The DM looks at the map and tells the players about how far away the monsters are. Based on that information, the PCs can attack with missile weapons or close to melee. Once in melee with an opponent, a PC needs to take a withdrawal action to avoid giving his opponent a free attack roll.
You don't need specific rules to facilitate TotM play. You simply need to not have rules that make it important to keep close track of positioning and movement during combat.
For me, the key issue is OAs.
In classic D&D these are provoked only by withdrawing; but as long as you just manoeuvre in melee you don't trigger them. Hence you only need to keep track of gross distances, engaged/disengaged, and roll % dice to resolve disagreement over who is in which AoEs.
5e seems simpler than 3E/4e - fewer OAs, and none for manoeuvring within threatened squares - but not as simple as classic D&D, because it still has quite a bit of rather granular forced movement.
(Also, if the GM is tracking positions on a grid, and the grid is just not being made public, I'm not sure that counts as fully TotM.)
Where I think 4e was most frustrating for "system-tactics neophytes" was that as soon as you get beyond simply making attack and damage rolls, you're drinking from the fire hose.
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Some players take to this naturally (especially experienced 3.x players). Others never seem to take to it because it feels more like work than play.
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I regret that I never had the opportunity to play 4e with a group composed entirely of dedicated and motivated players.
The group I play with incudes long-time RM players, wargamers, CCG-ers, PBM-gamers, etc. I've never tried to introduce a non-gamer to the system.
He (the character) is trying to crack his opponent upside the head whenever the opportunity presents itself.
You (the player) get to decide when the character is able to actually accomplish this.
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You are correct that this is done in the director/author stance, rather than the actor stance. It can take some mental gymnastics to wrap one's head around it, and I also find that it pulls me out of any sense of inhabiting the fictional world.
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Playing a martial character in 4e can involve a lot of switching between thinking in terms of "I do this" to "this happens, now I need to explain within the fiction of the game either how my character caused it or how it happened to my character."
It's a weird experience.
I think this is highly subjective across players.
At least for the players I play with, deciding "I want to do a lot of damgae
now, so I'll trigger my daily" doesn't involve any switching of mental perspectives. The character feels the urgency of giving it his/her all, just as the player does - it's clear, for instance, that the fight is harder than it looked at first. And so the player, playing in character, gives it his/her all ie uses a daily.
No dissociation.
The simplest character in the PHB was probably the Ranger, but even that character had Hunter's Quarry, which was almost like saying "add 1d6 damage to the first target you hit on your turn," but couldn't quite be played that way because you needed to use your minor action to designate the target closest to you as your Quarry, once per turn.
It's a bit simpler than you say: you don't have to do it 1x/turn, because the quarry lasts until the target is killed.
It's a bit more fiddly than you say, too: because if you hit with one attack and crit with the other, you get to put your quarry on the crit (and thereby maximise it).
It's not the most elegant mechanic of all time!