But there is a huge difference between an event that occurs by chance throughout a character's life, and one that occurs exactly once per day when the player decides to use it.
Even if the player pretends that in the fictional game world/story, the Daily occurred by chance.
I agree that there is a difference. But I think different postsers in this thread have different experiences of that difference and perhaps, therefore, different views on the nature of the difference.
Here is my go at it. I wonder how much it resembles your view of the difference!
A critical hit that is mechanically determined by chance can be interepreted, in game, in at least a couple of ways: (i) the PC struck wildly, or in the ordinary way, and got lucky; or, (ii) the PC got lucky in so far as their enemy presented a vulnerability or foolishly lowered their guard, enabling the PC to
deliberately get in a lucky shot. On (i), the lucky die roll models the PC's luck. On (ii), the lucky die roll models the enemy's misfortune, and the mechanics deem that the PC exploits that misfortune without need for the
player to do anything additional in terms of playing his/her PC.
Option (i) I would see as Tunnels & Trolls-y: it fits with a fairly lighthearted approach to play, and/or with playing novices or "farmboy"-type PCs, because it makes the experience of getting lucky a central part of "inhabiting" one's PC.
Option (ii) I would see as producing a somewhat more gritty and serious feel - this, I think is what Rolemaster and Runequest envisage in their critical and hit-location mechanics. As {url=http://www.indie-rpgs.com/articles/15/]Ron Edwards points out[/url], though, it can lead to some wonkiness from the simulationist point-of-view:
The causal sequence of task resolution in Simulationist play must be linear in time. He swings: on target or not? The other guy dodges or parries: well or badly? The weapon contacts the unit of armor + body: how hard? The armor stops some of it: how much? The remaining impact hits tissue: how deeply? With what psychological (stunning, pain) effects? With what continuing effects? All of this is settled in order . . . The few exceptions have always been accompanied by explanatory text, sometimes apologetic and sometimes blase. A good example is classic hit location, in which the characters first roll to-hit and to-parry, then hit location for anywhere on the body (RuneQuest, GURPS). Cognitively, to the Simulationist player, this requires a replay of the character's intent and action that is nearly intolerable. It often breaks down in play, either switching entirely to called shots and abandoning the location roll, or waiting on the parry roll until the hit location is known.
If we go to the 4e daily power or "Fate Point" approach, under which "critical" (ie superior) hits are threatened and/or occur not at the whim of the dice, but when the player chooses, than the same ingame interpretations are available - the PC got lucky, or the NPC got unlucky - but there is no longer any attempt at the mechanical level to model this good or bad fortune. It occurs, instead, by rationed stipulation (ie the player spends a limited resource).
This is clearly not simulationist. Although logically it is moving into Author or Director stance, in play I think it may or may not force a break from Actor stance, depending on how sel-fconscious the player is of his/her use of the mechanic. I don't think that it
need be any more disruptive than the issue, for simulationism, that Edwards identifies in relation to RQ-style mechanics. Which is to say, disruptive for some but not others.
Whether or not it disrupts Actor stance, the rationed stipulation approach will have other consequences - for example, "criticals" will tend to occur when they're needed, rather than "at random". Again, whether or not this breaks or hinders immersion will probably be highly variable from player to player and group to group. 4e adopts a range of mechanicsm to reduce this "dramatic hit only when needed" effect: there are random criticals as well as rationed powers; and there are minions, against whom every hit is a severe critical. (I've long argued that the best way of conceiving of minions is as ordinary NPCs/monsters that carry "anti-Fate" or "Unluck" points that make every hit against them a serious critical.)
Of course, because minions introduce further metagame mechanics - here, the GM is using stipulation to help determine the distribution of good/bad fortune - whether or not they help deal with the immersion issue is still going to be highly variable from group to group!