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Article Preview: Lucky Success Odds
🕑 Added 2018-12-07 23:41:35 +0000 UTC "You've got to ask yourself one question: 'Do I feel lucky?' Well do ya, punk?"It's no secret that the Lucky feat is one of the most powerful in 5th Edition Dungeons & Dragons. Along these same lines, The Divination Wizard's Portent dice allow them to use prerolled dice where they otherwise might be a victim of fate.
While the Halfling racial feature Lucky is often grouped with these two abilities in discussion, it is a much more limited feature, which can lead to it becoming overvalued by association.
Let's compare the mechanical advantages imparted by each of these feat(ure)s, and see what kind of benefits a character obtains from each.
Lucky Feat
Lucky gives you three shots at turning a potentially bad roll into a success. While this mechanically functions as advantage, the fact that you don't need to use it until after rolling extends the mileage of your three uses.
Lucky gets some real power when faced with disadvantage, due to an interesting quirk in the way that the rule works. After rolling both dice, you can use Lucky to roll a third die and take the best of the lot. This basically turns disadvantage into super advantage.
Analysis
When you're making a regular roll, the Lucky feat basically gives you advantage on the attack. You can see this additional benefit in the red bars stacked on top of the regular odds. The percentages in the chart are the odds that the feat will assist you on a given roll.
With a regular roll, you will get a benefit from the Lucky feat on 4.8% to 25.0% of your rolls. On average, you will get a benefit from the Lucky feat on 16.6% of your rolls.
While having advantage does diminish the difference that the Lucky feat makes, it still has a strong influence on your odds of success. The Lucky feat with advantage can increase your odds between 0.2% to 14.8%. You will get a benefit in 8.3% of cases on average.
Against disadvantage, the Lucky feat increases your odds between 9.7% to 63.1%. Your will experience a benefit from Lucky on 41.6% of your rolls on average.
As you can see, this is where Lucky really shines. The Lucky feat can help you with disadvantage on up to 63% of your rolls. If you are faced with disadvantage, your worst-case scenario is that you'll see a benefit in 10% of occasions. The greatest benefit is when you need a high roll--a miniscule success chance that becomes many times more likely with the Lucky feat. Any time you need a roll over 15 against disadvantage, the Lucky feat increases your odds of success at least sixfold.
Diviner Portent Dice
This comparison is a little tougher, since the Portent dice must be declared before the roll, unlike the Lucky features which allow you to roll again after the initial roll. When you get two Portent dice (at level #), the odds of having a die that can help you are the same as rolling with advantage. When you get three Portent dice (at level #), the odds go up to three dice, as if you were using Elven Accuracy. The dice recharge on a long rest.
Analysis
When you have access to the full unused set, Portent dice effectively give you advantage on any attack, ability check, or save. Since you need to apply the die before the roll, let's just look at the straight odds of two dice and three dice.
Portent dice are rarely useless. Since they can be used against opponent attack rolls, ability checks, and saving throws, they are the most versatile mechanic in the rerolling sphere. Even a low roll can be useful in this context.
GRAPH WITH ADVANTAGE AND SUPER ADVANTAGE SIDE BY SIDE BAR GRAPH
Halfling Lucky
Unlike the Lucky feat and Diviner's Portent dice, the Lucky racial feature only triggers on a natural 1, which occurs 5% of the time. In a concession to the limited power of this racial feature as compared to the feat and class feature, there is no limitation on its use. It procs every time you roll a natural 1, regardless of whether you're rested and recharged.
This feature is also limited in that it only applies to your own rolls. There's no imposing disadvantage on an opponent attack (Lucky feat) or dice swapping to ensure that an opponent misses an attack or fails a save (Portent dice).
Analysis
While Lucky may increase your chances to succeed on a given roll from 0.25% to 4.75%, this difference is quite small in comparison to the Lucky feat and the Diviner's Portent dice. This is because Lucky only benefits you when you roll a natural 1, and then you are successful on the succeeding roll. To see how much this helps, you multiply 5% (the chance of a natural 1) by your chance of success.
Here's the Lucky benefit for each die roll.
The benefit is overall smaller with advantage, although it can be a little higher if you need to roll a 13 or better:
On average, you will benefit from Halfling Lucky on 2.4% of your rolls. When rolling with advantage, you will benefit from Halfling Lucky on 1.3% of your rolls. These benefits are razor-thin as compared to the charts above.
Conclusions
On average, Halfling Lucky is about 7 times as strong as the Lucky feat.
Thankfully, the Lucky racial feature applies to every roll, as opposed to being selected by the player after the fact. This is a nice synergy, where the racial feature extends the longevity of the feat. Elegant design seeks to complement in this fashion instead of stepping on the toes of similar design elements.
