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First and foremost, the table has a quick summation of how #THAC0 works ("THAC0 - modified d20 == AC hit") at the top, so absent-minded players always have a reminder. Better to have them looking at the screen a lot than flipping through the rulebook for it.

(I use "The World's Greatest Screen," by Hammerdog Games, in case you're wondering.)
https://hammerdog-games.myshopify.com/collections/the-worlds-greatest-screen

The "If modified d20 >19, add +5 to hit" footnote preserves the "20 is repeated" principle explained on page 82 of the DMG. People using #THAC0 in 1E often forget that quirk of the attack matrices. Forgetting it makes hitting #ADnD monsters even harder than it was in the old days!

It's also why my table gives first-level thieves & magic-users 21 THAC0 when Gygax's matrices show 20 THAC0 -- that was the *second* 20 of the repeating 20s. We "correct" that to 21 because +5 replaces the repeating.

The "If modified d20 < 0 hits, subtract from damage" footnote refers to an obscure rule Gygax introduced in WG5 "Isle of the Ape" -- if a "negative die roll" hits a target, subtract that roll from the damage inflicted!

I've literally never seen that happen in an #ADnD game, but I paid good money for that adventure, so I put the note on my table. (And "Isle of the Ape" will have an effect on the DM's version of this table I'll share later.)

As for the body of the table, I'm using Gygax's optional rule for Fighters' Progression, so Fighter #THAC0 improves 1 point every level instead of 2 points every other level. It makes playing fighters a little more interesting, and makes the table look tidier, too.

The other character classes' THAC0 progressions are standard, and listing them next to each other has one added advantage: It help players better understand the relative combat ability of the different #ADnD classes.

And now... the #THAC0 table that's on my side of the screen. It had to include monsters (who also benefit from the "repeating 20" rule, so the first monster entry had to be "corrected" to 21, just as for magic-users).

Why did I phrase the summary differently on the version? I don't know. I just did!

You might notice this table extends several levels beyond the DMG attack matrices, in both directions. Here where we start getting really obscure.

Compared to the #ADnD DMG, this table has five additional entries for high Hit Dice monsters, because Gygax just casually extended the Attack Matrix For Monsters in "Isle of the Ape!" That's one way to make high-level adventures more challenging, I guess.

Gygax also added an insane rule about "additional damage inflicted to automatic hit," which doesn't play well with #THAC0, so I often forget about it. I really should add something to the table about that rule.

There are three *negative* fighter levels added to the DM's #THAC0 table because of an obscure (and comically sexist) rule on page 88 of the DMG.

There's actually something worse than being a zero-level NPC in First Edition #ADnD -- "sedentary females" are negative-third level NPCs!

It's very important that I remember this distinction, for situations where PCs get in fights with scribes and serving maids.

Finally, there are an excessive number of plus signs in the "Monsters" column because I incorporated a DMG footnote directly into the table, giving me one less thing to remember during play. Whenever possible, give yourself one less thing to remember!

(This touches on the *other* reason I sometimes reformat old #ADnD tables -- consolidating information from different notes, rules, and books speeds up actual play.)

I recently recreated these #THAC0 tables in Google Docs (because I misplaced my original Word files), so if you want to use them, here are the links:

Player's THAC0 Table: https://docs.google.com/document/d/1IEJ2TYOZS-g5uthsrqKuz2JDaEtQqpMn-eZEu0qNFjE/edit?usp=sharing

DM's THAC0 Table: https://docs.google.com/document/d/1O3i2E9XCd853W6Z4JQLCQU6WG6xZ4X5-TWLzt0tEHVA/edit?usp=sharing

(I just committed myself to maintaining those links forever, didn't I?)

@contrarian two notes: I don't think you explanation of the "repeating 20's" is very clear. dense certainly but it doesn't seem sensible. I think you are missing something from the explanation. Might be my Neurodiversity kicking in but it definitely makes me go hunh way more than those original tables. I'd go for the Extended monster table if you extended the fighters as well (Gary was quite the "make new rules to be mean to players" adversary wasn't he?)

@contrarian I also dislike the 21 expansion as that removes the assurance of combat viability for the players as well as low HD monsters. the 21 basically says "No you can't hit without a bonus" which is exactly the opposite of the intent of the repeating 20's. Compare "Hey I have a 5% chance" vs. "Oh, I have no shot."

@Alexander_Anotherskip_Davis I've never had that reaction from an actual player, once they understand the "automatic +5" footnote. I think for a lot of them, that insta-bonus gives the feeling of a "critical hit."

But if a player doesn't like #THAC0, they can still use the original attack matrices (even when other players at the same game table use THAC0), because the two systems have the exact same probabilities to hit. Nobody is disadvantaged by choosing one mechanic or the other.

@contrarian Sure mechanically consistent, psychologically very different for the poor mages who will struggle with a 21 or higher being needed even if of average combat ability. This is similar to when open ended d6 systems end up eliminating the 6 tn result from charts. Accurate? Yes. Mentally different? absolutely.