The Amber Diceless RPG (ADRPG) had a deceptively simple system: players in a contest compared the appropriate stat (there were only 4, so this was not hard) and the higher stat won. Simple as that, except for one small catch. See, while the stat established that baseline of victory, the GM took the fictional situation into account when figuring out the outcome. That meant that it was very much optimal to stack the deck in your favor whenever possible in hopes of overcoming your stat difference.
This absolutely reinforced a sort of backstabby theme by incentivizing betrayal, backstabbing, ambush and surprise, but it also shook up the static, predictable nature of the stats. Sure, everyone knew how a fair fight would go most of the time, but since fair fights were so rare, that only mattered so much.
This introduced some fascinating challenges to players and GMs. For players, it demanded creativity and an ability to really interact with the fiction. It also drove player descriptions towards advantage rather than outcome (something that translated well to the back-and-forth of online play). At the same time, it demanded a great deal of flexibility from the GM because the system provided very little in the way of guidelines for how much the elements of the fiction could really influence outcomes. That is to say, there was no hard and fast way to judge whether or not surprising that guy in his sleep was enough to overcome his badassery advantage. The information was not just obfuscated, it was entirely inaccessible, as it existed purely in the GM's head. The only way to find out was to try.
Obviously, there were downsides to it. The system favored the player who could sync up descriptions with the GM's sensibilities, and it could be arbitrary and unfair at times. Some GMs were entirely comfortable with that, but that possibility was placed front and center, so any GM with half a brain could grasp these risks and understand that she would need to rein in.
On the upside...man, it was a boot camp for how to run a good, engaging fight. Everything mattered, and every action was an opportunity to change things up, so you had every reason to bring your A game. As a GM, it forced you to develop a sense of how to interpret the fiction and the advantages it brought. You very quickly go "Ok, he has reach and better armor, but she brought the fight into close quarters, so that reach is less of an asset and may actually become a drawback. She's crazy strong, but he's willing to take a hit to hurt her." then come to a conclusion regarding how all those factors should impact the fight , then dynamically update them in reaction to player actions, all while making sure the whole conflict feels brutally real and dangerous to combatants.
(Curiously, while the game had no real guidelines on how to judge the effect of advantages, it had a very nicely tiered set of potential outcomes which, so far as I know, no one ever used literally, but rather took as a lesson of the many ways a fight might end).
It's pretty awesome. Totally subjective. Utterly subject to fiat. But awesome.
Anyway, the other thing this really taught you was to get a strong feel for advantage and diminishing returns, two things that are really essential for making a skill system feel like something other than a number crunching exercise. That, however, is a topic for another day.
[↑] 1- It's actually because of this that I vastly prefer using relative advantage in combat systems, rather than modifiers for individual weapons, armor and such. Assuming a fair fight (zero bonus), you look at all the situational modifiers (which includes arms and armors) and just assign a bonus weighted by those things. It's super fast, requires minimal bookkeeping, but requires enough practice that I'd hesitate to put it in any published book because I'm not sure how well it would be received.