Two questions, then. First, how do your players know when there is a reasonable opportunity to flank? Second, if you create a "map" in your head, doesn't it make sense to sometimes use a visual representation, however crude, in order to save mental processing capacity for something else?
It's generally agreed that when you have two characters in melee range of one enemy, they can, provided no movement hindrances or other extenuating circumstances. I have a three-PC party with two spellcasters (and one animal companion and sometimes a melee NPC ally) so tactical situations more complicated than that rarely arise. The battlemap is usually for when enemies outnumber those PCs. It does make some sense, which is why we have used a grid on occasion, but after playing together for a while, me and the players usually seem to be able to create compatible maps in our heads based on very simple descriptions. We had a new player in the group this campaign so the maps are mostly for her.
What about when it's not apparent?
Since I find that to be the exception and not the rule, I'm comfortable having a discussion and really takling it out. I can't remember the last time I felt really uncertain about that sort of thing.
Not even worth worrying about, really. To me, accuracy is a secondary concern; my concern would be, how does this situation become real to the players?
I can see where having a visual representation could help some people. My style is to try to keep everything verbal. I explain things to players, they ask questions and make statements that I respond to, and we build a shared image of what's going on. To me, representing movement in "squares" instead of feet breaks immersion. Looking at a painted piece of plastic that symbolizes your characer breaks immersion. I want the players looking at me or at each other. D&D also includes the assumption that foot speeds and bow ranges and weapon reaches are constant, but real combat is much more dynamic, so I find that the further in the background these rules are, the more real the combat seems.
I think, when I play something like D&D, I expect the rules to be used, and hence whether I or anyone is a "tactical gamer," I worry the lack of a map really means a lack of options supported by the game.
I think the rules in D&D aren't meant to be followed. You use houserules, the DM makes many rulings during play. To me, the outcome is what matters. Many other rules (carrying weight and food and drink for example) are often handwaved because they slow down play. I've found that using tactical maps slows down play, so I handwave it.
To give broader background before I started playing D&D I'd do a sort of improv story hour on occasion. I could keep an audience engaged simply by talking. To me, D&D adds to that an interactive element, and rules to arbitrate actions generate by it. If I'm reading a book or watching a movie, I don't arbitrate the story using maps, I just picture it in my head. I'm aware that D&D's history includes tactical wargames, but mine doesn't. I try to spend no more than one-quarter of each session in combat (down from probably half or more years ago). If I'm going to speed through characters eating and drinking and bathing without narration, if I'm going to force each character to articulate their personality in a couple of scenes each week, why would I spend the time looking at a map to see if two characters are 30 or 35 ft. from each other?
You could argue I'm playing the wrong rpg, and I've experimented successfully with rules-lite games. We keep coming back to D&D because we know it so well that it is sort of a rules-lite game for us (but with great depth and detail in character creation), and things like maps are optional. I'm phrasing everything the way I am because the OP's question was framed from the perspective that maps are inherently part of the game, and I am trying to provide a different perspective, to illustrate that such exists. The beauty of D&D is that both views are valid.
Jimlock “ I'm not going to give you a map. I can give you only a great passion to discover. Yes, a map is not needed; great passion, great desire to discover is needed. Then I leave you alone. Then you go on your own.”
In my most recent campaign, I did not give the players a world map because I wanted to represent that most of the world was undiscovered and very few were available. Of course, they all spited me by maxing Knowledge (Geography) and asking questions about where things are.
