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.

What is Agency?

I personally define agency by three criteria:

1. The player has control over their own character's decisions.
2. Those decisions have consequences within the game world.
3. The player has enough information to anticipate what those consequences might be before making them.

What does that mean?

To elaborate on those conditions, I'll give examples of ways that agency can be violated.

• A group of goblins surrenders to the PCs. Alice decides that her character, Johanna, would rather just kill all the goblins and says that she starts executing them. Devin (the DM) decides that Johanna wouldn't do that and forbids the action. In this scenario, agency condition 1 is violated because Alice is no longer in control of her characters actions.
• Devin has planned for the PCs to be ambushed by bandits on their way out of town - and he foreshadows the ambush by having the PCs overhear in the bar that a merchant got attacked by bandits on the road they're about to travel on. The PCs look at the map, and choose to take a longer route to avoid the bandits. Devin decides to spring the bandit ambush on them anyway - Devin moves the bandit lair on the campaign map so that they will still encounter it. Here, agency condition 2 is violated because the PCs decision to avoid the bandits was made meaningless.
• The party is making a plan to infiltrate a dungeon. Devin decides that the evil wizard who rules the dungeon is Scrying them and therefore knows their plan. Unless there is a reason which the players could have been aware of for why the Wizard might be scrying them at that exact moment, this is an agency condition 3 violation.
• The party encounters a troll, which keeps regenerating on them. Carl remembers that trolls are weak to fire or acid, and so he has his character, Percy, attempt to torch one of them after it goes down. Devin says that Percy wouldn't know trolls were weak to fire and so forbids the action. Agency condition 1 is violated.
• Same as above, but Carl convinces Devin that that's railroading. Devin still thinks it's unfair for a player to use that knowledge, so he changes the trolls into homebrew "trulls" which are like trolls, but their regeneration is countered by lightning instead of fire or acid. Agency condition 3 is violated, because the players have no reason to expect that lightning would behave any differently than other damage types.

And what is it good for?

Imagine if any one of those examples above led directly to a player death - or worse, a TPK. Any of these situations could be a group-killer:

• The GM forbids the player from killing the surrendered goblins - then has one of the surrendered goblins stab them in the night.
• The GM ignores the players' decision to avoid the bandits - then the bandits kill someone during the surprise round.
• The players go forward with their plan that assumes they will have the element of surprise. They get ambushed and die.
• The GM forbids the player from using fire to kill a troll, which allows the troll to mop up the party with impunity.
• The GM replaces the trolls with trulls that aren't weak to fire, and then the trulls make mush of the party before the players figure out the switcheroo.

A defeat in which the players had no agency will always feel arbitrary - the players will feel as if the GM cheated them. A defeat that follows from Agency is one that the players can feel responsible for - because they knew the risk (condition 3) and did it anyway (condition 2) by their own free will (condition 1).

Is more Agency always better?

Probably not, but it depends on the group. I maintain that an undesired outcome (especially a character death) will never feel satisfying unless the player had sufficient agency to prevent it. Outside of that bubble, however, there a numerous other good things that it might be worth it to give up some agency for.

As a comment KRyan pointed out, running a game with absolute 100% agency would mean that the GM is never allowed to ever surprise the players - and many players want to be surprised sometimes. Additionally, agency might be worth suspending to prevent disruptive or egregious metagaming, or to make an overly-gregarious player to share the spotlight.

Can I run a game without agency?

Not completely - that would be silly. If you wanted to completely squash agency, you'd have to dictate to players what they do on their turns for them in combat. However, there's an entire school of play (called Participationism) where the DM basically controls the party outside of combat and dungeon exploration.

If you go down the road of playing a low-agency game, you should first make sure that your players are on-board with it and won't be trying to make decisions for their characters outside of the rails. Second, you make sure that you clearly define where the border is between your dictatorship and their agency, and make sure that you respect the line. Lastly, make sure that either any defeat they incur is a result of their agency, or you have their absolute trust that if you lead them into a defeat/setback, they will believe you that the game will be better off for it.