Dice equivalence

UPDATE: I have made a website of the simulator (dnd.matteoferla.com).
SEEN ALSO: Description of battle simulator and some analysis, the GitHub code for the encounter simulator, analysis of dice equivalence

As explored previously, dice with the same mean can safely be replaced with each, a principle nicknamed dice equivalence in a previous post.

Utility: Changing a boring 1d8 for a crazier dice combination spices things up.
Sidedness: The number of sides of a die. Not sure if there is a word to describe the number of sides of a polyhedron. Hence this made up word.
Mean: This is half its sidedness plus 0.5. The 0.5 is because a die starts from 1, otherwise one would make a fencepost error. As a result a 2d4 is actually equivalent of a 1d9, not a 1d8. A bonus of +1 is equivalent to increasing the sidedness by 2.
Variance:

• The variance greatly increases with sidedness.
• The variance of multiple dice is the sum of each variance (Bienaymé formula).
• Bonuses do not affect variance and a fixed damage has therefore zero variance —damage dealt as when visiting the plane of Mechanus.
• Variance decreases the more dice are used and the distribution becomes closer to a bell curve —flipping coins would give a bell curve.

D&D5: planar pub crawl

I once run a very successful high level one-off D&D 5 game across the Outer Planes with a twist.
It was a group of angels on a pubcrawl across the various planes send by their superiors following a challenge.

The chemistry of D&D

In D&D there are 4 elemental planes and matter is made of the four classical elements differentially permeated by positive (life) and negative (death) energy, and with the magical weave thrown in.

The four elements were briefly supplanted by phlogiston, the essence of combistion, which along with dephlogistonated residue made all matter. In Spelljammer 'phlogiston' has terrible usage as the interstellar medium, which in all likelihood is from someone's laziness at not checking their words as they meant æther.

Modern atomic elements do not explicitly feature, except in Order of the Stick and in games that are higher than progress level 5 (Alternity/D20 modern term).

Radiation features in Pathfinder Technology guide, which means that nuclear physics is possible. This means that if the minor conjuration were still around he could have summoned a critical amount of a fissile material, which combined with poison and fire immunity would be unspeakably awesome.

Also, atomic theory elements would mean different planar realms. It would not be recommendable visiting the trans-uranic planar realms. But the gold plane would probably make the GM cry the most.

Technomagic

One thing that has always fascinated me is technology in D&D. Introducing technology to a D&D game can come in many shapes and sizes and there are many sources, including the 5e Dungeonmaster's guide, which has one or two pages on laser weapons.

Unlucky dice? SkipBo as a die

Most players at some point will swear at their die and start to doubt the laws of physics. Having a random output is half the fun of it, as is clear when NPCs deal damage by the set output or when the encounter is in the plane of Mechanus (the latter is fun due to madness of the plane, but that's a different point). One way to stop complaints about accursed dice is to not use dice and use cards.

Blank tokens

I have uploaded my blank token sheets here:
https://www.scribd.com/doc/269498383/Blank-character-tokens
They are a modification of Paizo's to make them blank.

I (not the artists) kept them all in a box and they even get used in games they were not drawn for, each one tells a story. I really recommend any GM who has a printer to buy 200 gsm cardstock and make the players use them. Some are well drawn, while others are not, but they are all reminders of awesome games played.

And are a good hook for people to ask questions like "Why is there a picture of a horse walking on the ceiling?" or "Why are there two tokens, one of an old man in a dressing gown and harp, while the second all begadgeted?"... Which is your cue to tell the amazing tale of that game.


Other files you might find useful are:

• An item tracking sheet with details of locations on one's body (overkill RAW, but fun for gameplay).  https://www.scribd.com/doc/269479389/D-D-item-sheet
• A kill tally sheet to be able to assess the effectiveness of a various players. https://www.scribd.com/doc/269478981/Kill-Tally-sheet-for-D-D
• Sindarin character sheets https://www.scribd.com/doc/269477627/D-D-chr-sheet-in-Sindarin-Elvish (see another post for more)
• Other stuff that may be posted here.

D&D battle simulator, part 2

UPDATE: I have made a website of the simulator (dnd.matteoferla.com).
SEEN ALSO: Description of battle simulator and some analysis, the GitHub code for the encounter simulator, analysis of dice equivalence

Dice equivalency

I have had several conversations about "dice equivalency" in terms of damage:
y = average value
n = number of dice
x = maximum value of dice
k = damage bonus
y = n (x+1)/2 + k
Hypothesis: all creatures with identical stats except for (n,x,k), but that do y damage have the same victory probability. The average damage is the same, the distribution of the damage is different, so under some conditions one could argue that it would differ. The simulations show there is no difference regardless of whether the fight is easy or challenging or whether there are multiple team-members.
In other words, a special weapon variant of 2d6 can be d7+d5 —assuming if you can get over the d5's ugly shape—, 2d8 –2, 3d3+1, 4d2+1 or 7, yet it will not affect the game in the very long run.