Sicarii Jaih Scarf - Brownian Motion Weapon

So, I made this weapon based upon the principle of Brownian movement. Brownian movement models can be used to predict the concentration of particles in a confined spaces, or the possible behavior of large groups of data points. If you are a math nerd (not me), or someone who wishes they were a math nerd (me), I have included an explanation of how I came up with the stuff for the Scarves/Eneedru at the bottom of the page. If math doesn't interest you, no worries, the explanation has no real impact on the use of the item in your games!

A portrait of a Sicarii woman.

Our scarves (Eneedru) are the breath of Jaih, scalding without heat, cutting without edge. - Line 374 of the Sicarii Fragments.

Murderers and artists, dancers and bloodletters, the Sicarii Jaih brought grace and art to the death they gave. Each was trained to weave their weapons, called Eneedru, into a dance that surrounded them with gray bands of cloud. Steps were unique to each dancer, though if possessed of the knowledge, one could identify which house trained them. Dancers would wear bells as they wove their weapon into art, the rhythmic movements creating a sort of song that was as unique to the dancer as the dance itself. Their lethal dance was called the Tandallum, the dance of culling that the universe continuously moves to. While no mere singular being, be they god or mortal, could reproduce the Tandallum perfectly, each unique dance of every dancer sought to, in some way, ape the universal culling movement. 

A woman wearing a matched pair of Endeeru

The Eneedru that the Sicarii Jaih wielded were things of gray smoke contained within rings and bracelets connected by chains. When loosed from the gloves, the gray smoke dances between the hands of the wielder, swirling and flowing like a scarf. Eneedru are capable of creating wounds that can range from minor to lethal, depending on the thickness of the smoke that 'struck' the target. Much like their arrows, the gloves of the Sicarii Jaih have outlived the memory of their makers.

The released blade, or scarf, of an Endeeru

Sicarii Scarf / Eneedru – AD&D/OSR/LotFP

Depending on the concentration of the smoke that strikes the target, different levels of damage can occur. To translate this concept into game mechanics, the smoke has the ability to do minor damage (1D6) to lethal damage (1D20). The probability spread is based upon one dimensional Brownian movement.

Damage:

1-6: 1D6

7-31: 1D8

32-68: 1D10

69-93: 1D12

94-100: 1D20

Damage Type: Slashing

Weapon Type: 2 Handed

Speed Factor: 8 (If you use speed factors in your game)

Notes: This weapon is complicated, but it can be fun. So, each time the character successfully strikes an opponent, roll 1D100 and consult the info above, that's the damage die used. The 'smoke' is actually a moveable field filled with gray particles that rasp away anything in their path like a sandblaster. While the weapon is considered 'two-handed' it can still benefit from the previous item I made called 'Sicarii Jaih Arrow'.

Proficiency: So, if you are using Weapon Proficiency Slots, this weapon requires its own slot. If you are not using weapon proficiencies with all character's being able to use all weapons, then a character starts at -3 to all to hit rolls with it. When the character has successfully defeated an enemy with HD equal to the user while using the weapon, reduce the penalty by 1. It is also recommended that until a person become proficient, a roll of a natural 1 should come with some hard consequences, such as the character accidentally hitting themselves.

Three Dimensional Brownian Motion.

Notes for Math Nerds: Recently, I learned about Brownian Movement from a Math-Magician friend. I did some research, and Brownian Movement can be used to describe the movement of smoke or other particles and how they can conglomerate together given a limited area in which to move. To come up with the percentile spread I used for 5 die types I used a Brownian Movement model along a single dimension with whole number unit types, like a number line. With 5 possible points, at the lowest and highest extremes there is a 1/16 chance of reaching such a distance. The second largest distances in either direction have a 4/16 chance of reach said distances. The middle point, or 0 on the number line, has a 6/16 chance of staying put. I put 1D10 at the start, or 0 point, then figured the percentages as an expansion from there. There is a guy named Toth who did a lot of work with the most visited sites along a line with set units. Along with proving that there is a maximum of 3 most visited site from each side of the start point of line with units, he also worked out the basic probabilities for each point. Common sites along the number line like to be symmetrical, since the there is no greater likelihood for any particular direction. With 5 possible points, the 0 point/start point is given the highest likelihood, though presently I am not sure why. I don't understand this stuff completely, but I am learning. Here is one of the websites I have been using to learn about 1-Dimensional Brownian Movement. Let me know if my math is off:

http://mathworld.wolfram.com/RandomWalk1-Dimensional.html

With the Scarf/Endeeru, the gray particles that make up the 'smoke' are 330 picometers that are thrown about with incredible force. The weapon is a sand-blaster that is sharper than a razor, which has a width of 101 Million picometers wide. The particles conglomerate in masses like smoke, with each particle moving around randomly (Brownian Movement) with a speed of 400 m/s. The force of each particle is enough to easily rasp away skin and bone.