It began with Harvey.
A little odd piece of trivia for you. Back in High School and College my knick-name was Harvey. Not because of the movie of the same name, but for other reasons too long to get into here. But people always asked me if it was because of the movie. I got tired of hearing about it so I watched the movie, as was my habit, with my dad. He loved it of course, it had been a you man (younger than I am now) when it came out so he had good memories of it. I enjoyed it too, but I enjoyed mostly because my dad did. But that was my first introduction to a "Pooka."
Since then I have run into the pooka in other places. Robin Goodfellow of the Bard's Midsummer Night's Dream is another fine example. The creature always seemed perfect for D&D yet I can't find many examples of it outside of Celtic-focused gamebooks.
Púca
AKA Phooka, Puka, Pwca
Small or Medium Fey (Chaotic)
Frequency: Very Rare
Number Appearing: 1 (1)
Alignment: Neutral [Chaotic Neutral]
Movement: 120' (40') [12"]
Armor Class: 7 [10]
Hit Dice: 2d8+2* (11 hp)
Small: 2d10+2* (9 hp)
THAC0: 9 (+10)
Attacks: 1 bash
Damage: 1d6-1
Special: Fey, invisibility, shape-shifter, vulnerable to cold iron
Save: Monster 2
Morale: 10 (NA)
Treasure Hoard Class: None
XP: 35 (OSE) 47 (LL)
Str: 8 (-1) Dex: 16 (+2) Con: 14 (+1) Int: 12 (0) Wis: 10 (0) Cha: 14 (+1)
The púca (pl. púcaí) is a shape-shifting fey creature related to both goblins and to brownies. The natural shape of the púca is debated by scholars, but it is believed to be a small fey creature with animal-like features such as rabbit years, whiskers and pronounce front teeth. It is suggested that they even have little horns.
While not an evil creature, the púca delights in causing all sorts of mischief. They can take the shape of any animal they choose from Small to Large. They can even shapeshift into a medium humanoid creature. They will appear human, or elflike, but will have some feature of an animal such as goat legs, rabbit ears, or a tail. A favorite trick of a púca is to shift to a magnificent horse and tempt humans to ride it. Once the rider is on they burst into breakneck speeds and give their rider a terrifying ride. They will then deposit the confused and worn-out rider miles away from where they started. Another favorite trick is to shift into a small adorable animal such a baby bunny or kitten. When a human picks them up they will begin to yell at them in common speech and shift to a small, but ugly goblin. The púca delights in these pranks and never means to cause injury or harm.
The púca prefers to avoid all combat situations. They are not strong fighters at all and will use their invisibility to stay out of most fights. They can become invisible at will and remain invisible until attacked. If force they can usually bask with a fist or head bash. The púca's innate fear of iron prevents them from picking up and using any weapon. Iron weapons cause double damage to a púca.
Púcaí though can be bribed and even befriended if presented with their favorite blackberry wine. A drunk púca can foretell the future in a limited fashion, resulting in anyone sharing wine and stories with one a +1 on any roll between the sunrise the next day and the next new moon. A drunk púca though is a handful as it randomly shape-shifts throughout the night.
There are tales of evil púca the eat humans or drink their blood. But this is likely some other creature.
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So not a creature you are going to go out to pick a fight with. Not that you can't but there is not much point in that. While I am keenly aware that D&D can often devolve into a game of just fighting monsters (and I have enjoyed those games in the past too), monsters don't have to exist just to be killed by the PCs. Our púca here is a good example of that.