If you haven't heard of The Black Hack, you're in for a treat. It's an ultra-slim, incredibly simple respinning of the OD&D ruleset, with all the pick-up-and-play aspects you'd expect. It's only twenty pages long, including the very cool cover art and the OGL, making it the perfect way to introduce new players to the hobby without bogging them down with obtuse mechanics and tables upon tables of content.
The Black Hack is part of the new OSR wave of rules-lite games (see Swords and Wizardry Light, Whitehack, Troika, Into the Odd, etc.) that was 1000% funded through Kickstarter way back in 2016. The original goal, a meager £500, certainly wasn't wasted: the book, while devoid of art, is incredibly clean in its layout, and somehow manages to bring a style all its own to each page. Much like Whitehack, with its typewriter design and tight column, you could show me any page of the document and I would know I was reading The Black Hack.
On to the system. It's roll-under, which as an optional rule dates back to the Moldvay B/X days; basically, any ability check you make requires you to roll a d20 and attempt to score under the associated ability score. Clever readers will notice the inherent simplicity of this: as your ability scores increase, so do your chances of success, without ever introducing unnecessary concepts like "modifiers" and "to-hit" bonuses. I've always been a fan of the roll-under system (for those seeking a little extra "crunch" in their game, TAAC is a full B/X retroclone that completely embraces roll-under).
But don't think that's the only thing that's endearing The Black Hack to the people. While available to purchase at very reasonable prices (£7.50 plus shipping for the whole set in print, including core rules, GM screen, character sheets, and a micro-setting), being OGL pretty much the entire ruleset is online for free. I read through it, and it's all there: everything you'd need to set up and run a game using the system can be had for exactly zero dollars and change. It's never been a better time to be in the OSR.
There are some other interesting quirks of the system: it uses the advantage/disadvantage system from 5e, which I've always thought was an ingenious alternative to giving out arbitrary +2s and +4s to various checks. There's the usage die, which is another very effective way to abstractly track ammunition and resources. In essence, whenever a character uses a consumable item -- be it arrows, rations, or torches -- they roll the associated usage die. On a roll of 1-2, the item is consumed, and the usage die decreases by a size, from d20-d12-d10-d8-d6-d4. If you roll a 1-2 on a d4, the item is expended completely. This saves GMs from having The Ammo Talk:
"You can't fire any more, you shot your last arrow at the orc guard in the entrance hall."
"I thought I was picking them back up as I go! My character wouldn't waste arrows."
"You never mentioned that, plus you missed a few shots. Some of the arrows broke."
"I go back to retrieve my arrows."
"...we're already in initiative."
"I retreat to go get my arrows."
I've always been an abstract-combat kind of guy, so usage dice appeal to my simple, cinematic sensibilities. The archer always has enough arrows, until she doesn't. A strong gust of wind blows out the torches, and the party realizes they don't have any more. Introducing randomness into what was previously bookkeeping keeps the tension high, because you never know if the next ration you eat might be your last.
Armor, too, works differently than in most other games. Instead of decreasing an enemies chance to hit, it reduces damage directly, so a character wearing full plate (8 Armor) can take an extra 8 damage before she's out of the fight. Armor values reset upon a rest, which keeps the game fast and fun and perfect for dungeoncrawls.
The monster section assumes you've owned and run RPG's before (which I'd imagine you have, if you're reading the rules of an indie retroclone of OD&D) and are therefore sparse in their details. Each enemy is given basic stats and a unique fighting style or ability to distance them from each other. Fixing a problem that D&D has had since the first Monster Manual, you won't find page after page of bugbears and goblins and hobgoblins and kobolds and orcs, all tangentially different from each other. All the classics are there, but with enough specialization that fighting each one should feel vastly different. It's a small touch, but a good one regardless.
So there you have it: an ultra-lean, aesthetically pleasing, logically sensible 'hack, practically tailor made for new groups, kids, or Cons. It's free. It's got a cool name. It's perfect for dungeoncrawls and hexes, for bringing 5e groups into the OSR or for rekindling the fire in an old grognards heart. David Black, Your RPG is Great!