A formal statement of the system I actually use when running Tartary

Tartary has a couple of special systems for subgames, which are supposed to support more exciting, crunchy scenes (mecha combat, basically), but most of the time it’s just basic task resolution. And as I have drunk more martinis and DMed more on the fly, my worn little pebble of a resolution mechanic has become streamlined to the point where I think it might be of service to other gin-swilling DMs. Thus:

We roll 1D10. This is because dice snobs hate the non-Platonic D10 and because I find it easy to calculate in base 10. It’s a habit.

All rolls are contested, ie. both the player and the DM roll.* Whoever rolls higher gets their way.
The margin of success = damage in combat, some rough estimate of efficiency, and flair.
You can modify this roll in various ways – with a skill or attribute bonus (one or the other), situational modifiers, special pleading, bribery etc.
Also by taking extra risk. This means you say “I want to add (eg) +3 to this roll.” If you do that, then rolling under that modifier number (in this case 3) on the die is an auto failure and something terrible happens.**

All resolution rolls explode.
1 is automatic failure anyway. Reroll – if you get another 1 something terrible happens. A third 1: the terrible thing spreads to involve the whole party/army/country.
If you roll a 10, reroll and add to your 10, ad infinitum.

* inanimate stuff in the environment gets to contest your roll because all of Tartary hates you.

** terrible things are, in fact, terrible. If you happen to be handling explosives (as you often are in Tartary) you’ll likely be rolling up another character and apologizing to anyone else whose character was nearby.

So then there are some standard complications; weapons add a flat bonus to damage (a sword adds +2), unless they are (a) big-ass or (b) explosives, in which case they add 1 or more d10 (more on combat here). There’s a death and dismemberment table, mishaps for psychics and vehicles and doomsday devices, technomagic items and spirit possession and Mi-go and stuff stolen from all over…
…but essentially everything else is an ad hoc ruling.

Clear?

I guess you’d want chargen here to understand the level of standard mods, but as a baseline, +6 is an excellent skill and +3 an excellent attribute and +4 is an extraordinary situational mod.