[RPG] What’s a good fast-combat system that scales to 6-10 players?

Sounds like one of the older (pre-3e) editions of D&D would suit. They were written when large groups were normal, and your bullet points match up exactly. I've only run a B/X D&D variant for a large group once, and it had problems, but slow combat wasn't one of them. This was in a campaign that had a variable attendance (on purpose), so most sessions were fewer, but a few sessions like that one were larger.

The problems that I did have were mostly from inexperience running for a large group, so I wasn't managing spotlight and attention very well, but I saw no obstacles aside from lack of practice to fixing those problems. (The effect of inexperience wasn't even that bad – the group had fun, got through an entire dungeon from start to finish, and the downside was mostly that I was feeling overwhelmed by managing the size of the table. The in-game stuff worked great.) Having run every edition of D&D except the 1974 edition, I can say that TSR D&D is categorically faster in combat, for exactly the reasons in your bullet points, than the WotC editions with their focus on the complexities of tactical combat.

There are a few variations on old editions of D&D, many of them retroclones that subtly tweak the rules to make them run even more smoothly than the originals. The one I used (and am currently using) is Adventurer Conqueror King System, but any Basic D&D retroclone is functionally identical in the aspects relevant to speed and party size, so you could pick up Labyrinth Lord or Swords & Wizardry Complete and get the effectively the same game as I've used for large groups. (Those come in free versions too, whereas ACKS starts at $10 for the PDF.) You can freely move between old-school retroclones too, so you can try one and move to another as you learn more about the minor differences and which flavour appeals to you and your group.

I've also played in a game of actual B/X D&D with about eight players under a DM that had more experience managing large groups, and it went very smoothly. We got through about four combats during that con slot, and those were only about 10% of our play time. The rest of the time was exploring, scouting, parleying with NPCs living in the dungeon, finding things, running away, debating the next course of action, and generally having fun in this fantasy world.

To address your bullet points:

• Is pen and paper/tabletop, and does not require large amounts of space (without minis is preferable, but anything that I can run on a dining room table is okay)

  Older D&D didn't use (and didn't even work well with) miniatures during combat. Typically, miniatures were used, if at all, to show the "standing marching order". They weren't used in combat, because combat is much simpler.

• Is in a fantasy setting, or has no specific setting.

  D&D fantasy is about as generic as you get – older editions of D&D created our current standard of generic fantasy roleplaying.

• Has a character creation time of LESS than five minutes (as the first session I'll be making all the characters for them)

  Character creation is as quick as rolling 3d6 seven times (seventh is for starting gold), writing down a class, name, alignment, and equipment. Equipment takes the longest for new players, but for pregens (where you aren't all super-anxious about packing everything-and-a-10'-pole onto one character) it will be fairly quick. (Here, I'd actually recommend B/X D&D itself or any retroclone other than ACKS – ACKS is great, but it adds a simple skill-aptitude system to characters, which just tips character creation over 5 minutes due to the time it takes to choose which two skills to take for a new PC.)

  For someone with any experience, creating characters easily takes only 5 minutes. Your first PC will take longer since it'll be the first time you've used the character-creation rules and you'll still be getting the habits for where to look in the book, but the rest will be about 5 minutes each.

  Spell choice isn't a problem either: there are only about a dozen to choose from, and you only get about two (depending on the exact retroclone you use), and often they're assigned by random roll. Clerics don't get any spells in most older D&Ds until 2nd level, when they've proved their faith in the eyes of their god.

• Has a "low-crunch" combat system (IE: minimal choice of options avialble to players) [I feel I should clarify this one further. By 'minimal choice' I don't mean they can't do anything they can think of, I mean that the rules for doing so should be simple. IE: "attack, run, investigate, use a skill", and maybe 2-3 options per choice]

  Combat is super-low crunch. Your mechanical options are move, melee, shoot, cast, withdraw, and retreat, and most rounds you will only actually have the choice of two of those due to your situation and equipment. Combat tactics remain the realm of creative use of the environment and how you arrange your forces; the most meaningful combat options are not actually tactical, but strategic: do we get into this fight or not, and have we ensured that we're able to overwhelmingly smash the opposition before we risk our necks? What equipment did we already choose to give us an edge?

  Old D&Ds also have very few HPs. Low-level combats are typically over in one to two rounds, simply because one side or the other is "done" by then and either dead or running/surrendering. 80% of fights are either cakewalks or suicide, so you rarely get into even fights that drag on and turn into battles of HP attrition, and when you do, it's because something went wrong or you're taking on a Big Bad (or both).

  Positioning is also less of an issue (and hence the lack of using minis). Partly, fast combats simply don't have much variation in positioning, because you engage the enemy and then the fight is decided. Partly, because mechanically you simply don't move around a whole lot: you melee-engage with a particular enemy and then it's hard to disengage safely without killing them. (That's what the withdraw and retreat actions are for, and takes care of the "opportunity attack" concept in an elegant way, too). What you tend to get (unless something went wrong) is a front-line of melee with casters in the back. Rogue-types are generally hanging around and sometimes not even participating in the fight, because rogues are not strikers – their strengths are before and after combat, not during. (Which is OK for rogue players, because fights are short and the minority of your table time.)

• Each individual's turn should only take 15-45 seconds. IE: about the same as a board game.

  Yep. In general, a player's turn will be under a minute, if not under 15 seconds. When it takes longer won't be because the system is slowing you down – it'll be because something interesting is happening that you have decided is worth spotlighting and usually engages the whole group's attention. A round for our very-large group took a handful of minutes for a combat between over 20 characters (PC, follower, and enemy).

• Is not entirely combat-oriented.

  The combat rules form a very small section of the rules. From a player perspective the majority of your mechanical interactions are combat but it's a minority of table time. From a DM's perspective the majority of your mechanical interactions are related to the PCs' exploration: random event rolls and reaction rolls and time systems and stuff like that takes up most of your mechanical attention. The actual focus of the game is on exploration (wilderness, underground, and town) and roleplaying situations, with fights being something the players will avoid unless necessary or easy. The majority of the time you'll be describing the PCs' environment and they'll be responding with things they do and what they poke, which won't often engage the mechanics for more than a moment if at all.

• Has no, or very few, conditions to track. One or two like "wounded" is fine, but when you have to track 'fear', 'poison', 'ongoing damage', etc. or pretty much any "at the start of your next turn" effects, it get's tedious. I'd like to avoid it entirely.

  Almost no conditions. (Most things that are "conditions" in later D&Ds are fight-and-life-ending in older D&Ds.) You're either alive or dead, and special effects of spells are uncommon and usually a big deal: you're not dealing with layers of effects normally, because solving one effect is going to consume the group's attention. Poison isn't a condition: it's instantly deadly and should make the PCs run in fear until they're higher level. There's very few kinds of ongoing damage: acid and fire, which usually last one round. Fear isn't an effect you really need to track either: it doesn't debuff, it makes the target flee so they're out of the fight – and maybe lost/dead! Fear is something to, uh, fear about as much as poison.

  In particular, there are no "buff" spells as you know them. Those are a staple of WotC D&Ds, but they were invented for 3e and simply didn't exist before. There is much less of a focus on stats in older D&Ds, so there simply wasn't a need for that kind of buff spell before.

You didn't cover variable party size in a bullet point, but you mentioned it earlier and it should be touched on too. Early D&Ds with their focus on exploration-based play is much more forgiving of variable player attendance. The driving force behind play isn't a big, overarching plot, so you don't get that problem where a player with a plot-central PC doesn't show up one night and now you can't continue with the plot. On the mechanical side, party size is often padded with follower NPCs, which absorbs some of the variability and makes the party less sensitive to missing PCs.

In the campaign I mentioned at the beginning, we had sessions with two players all the way up to an overflowing table of eight (well, nine including myself DMing; a party of eight). The party itself was larger: there were about half a dozen followers plus pack mule, making it a party of 12ish going into the dungeon. The hardest part was spotlight time: when someone went ahead to scout, I had a hard time resolving that quickly without it being uselessly quick and balancing that with giving attention to the majority who were waiting behind for the scout to come back. Other than that, we had no trouble with combats (they were over really quick, with such an overwhelming force).

When we had fewer players, ACKS (aka B/X D&D) worked fine too. Due to the exploration focus and the ability to hire followers, the players could tune the difficulty of the game to their party size by choosing where to go, what fights to take on and which to flee from, and how many extra bodies to pay to come along with them. The small party sessions were not really different from a game-mechanical perspective than the larger party sessions.