Karma resolution relies on referring to listed attributes or quantitative elements without a random element.
The premise is simple. The side in a conflict with more force to exert automatically wins. If one character has a combat skill of 3 and another character has a combat skill of 5, the character with 5 will win the fight.
But most forms of karma resolution have some kind of twist in them. Naturally, it's these twists that get me interested.
Short Term effort versus Long Term endurance
In some systems a player can temporarily increase their ability to influence a situation in exchange for a later reduction. In our hypothetical earlier situation, the character with a combat skill of 3 might be able to temporarily add a couple of points to even the fight, but in exchange for this they might tire themselves out. Perhaps a character can temporarily add a number "X" to their value being compared, but for "X" scenes thereafter they will suffer a 1 point reduction indicating the degree to which this has tired them out.
If the same character needs to boost their value for a later comparison, they will need to increase it by "X+1"...the first point to get back to their initial score, and the remaining points provide an actual advantage...but the character might then suffer a 2 point reduction for a while.
Tiredness might apply across a range of numbers within a field. If you boost something requiring physical exertion, then all physical tasks get penalised for a while. If you boost something requiring mental, social, spiritual or some other field of endeavour, then everything else within this specific field also suffers from the exertion.
A war of attrition in this manner will really cause problems for the lower ranked character, especially if every other value is equal.
In a tabletop game, characters could gradually overcome this tiring factor on a scene by scene basis. In a live environment, an actual timer might be more suitable (overcoming such tiredness on a 15-minute basis).
Changing the Conflict
Another method of making things a bit more unpredictable is to allow players to change te nature of a conflict as it occurs. This is the method used in Amber but it seems to have some very erratic behaviour depending on the GM and the group playing the game. If a conflict initially seems to favour one participant, then the loser may make an effort to change the nature of the conflict. A fight scene could become a chase when the weaker participant decides to run away, the loser suffers a penalty for the initial conflict, but hopefully the new nature of the conflict will give them enough of an advantage to even the score (or maybe even get ahead).
It's not a bad system in that the victim player gains a narrative advantage even as their character suffer problems within the game.
Another great way to play with purely karma based resolution is to allow players to work together to achieve communal goals. Perhaps using the highest trait of the group and adding a bonus for each assisting participant.
The actual bonus provided by assistants would be dependant on the number of players in the game, the scale used for the values being compared, and the degree to which teamwork is valued in the setting.
More players = more potential for the group bonus to overshadow the individual's skill.
Wider range in the value being compared = more potential for fiddly details to be implemented.
If teamwork is well valued, then the system probably should provide a bigger bonus for assistance. If a setting wants to mimic the "stormtrooper effect", the advantage from groups would be reduced to a minimum.
Making use of the Environment
When a Karma based system is being used with a heavily story oriented game, it is usually a good idea to allow players to interact with the story as much as possible through their avatars in the game world. If a player is able to incorporate an element that has been previously described in a scene, they get to add a bonus to their comparison value. Once one player has claimed the scene aspect, it should be unavailable to their opponent. There should probably be enough elements to potentially balance out a conflict, but it is up to the imagination of the players to gain all of the potential bonuses on offer.
Probably my least favoured method. The GM adds a value to each participant based on what they'd like to see happen in the conflict.
These systems are all options that completely eliminate the random element. There are far more combinations of mechanism available when the Drama, Fortune and Karma elements are mixed together.