The Idea:
Use Advantage (in combat), Luck (while adventuring) and Karma (in social encounters) to let players have their will - at a cost.
What a characters want in combat: Hit others while not getting hit themselves
While adventuring: Succeed in tasks
While socialising with NPC's: Get them to do what they want while not doing what the NPC's want

Yeah i know thats pretty rough, but thats basicly what the idea is based on

The Problem:
When using a task-resolution based system, sometimes things just don't turn out the way that would be best (in this case: the most fun for the group).
Especially social encounters always seem to be a problem, since players don't want their characters to be puppets of the will of some NPC, even if they succeed in their persuation roll. And sometimes players just want to get past those guards bluffing them, even if they fail their roll...

The Solution:
Everytime a player fails to succeed their roll, they can choose to rely on their combat advantage, their luck or their karma.
Example 1:
Adam vs Xena in combat. Xena hits Adam, now Adam does not want to be hurt so he decides to lose combat advantage and not be hit. Since he loses the Advantage, Xena gains some she can spent to not get hit as well.
Example 2:
Adam is trying to steal a key off a guard. He fails his roll, but decides to lose some luck and 'be lucky' this time. This way he builds up bad luck, that will eventually come back on him.
Example 3:
Xena is trying to convince a rich merchant to sell her an unique sword. She fails the roll, but decides to loose some karma and succeed. Bad Karma, well same with luck.. sooner or later it will come back to her.

This is an easy way to get rid of hitpoints as well, since combat advantage replaces it (and is a resource that can be gained and lost all the time).
After each fight, just set the combat advantage back to 0. After each adventure (or never, which is pretty much up to the GM) set luck back to zero. Karma should keep its value forever, since most social encounters have longer lasting impact on the story than single rolls in combat or skill checks.

Gaining combat advantage works the same way as losing it, just the other way round.
Luck and Karma can be gained whenever the GM offers it as a trade.
Example: Adam is talking to a potential employer, who wants Adam to prove his worth by doing his first adventurous job for free. The Man fails his persuation roll, and the GM offers Adam to gain Karma if he accepts the offer.

Last but not least, of course there is somekind of a 'Bad Luck Overdose': If a player is relying on his luck all the time, and building up too much bad luck, something bad is going to happen. I'm too lazy to come up with anything now, but it sounds like a good opportunity for GM's to come up with punishments.
This of course applies to combat advantage and karma as well.

I just thought it would be nice to share the thought. No questions this time, but comments and ideas are welcome!

sometimes things just don't turn out the way that would be best (in this case: the most fun for the group).

Thanks Callan! The idea was definitely not intended to make player immune to losing. I see losing as a part of the gaming experience as well, and i completely agree that it has to be part of playing. After all, whats success when you never lose?
To answer your question: As long as there's no real conflict in the task of climbing the wall, there's no need to roll.

One thing that really needs some emphasis is the big negative impact that should be implied in overusing this option. A success 'by luck' should really just be a temporary success, since in the long run it will cause you to be less lucky in the future.

Some example might be a thief who uses his luck to pickpocket rich merchants over and over again. Well eventually his luck will turn against him and he will be knocked out by a guard and taken to prison on his 5th attempt to make some money. Or his favourite dagger will break in combat. Or he might be chased on the rooftops of the city and, instead of jumping across to the next building, he might end up jumping short and fall down 3 stories onto hard cobblestones...

The aim is not to eliminate failure but to make success possible, in a way that is more like 'delaying failure'.

This reminds me a lot of a "bidding system" such as I've seen in more than a few games I cannot recall now that I'm at work. ;)

I think it could work, but it needs a couple of things, and I have a couple of questions.

First, the needs:

1) A clear economy, so that the players are aware of where they stand -- does the GM have a limitless pool of "karma/luck/advantage" to offer? If so, then it will be hard to avoid the impression that the GM is fudging the odds, one way or another.  This may not be a concern, but...
2) A way to ensure *success* that is not just "failure that hasn't hit us yet" -- a way to erase bad karma/overcome advantage/etc.  Something like Prime Time Adventures' Fan Mail might work -- you (a player) can give it to another player who's done something cool.  This way the players will be encouraging each other to take risks/do interesting things/etc.

(To give you an example; in my current project, "Free Your Mind", Karma is something the players vote on *after* an action has been taken -- where does it fit in re: the character/game-world's moral view. This way, they can gain or lose Karma, which the GM can later use against them if it's bad, while another attribute, Flow, allows people to delay bad Karma coming down the pike.)

Then the questions:
1) I can see the clear reason for the division between in-combat "advantage" and the other two, but I'm not-so-much seeing why the others are separate, other than to provide a more complicated mechanic; social interaction is no more particularly likely to be long-lived than many of the other "adventuring" interactions -- steal the King's treasury, even if you never talk to him, and he'll be gunning for you. ;)  Why did you pick social/adventuring vs. simply a time-frame choice, or a "Can I do it?/Should I do it?" division (which would be even closer to the luck/karma you've picked for your names.
2)  Looking at your example for gaining Karma, it feels like it's 'rewarding the player for going along with the GM', which feels...um.  Wrong. ;)  I think it's because it seems to imply in the "trade" mechanism that there's an adversarial relationship going on here; "You beat me, so I'll pay you to get what I want" -- sort of GM ransom. Is this really the sort of mindset you want to bring out in your players?

Bear in mind that the "pay the GM" paradigm already works quite successfully in the fate system; in that situation, using any such points is dependent on using aspects, which relate the advantages to your specific character concept, and you regain them by taking disadvantageous actions according to the same or other aspects.

Basically it allows players to avoid having to split their attention between pushing forward the intentions of their character and doing plot-forwarding things that disadvantage them, because they are compensated for them. Both players and the GM can suggest that the character gets fate points for an action and it means that players can chill out a bit, let bad things happen, because in a game sense they are compensated for them, and in a world sense they fit with what has already been suggested.

A similar approach applies in the thematic batteries of full light full steam, which are "recharged" when stuff doesn't go your way.

These systems are also helpful because they allow you to focus on two levels of plausibility separately; "what would likely happen" and "what should happen given the story". The second is layered on top of the first, and their relative strengths can be adjusted by changing how much the second can influence or overrule the first, and how easy it is to recharge.

The "bad luck overdose" idea works like this in fate: If you don't want to accept fate points from the GM for some disadvantage, you can match the fate points he is giving you and give him that many instead (the GM doesn't have a pool or anything, he acts as an infinite source or sink), if you don't have any, then you can't match him, and so you have to go along with it.

Now you'll note that since the GM can create as much fate points as he wants, he can always compel any character to do anything, which you could change in your version to put a limit on how many points a GM can offer for any one "compel". Also, conventionally, in fate, challenges set by the GM are arbitrary, he can put you up against whatever he wants, but you could adjust this to require all challenges that aren't direct opposition to something a character is attempting to be compels on aspects of the characters or the environment, in other words the GM is limited to only chucking something from the blue at the players if he also compensates them in fate points.

Don't forget that players can literally rely on luck by just rolling for stuff! If the consequences for failure are substantial enough, and the failure probability low enough, then the idea of pushing your luck can be replicated. So one system that would replicate that dynamic is people being able to increase the probability of success at the risk of increasing the penalty for failure. Eventually that small probability would come back to haunt them if they pushed it.

I've seen a few systems which include fighting defensively, but most that I've seen have people make the choice before rolling about how much they are putting into defence. One thing to watch out for in your system is situations where the interests of the characters are not symmetric; if I'm much more likely to kill you, or I'm unlikely to be fighting again soon or have otherwise less concern for my health; you giving me loads of combat advantage is not going to do me much good, whereas it will keep you alive. If the system of combat advantage is unbounded it will lead to the following conclusion: Cowards are impossible to hit!

If it is bounded then it could act as quite a nice mechanism for people to get out of fights, meaning you only easily get to kill someone if they want to kill you, similar to the effect in "combat pool" systems like earlier shadowrun editions.

One simple note I can add is that your mechanic only works for role playing when rolling dice.  It might be possible for a party or GM to forgo a lot of rolling.  Different groups have different ideas on when rolling in social instances should occur.  This means that a savvy player could only use the luck stuff when failing an important roll.  This means that they might initiate instances just to fail to drop the luck stuff penalty but not really take a real penalty.  This also means that they would essentially always succeed.