Lots of good stuff by Reynard
I'm with you- I prefer immersion over transparency, both as a player and a DM. For a period of about 12 years, I ran a regular 2e D&D game where the players had NO NUMBERS at all. No ability scores, AC, HP, THAC0, saves....nothing. At first, it was kind of a shock to them, but we were trying it as an experiment to see if it could get one of the guys from powergaming quite so badly...and it did! Later, the players told me the loved not having to keep track of the numbers, and it allowed them to see the world through their character's eyes more than as a game. To this day, they still say its the best campaign they have ever played in. We still play that game once a year or so, when we can get everybody together from around the country again.
I'm running two 4e games right now- one by the book, and one immersive. I was a little worried that 4e's powers element might make it hard to do immersively, but so far it hasn't been a problem. Players still know the effects of a power and how much damage it does relatively speaking, but don't have the numbers or fiddley bits in front of them. I don't state DCs, ACs, defenses, hit point damage, etc- the players don't know the numbers. There are a few little hiccups since 4e is a more gamist system, but nothing that can't be handled pretty easily (healing surges mainly). I'm running the game for some people completely new to RPGs (and two guys who are gamer veterans and who were in the 2e game referenced above), and so far they are loving it.
This isn't an edition wars statement at all, but I never could run an immersion, numberless game like this in 3e. Character build, synergies, buff spells, and items were so important that it quickly taxed my ability to keep up with it all. The players didn't like it because they felt my attention was divided in too many ways, and it was stressful to DM. 3e is a game that requires a high degree of transparency, and from my experiences as both a player and DM, I found deep immersion almost impossible with it.
I'll first narrate my character's actions ("I'll get up off the ground, run for the wall and dive behind it . . . ") then clarify the mechanics if necessary (". . . so that's a move action to rise from prone, a move action to reach the wall, and a free action to drop prone again.").
I like to game the system - exploit mechanical advantages provided in the rules - but I think describing those actions in such a way as to set the scene is important to enjoying the experience around the table.
Think mechanically, narrate immersively, perhaps?
Yep, thats what I do as well when playing and DMing. I also encourage my players do this when performing actions, using powers, etc- and if they come up with something really clever or creative, they get a bonus to the roll or get some special effect in addition to their attempted action. Conversely, if they try to use the same trick or description over and over on the same enemy, I might give a small (-1 or -2) penalty since the enemy is expecting it.