History
The reason for the set mix as it exists is that, originally, the dice available were a set of platonic solids, sold by an educational company and repurposed by TSR. Namely, a tetrahedron (d4), cube (square hexahedron, d6), equilateral octohedron (d8), dodecahedron (d12), icosahedron (d20). This was a "platonic solids" set.
D20's were routinely read as d10's in wargaming, and used for generating percentiles, which made use of the d20 as a d10 or pair as a d100 a standard practice, going back as early as 1972.
A 1938 dodecahedron with 2 rounded faces opposite each other was available in 1938 for stock simulations. ➀ It wasn't used by TSR, but shows the probable origins of the pentagonal dipyramid we now think of as the d10.
Names
As to names - the earliest modern set (with dipyramid d10) I can readily find documented by name is the "Dragon Dice" set from 1981 (as evidenced on the packaging copyright notice), as photographed at Dice Collector. ➁
I can, however, cite TSR "catalogue" from a ©1979 TSR product - Swords & Spells lists the older set as "Multi-Sided Dice Set" in the catalogue extract on the back flyleaf. ➂ It reads:
Multi-Sided Dice Sets — Each set contains one 20-, 12-, 8-, 6-, and 4-sided die
The same title and text was used in the 1975 product list in Strategic Review Vol 1. Issue 3 (1975). ➃
So:
Multi-Sided Dice Set - the original d20 d12 d8 d6 d4 platonic set.
Dragon Dice - the "mud dice" set with d10's.
➀ Dice Collector - Mason & Co Stock Exchange Dice - www.dicecollector.com/MINT39_MASON_&_CO_STOCK_EXCHANGE_DICE.jpg
➁ Dice Collector - TSR - www.dicecollector.com/THE_DICE_THEME_TSR.html
➂ Gygax, [E.] Gary, Swords & Spells, 6th printing, Tactical Studies Rules, 1979. Original copyright 1976.
➃ Tactical Studies Rules, Strategic Review, Vol. 1, No. 3, Autumn 1975, Ed. [E.] Gary Gygax. TSR advert on page 8. From the Dragon Archive CD.
Such systems are called "player-facing"
I don't know how ubiquitous this terminology is, but it certainly exists. I first came upon it in tremulus (p. 4):
All rolls of the dice are “player-facing,” meaning that all the rolls in the game are done exclusively by the players.
A quick search reveals the term being used in blogposts and forum discussions.
Here's a slightly expanded definition from one such post:
Of all the innovations in roleplaying over the years my favorite is the concept of “player-facing” mechanics. For those unfamiliar with the term, player-facing refers to game elements that require the player to roll dice, react, or make decisions instead of the gamemaster. Most every game out there features a majority of player-facing elements such as attack rolls, skill checks, or saving throws along with several gamemaster-facing elements such as NPC attack rolls and damage rolls.
As the term may not be well-known, perhaps describing such games as having "player-facing rolls" would be better.
Best Answer
"Introducing the Rock of Tahamaat, Tyrant of IIEE."
That's the way I heard it said, though it wasn't on the Forge and it wasn't Ron Edwards and it wasn't four points to roll but three rolls to navigate four points. Anyway, here's
WonderwallD. Vincent Baker's personal blog (excerpt follows, emphasis mine):The four steps, to be clear, are:
The joke of "Rock of Tahamaat" (and it is a joke) is that as a space tyrant whose will is read by psychics and carried out by agents without his personal intervention, the Rock of Tahamaat can make one roll to go directly from intent to effect, but his circumstances are, shall we say, somewhat unique?
A Brief Aside: Where The One Roll Actually Is
Now, Vincent Baker would go on from this to make Apocalypse World, a game which somewhat famously lets its characters boss gangs around, outlast desert pursuers, delve into the psychic maelstrom for answers, and take all other manner of dramatic post-apocalyptic actions, all with one single roll.
99% of the time, this is done by assuming all characters are capable of initiating actions based on their intent, and then either:
Go Aggro works the first way: you roll +hard to try and force someone else to the choice between obedience and pain, but they may be able to find another way out. Read a Person works the second way: you'll always get a question about what's making them tick, but if you roll +sharp well you might get more than one.