How good is the Halfling “Lucky” trait? Discover the benefits of re-rolling 1’s on attack rolls, ability checks and saving throws!
Chapter II: A Rogue’s Luck, Or, Bilba Meets Slobberfink
Deep in a grim dungeon, Slobberfink the troll sleeps fitfully on a pile of trash. Clutched in his sinewy grasp is a long golden dagger. Out of the shadows, a young
hobbit halfling, Bilba the Burglar Rogue, slinks toward the troll. Suddenly, she trips over an old tin goblet lying discarded on the ground. The goblet clatters across the floor and Slobberfink sits bolt upright. His eyes stare into the gloom but, by some miracle, he is facing away from Bilba and doesn’t turn around. Wiping his eyes, he lies back down and his breathing slows as sleep overtakes him. The golden dagger lies forgotten beside him — easy pickings for the young thief.
Bilba seems to live a charmed life. Not that everything goes her way, of course, but she does seem to have a knack for getting out of trouble. Why do the gods favour her? Was she born under a lucky star? Maybe it’s the four-leaf clover she has pinned in her hair, or is there something else going on? Perhaps her player knows…
Of course Bilba’s player knows… Bilba’s “Lucky” trait allows her player to re-roll 1’s on attack rolls, ability checks and saving throws.1 So, just how lucky are halflings? Let’s compare them to humans and see what we can learn.
Human vs Halfling Luck
Whether a D&D character is a human or halfling, her player’s attack roll must meet or exceed her target’s armour class (AC). Similarly, ability checks and saving throws are measured against a difficulty class (DC). Intuitively, re-rolling 1’s will increase the odds of success. However, by looking into the Pool of Probability, we can see that the effect is relatively modest.
In fact, when rolling 1D20, re-rolling 1’s only increases the probability of success by an average of 1.22%. And, the benefits of being lucky shrink with both advantage and disadvantage! There is a minuscule 0.52% average increase in success with advantage. Rolling with disadvantage yields an average increase of 1.04%. Bilba the Halfling may be a little lucky, but her player is going to be hard pressed to notice her luck at the table!
Nevertheless, there is one obvious benefit to being a
hobbit halfling. As the chart below shows, Bilba’s player is almost half as likely to roll a natural 1. And, the feeling of rolling a critical failure and then snatching success (or at least a smaller loss) from the jaws of total defeat feels pretty lucky!
Check out these pages for more on Dungeons & Dragons 5E and probability theory:
- What is the Advantage of Rolling with Advantage? — A short article comparing the benefits rolling with advantage and adding a modifier.
- Feeling Lucky? — A comparison of the Lucky Feat, Diviner Portent Dice, and Halfling Lucky trait, by Michael O’Connor (an RPG blogger with a mathematical bent).