight-up roll (no advantage or disadvantage) with a baseline success chance of p, Lucky increases the success chance to p + 0.05 * p, that is by 5% of the baseline success chance. For a typical case where the success chance is around 60% or so, that's an increase of 3%.

For the same DC but with advantage, the non-halfling has a 1 - (1 - p)^2 success chance (for the 60% case without advantage, that's 84%). Applying Lucky, we typically only care about rerolls when we otherwise failed (on attack rolls we can still reroll for another chance at a crit, but that's a separate case). The chance that the first die shows a 1 and the second die is low enough for a failure is 0.05 * (1 - p). The chance that the second die shows a 1 and the first is low enough for a failure is (1 - p) * 0.05. So the chance that we get to reroll in a situation where we would have failed otherwise is approximately 0.10 * (1 - p). (We technically need to reduce that by 0.05^2 since we're double counting the double ones case, but let's set that aside for simplicity). Then, the chance that the reroll nets us a success is just p. So we have a marginal benefit of 0.10*(1-p)*p. This represents an extra factor of 2 * (1 - p) compared to the non-advantage case.

That means for rolls where we need a natural 11 or better to succeed, it's the same benefit that we have without advantage (well, 0.25% less). For more difficult rolls, the benefit is more than that; for easier ones, less. Taking 60% as a typical case, that means the halfling actually benefits slightly less from Lucky when they have advantage, if we measure in terms of the additive increase to the chance of success.

The increase to crit chance is simpler: 0.05^2 in the straight-roll case, and a bit less than twice that in the advantage case. Since going from a miss to a hit is worth more than going from a hit to a crit, the extra 0.05^2 ish crit chance we get with advantage doesn't balance the 0.05^2 that we ignored for simplicity above.
 
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Blue

Ravenous Bugblatter Beast of Traal
I think your conclusion -- that Lucky helps about as much when you have advantage as when it doesn't, on average -- is more or less right, but I think the reasoning is missing some pieces.
Thank you taking my intuitive take on it and showing the mathematics behind. Some people get caught on the "more rolls = more Lucky", but the real test of Halfling's Lucky isn't if it triggers, but how much more often the roll succeeds due to that trigger. People thinking only of the first part prioritize Advantage.
 

Esker

Explorer
The disadvantage case is nearly the exact opposite, by the way. Here, a 1 on either die corresponds to a failure, but the reroll only matters if the other die would have been a success. So the chance of getting to make a reroll that matters is just 0.05 * p + p * 0.05 = 0.10*p. Then, the chance that that reroll is a success is p. So the benefit is 0.10^p^2, which is more than the straight roll case when the straight roll would have been more likely to succeed than fail. Since that's arguably the most common case, you could argue that a halfling gets the most out of Lucky when they would be making lots of rolls with disadvantage! Can you think of any builds that pay for benefits by inflicting disadvantage on themselves? How about a character in a highly basilisk-heavy campaign? :)
 

Esker

Explorer
Actually, something this analysis implies is that builds that take a lot of penalized rolls with advantage will benefit (relatively) a lot from Lucky, and also that, when advantage is available often, feats become a little better compared to ASIs, since the Lucky benefit does a bit more work to offset the loss in accuracy incurred by foregoing the ASI. That suggests to me that a halfling barbarian with GWM making constant reckless attacks at -5/+10 is in a position to benefit a lot from their race (I mean, other than the fact that they don't get a racial STR bonus). Especially if they take PAM at level 8.
 

Blue

Ravenous Bugblatter Beast of Traal
That suggests to me that a halfling barbarian with GWM making constant reckless attacks at -5/+10 is in a position to benefit a lot from their race (I mean, other than the fact that they don't get a racial STR bonus).
Size though kills this. With their small size any weapon with Heavy is at Disadvantage, which would cancel out the Advantage of Reckless. GWM requires Heavy.

Any medium race could get the same (neither advantage or disadvantage) without the penalty from Reckless, or could get advantage with the penalty for Reckless.

So an apple-to-apples of a +STR medium sized race vs. Halfling, both with a heavy weapon, using -5/+10 from GWM, and using Reckless would go fairly easily to the non-halfling.
 

Esker

Explorer
Size though kills this. With their small size any weapon with Heavy is at Disadvantage, which would cancel out the Advantage of Reckless. GWM requires Heavy.
Ah, yeah. Forgot about the heavy property. It was already going to be pretty lousy anyway since they can't start with 16 STR so they'd perpetually be at -1 to hit and damage compared to any other race that gets a boost to strength. How about a sword bard xbow expert/sharpshooter using faerie fire constantly?
 

Esker

Explorer
You know, it occurs to me that it's not only the "multiple d20s = better value from Lucky" thing that's a fallacy, but actually, so is the "multiple attacks = better value from Lucky" thing. Since the increase in accuracy is the same on every roll, rerolling 1s gives you the exact same benefit on one big attack that it does on multiple small ones, if the total damage is the same (since average DPR is just accuracy * average DPhR). You don't use it as often, but when you do, the increase in accuracy buys you more. Which means that a ranged arcane trickster with sharpshooter and a familiar might actually be one of the best to take advantage of the ability, since they can hide / get help for advantage on their single attack pretty often without spending anything, except sometimes their owl's HP. Though again, halfling is not without downsides (no darkvision, no access to elven accuracy).
 
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Fenris-77

Explorer
If you want to take something really swingy, like rerolling 1's on a d20, and see that benefit on a nightly basis, you want to roll more dice. Obviously, if you roll X number of D20s the mathematical upside of rerolling 1's is the same regardless of the time frame of those roles. However, the occurrence of those roles in a given gaming evening, and thus the impact on how the ability feels like part of the character, number of dice does change the results dramatically.

That said, advantage is a clear winner in the roll more d20s competition, so it's not a bad idea anyway.
 

Esker

Explorer
If you want to take something really swingy, like rerolling 1's on a d20, and see that benefit on a nightly basis, you want to roll more dice. Obviously, if you roll X number of D20s the mathematical upside of rerolling 1's is the same regardless of the time frame of those roles. However, the occurrence of those roles in a given gaming evening, and thus the impact on how the ability feels like part of the character, number of dice does change the results dramatically. That said, advantage is a clear winner in the roll more d20s competition, so it's not a bad idea anyway.
Well, ok, if we're just optimizing for frequency of use, then sure, roll often and roll with advantage often. Blue's OP indicated that he cared about actual impact, not just how often you reroll. I guess you could optimize for frequency of rerolls making a difference, which lies between raw frequency of rerolls and expected gain from rerolls. I was just pointing out that expected gain isn't increased by spreading out impact over more rolls.
 

Blue

Ravenous Bugblatter Beast of Traal
If you want to take something really swingy, like rerolling 1's on a d20, and see that benefit on a nightly basis, you want to roll more dice. Obviously, if you roll X number of D20s the mathematical upside of rerolling 1's is the same regardless of the time frame of those roles. However, the occurrence of those roles in a given gaming evening, and thus the impact on how the ability feels like part of the character, number of dice does change the results dramatically.

That said, advantage is a clear winner in the roll more d20s competition, so it's not a bad idea anyway.
However, the obvious is a trap that will lead you astray.

We're not optimizing for number of times it comes into play. We're optimizing for the change it makes. The amout the boolean succeed/fail changes.

For example, if we hit on a 2+, our chance to miss diminishes twentyfold with lucky, since we go from 1/20 chance (a 1) to a 1/400 chance (a 1 then a 1). Getting four attacks instead of two won't make that kind of difference.

Same for advantage - advantage gives twice as many chances to roll, sure. But it also gives halves the number of times it matters. Say you have advantage and reroll 1. The other, because we're not rerolling, is from 2 to 19, which is an average of exactly 11. So that reroll won't increase the advantage roll 55% of the time - any reroll from 1 to 11. So twice as many times to trigger but only half the effect make Advantage NOT a big winner for in making lucky more effect, just in making it trigger more often which not the goal itself.

If you need more average numbers, like 60% chance to succeed, that's the places more attacks help. You go from a 40% chance of failure to a 35% + (5% * 40%) = 37% chance of failure. Yes, that 3% will make a difference over a large number of attacks, but it's not a dramatic chance. Say in 33 attacks the PC with lucky will have 1 more hit then the PC without it. Sure, reaching 33 swings sooner is nice, and any weapon wielder is happy with more attacks, but it's such a small change that Lucky isn't making a big difference over another character with the same number of attacks but without the Halfling's Lucky.
 

Fenris-77

Explorer
Do you think triggering lucky in combat regularly with advantage is aimed at hitting or crit fishing? I think crit fishing is where you'll see the biggest actual impact on effectiveness, and that is maybe the one case where rerolling ones with advantage actually might mean something even if the other roll hits.
 

Esker

Explorer
The impact of Lucky on crits is exceedingly tiny. Even with advantage, the proportion of rolls that become crits that wouldn't otherwise be crits is about one in every 200 attack rolls. I don't know about your table but I probably get something like six combat turns in a typical night. Assuming a martial class with two attacks, that's about one extra crit per 15 game sessions if every roll is with advantage (which is not realistic). In a dedicated weekly game, that's maybe two or three extra crits per real-time year? Maybe twice that if you've got an expanded crit range? But as a crit fishing choice it loses handily to being an elf and getting elven accuracy.
 
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Fenris-77

Explorer
Of course it loses to Elven Accuracy. That rule is bloody fantastic and changes the whole game for characters who have it. We were just talking about trying to massage some feeling into what is a much smaller and less impactful rule. Your comment about chances of rerolling for that crit are on the nose btw, it's what, half a percent or something? It's little. Noticeable, but little. That's why my suggestion initially was aimed far more at increasing the occurrence of the reroll per session, rather than based on the math of the statistical impact. Regardless of the math, if you actually get to reroll a d20 or two per session then you'll feel like the rule is part of the character. That means rolling 20-40 d20s per session, or 6-7 per encounter (minimum, assuming 6 encounters). If you can throw that many dice, you'll probably get the chance to reroll a couple and feel lucky, and the more dice you toss, the more rerolls you'll get, etc etc. Completely about the feels, not the maths.
 

UngeheuerLich

Adventurer
I'm in the mood to roleplay a martial halfling. I was looking at Lucky and thinking about how I can make the most use of it. More as a fun exercise for what I could do with the character, not because I expect to come up with a DPR-king or anything like that. Lucky doesn't move the needle enough to optimize around it - unless you're doing it for the joy of playing around. Which I am.

For my actual played character I'll be going with whatever will be fun to run, but I had a bunch of thoughts about Lucky and I wanted to have a theoretical discussion with folks. Get your ideas so we can really make a halfling shine regardless if it's the exact one I play.

The follows is me sharing a bit of my journey of discovery, and I hope your comments lead me to unexplored territory I hadn't considered.

So, let's set a foundation: Point buy, official books only, can't rely of getting specific magic items, played levels 1-12. We can talk up to 20 but who knows if a campaign will really reach there.

That last part is a bit telling. You see, my original thought was that the best way to make use of lucky was the most attack roles. Both fighter and warlock's Eldritch Blast can manage 4 without a bonus action. But ... at the levels likely to be played the best they can do is get 3 attacks (without a bonus action) and even there most other martial classes keep up with them until 11th, which is the last 10%-ish of play. So maybe that's not as big of a deal if it's only for a bit of play.

Halfling +2 DEX talks toward finesse or ranged weapons, though +1 CHR for Lightfoot can make warlock for EB (or Hexblade I guess) reasonable.

Bonus action attacks: two weapon fighting with the fighting style is pretty accessible, and damage drop compared to finesse weapons isn't a big deal. Monk also gives a bonus action attack, with the chance to get a second for a Ki. Monk is pretty MAD though, which might take up feat space. Would have to play with it. Polearm Master gives a bigger weapon die and some other goodies, but none of the weapons (even the errata'd in Spear) are finesse, so it would have to go STR.

And really, it seems like chance to hit is big for making the most of Halfling's Lucky. The smaller the die results that miss, the bigger the boolean hit/miss effect on rerolling one of them. If you hit on a 2 you normally have a 1/20 chance to miss. But if you reroll 1s, even if you need to keep it if it's another 1, it reduces that failure to 1/400. Now hitting on a 2+ isn't likely with bounded accuracy, but it's why moving to STR would dilute the talent a noticeable amount.

Advantage is helped by lucky in a different way. It's two rolls, so two chances of Lucky coming into play. But ignoring the double 1 case, the chance that the reroll is the best roll is a little less than half (since we already know the other roll is above a 1). So it triggers twice as much but is only meaningful half as much - not that it's bad, but it's not as huge a help as it might seem on first blush.

The more I think of it though Halfling's Lucky seems to give the most bang for the buck with the smallest chance to miss - that's a big impact vs. without Lucky. Compared to that, the chance of a "standard" 65% chance to hit increasing to 68% or something seems like not that huge of a change even with four attacks a round. Though as the saying goes, Quantity has it own Quality.

If reducing chance to hit is the best case, going ranged with the Archery fighting style is attractive. Sharpshooter with its -5 dilutes Lucky even if normally it's a great feat. Crossbow Expert on the other hand adds more of that quantity. But is the opportunity cost for that worth delaying +2 DEX (which increases chance to hit and damage), or is it only worth it once DEX 20 has been achieved?

And still, could Monk be the way to go? Does two-weapon come on early enough that it's the superior choice over levels 1-12 even if it doesn't finish quite as strong? EB Warlock with Devil's Sight and Darkness? Or, more excitingly, something I haven't thought about at all?

What's your thoughts?
I have a halfling monk and lucky rerolls happened quite often. 3 attacks on many rounds at level 2 and beyond is quite huge. You see a lucky reroll at least 1 per day.
 

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