Why d20?

Why d20?

It's one of 2 platonic solids whose number of faces is a divisor of 100, so it's easy to attach a percentage to rolls (rolling 1d20 + 3 with a target of 15 = 45% chance). The other, the tetrahedron (d4), has too few faces to model a fine spectrum of possibilities.
>but muh d10
Not a platonic solid.

1/5 of 100, as the above user points out.

A perhaps more accurate point (that business folk care about) would be that the d20 is simply larger and better known than a d10. Whether this is tied to platonic solids or the result of just making the d20 and getting lucky, it has the benefit of name recognition.

d20-system was /the/ main system because it attached itself to valuable IP.
It remained the main system for quite some time, because it trained it's player base (of mostly new players) to expect concepts that were wild departures for older RPGs.
"Surplus of options" but "minimal homebrew" is one of the bigger one's, but the clincher was "the rules exist for the player's sake, as a restraint on the referee."

Also the Open Game License.
It was so prolific that for a while, "different system" just meant "reskinned d20."

3d6 is used because d6 is a common dice
3d6 is used isntead of d6 because dont produce enought results, 3d6 produce 216 results
the sum of 3d6 is used instead of thinking about it as base 6 digits, because its simple to most.

d20 is used because 3d6 have results between 3 and 18, and some stupid people are ok with changing it to 1d20

I'm not a big fan of single-die resolution systems, because throwing several dice is a lot more fun.
If it's gonna be single-dice though, the d20 hits a sweetspot. d6 and d10 have too little granularity and the d100 has too much. Having a range of 1 to 100 is nice in theory, but in practice GMs and systems usually give a modifier in steps of five, making the smaller numbers superfluous.

>d20 is used because 3d6 have results between 3 and 18, and some stupid people are ok with changing it to 1d20

Actually, that's pretty, pretty far from the genesis of the d20's prevalence.

War games used many different dice configurations, but most actually used 1 or 2 d6's, because when rolling for many units, less dice per roll but using many rolls was the fashion. Very few (if any) using 3d6 as their main rolling function. Other dice beyond the d6 were a rarity, but there were special cube dice that also provided d3, d2, and odd configurations like 2 sides being positive,3 neutral, and 1 negative.

When Arneson and Gygax were designing D&D, Arneson found some odd dice in a London game shop, and brought them back with him to America. While Chainmail only used the d6's, they decided to introduce the d20 as the main die because it provided an easy, flat distribution that made it simple to calculate and resolve while still providing a fair amount of potential values.

Rather than the d20 being used to emulate 3d6, later roleplaying games decided to use 3d6 to emulate the d20. While the 3d6 does give a similar total range, it's curved distribution actually makes it actually much more narrower, with the results ultimately feeling more like the distribution of a d10 rather than a d20. But, since 4d6 is more of a hassle than 3d6, and some people actually prefer the narrower range, since it makes actions more predictable. But, since most people prefer exciting outcomes when rolling dice, the d20 remains far more popular than 3d6.

>why d20?
People can give long winded explanations as to why and as to the science and history behind them but the answer is simple. It's the most satisfying die to roll

Is there a d5?
Get four of those, Then the "FUN!" begins.

There certainly is, but it looks like it was designed by someone who was in a car accident