In NetHack, the trait is solely associated with Vorpal Blade which is retained in variants; it is defined by
When a monster (including you) is hit with Vorpal Blade, there is a 5% chance that Vorpal Blade will behead the victim - this deals HP damage equal to twice their maximum HP, and thus is technically not considered an instadeath. A player polymorphed into a monster with a head will die and be returned to their base form.
This chance does not change if the target monster has a headless form, but the sword will instead "miss <foo> wildly", dealing no damage. If the target is unsolid, the sword may slice "harmlessly" through its neck. If Vorpal Blade hits a jabberwock (including a player in the form of one), it will always behead them.
As implied by a comment in the code, how many heads the monster actually has (e.g. ettins and their zombie/mummy forms) is ignored - so long as it meets the above conditions, Vorpal Blade can behead and kill it.
Despite its name, the unused monster vorpal jabberwock does not have any beheading attacks and is simply a tougher jabberwock. Variants that implement the monster often give it this ability, and also make it so that Vorpal Blade always decapitates them as with normal jabberwocks, with the exception of SLASH'EM.
In SLASH'EM, Vorpal Blade beheads foes 10% of the time instead of 5%, making it considerably more powerful. A similar weapon, Thiefbane, has a 10% chance of beheading any @. The vorpal jabberwock will not be instantly beheaded by Vorpal Blade, and has the same 10% chance as any other monster.
The potion of invulnerability does not protect you from beheading, since it only prevents standard HP loss.
In Slash'EM Extended, the Zyborg quest artifact is the Verbal Blade, which can behead monsters like the similarly-named Vorpal Blade. The Ninja role has the Dragonclan Sword, a lawful katana which has a chance of beheading enemies, as their quest artifact.
A complete helmet protects against beheading attacks when worn.
UnNetHack also makes use of the vorpal jabberwock, though the chance of its claw attacks decapitating targets is halved to 2.5%.
GruntHack has the "vorpal" object property, which can only occur with bladed weapons. Single-handed weapons with the vorpal property function the same as Vorpal Blade, beheading solid non-headless targets with a 5% chance and always beheading jabberwocks. A two-handed vorpal weapon will instead bisect enemies as with The Tsurugi of Muramasa, having a 5% chance to instakill small creatures and cut deeply into large creatures.
GruntHack also implements the vorpal jabberwock and gives this property to its two claw attacks.
DynaHack and FIQHack
In EvilHack, the vorpal jabberwock behaves very similarly to GruntHack's version. Cerberus is also made immune to instadeath in this manner, as he will instantly grow a new head in its place before the other two can be removed.
dNetHack also has the vorpal object property, though it functions differently: the vorpal type is chosen based on the object's damage types, and vorpal weapons that are both slashing and piercing will decapitate the target. The chance to do so is 5%, as in vanilla NetHack.
In addition, dNetHack introduces several new artifacts capable of decapitation:
- Release from Care and Crescent Blade can behead their targets, with the same chance as Vorpal Blade.
- The Lifehunt Scythe will only behead targets while sneak attacking with it, with the normal 5% chance per hit.
- The Dragon's Heart-Stone can behead monsters that are not aware of your location.
- Snickersnee and The Kusanagi no Tsurugi are capable of beheading monsters.
- Levistus's Shadowlock can behead its target.