Considering that the thief isn't invisible, I would assume he is burnt to a crisp, barring some extenuating circumstance. If he had been invisible and undetected by the dragon, however, I would assume he was able to take cover in some recess of the corridor to avoid the breath weapon. Also, assuming this is an average size young red dragon, it has a 20% chance of automatically detecting an invisible creature, so I'd check for that first.
I think I posted something similar to this analysis upthread - that the halfling hiding in a recess of the corridor is similar to the saving throw rules.
Also, on the dragon's detection of invisiblity - per the MM, p 29, "Because of these keen senses, all dragons are able to detect hidden or invisible creatures within 1” per age level." So if the halfling is 30' away it is noticed by the dragon unless the dragon is only age category 2 or less.
The only reference in the MM that I see to dragons being able to detect invisible says that the ability is not a % chance, but rather is limited in range based on the dragon's age. A young dragon's ability has a range of 20 ft., so the thief is not in range.
Hriston's 20% chance was taken from the table for detection of invisibility by level and HD, on p 60 of the DMG.
This corridor has no recesses.
This is the heart of the matter, in my view. (It also applies to [MENTION=23751]Maxperson[/MENTION]'s objection to Hriston's answer that the elves move from room to room.)
AD&D, as presented by Gygax, takes for granted that the fiction is sufficiently unspecified as to admit of these sorts of modifications to accommodate the outcome of applying the mechanics. This particular instance, of the inability of invisible and undetected beings to be attacked, is a relatively unusual one. But hit points and saving throws are well-known and have been much debated for about 40 years now.
With respect to hit points, it's well known that Gygax says that whether or not a successful "hit" really does damage to a character (and in some cases, at least, to a monster) depends on how many hp the character has remaining. Per p 61 of his DMG, "hit points are not actually a measure of physical damage", and hit point loss is "a mere nick or scratch until the lost handful of hit points are considered - it is a matter of wearing away the endurance, the luck, the magical protections." This is why "the location of hits and the type of damage caused are not germane to" hit point loss. And Gygax extends this idea to account for saves vs poison, when he says (DMG p 81) that
For those who wonder why poison does either killing damage (usually) or no harm whatsoever, recall the justification for character hit points. That is, damage is not actually sustained -at least in proportion to the number of hit points marked off in most cases. The so called damage is the expenditure of favor from deities, luck, skill, and perhaps a scratch, and thus the saving throw. If that mere scratch managed to be venomous, then DEATH. If no such wound was delivered, then NO DAMAGE FROM THE POISON.
When it comes to other saving throws, he offers (pp 80-81) a similar account of how the mechanics and the fiction are connected - first roll the save, then narrate the fiction to accommodate the result:
Someone once sharply criticized the concept of the saving throw as ridiculous. Could a man chained to a rock, they asked, save himself from the blast of a red dragon's breath? Why not?, I replied. If you accept firebreathing dragons, why doubt the chance to reduce the damage sustained from such a creature's attack? Imagine that the figure, at the last moment, of course, manages to drop beneath the licking flames, or finds a crevice in which to shield his or her body, or succeeds in finding a way to be free of the fetters. Why not?
In other words, the rules of the game simply don't allow the GM to specify, in advance, that the rock face has no crevices, or that the corridor has no recesses. We don't find these things out until after the actions are declared and resolved.
Here is Gygax's reason for setting the game up this way (pp 61, 81):
It is not in the best interests of an adventure game, however, to delve too deeply into cut and thrust, parry and riposte. The location of a hit or wound, the sort of damage done, sprains, breaks, and dislocations are not the stuff of heroic fantasy. . . .
Lest some purist immediately object, consider the many charts and tables necessary to handle this sort of detail, and then think about how area effect spells would work. In like manner, consider all of the nasty things which face adventurers as the rules stand. Are crippling disabilities and yet more ways to meet instant death desirable in an open-ended, episodic game where participants seek to identify with lovingly detailed and developed player-character personae? Not likely! Certain death is as undesirable as a give-away campaign. Combat is a common pursuit in the vast majority of adventures, and the participants in the campaign deserve a chance to exercise intelligent choice during such confrontations. As hit points dwindle they can opt to break off the encounter and attempt to flee. With complex combat systems which stress so-called realism and feature hit location, special damage, and so on, either this option is severely limited or the rules are highly slanted towards favoring the player characters at the expense of their opponents. . . .
The mechanics of combat or the details of the injury caused by some horrible weapon are not the key to heroic fantasy and adventure games. It is the character, how he or she becomes involved in the combat, how he or she somehow escapes - or fails to escape - the mortal threat which is important to the enjoyment and longevity of the game.
Re-reading all this is making me agree more firmly with [MENTION=6787503]Hriston[/MENTION]. When it comes to the invisible halfling, the dragon's chance to defeat the invisibility is bound up in the special monster ability to detect out to 1" per age category, plus the general ability stated in the DMG. The breath weapon is not, in Gygax's AD&D, a further anti-invisibility capability. If, for whatever reason, the halfling hasn't been detected, s/he has the benefit of being unable to be attacked. That's part of AD&D's conception of heroic fantasy.
