turbo tag: the simple quick combat system you already know how to run

I've made some quick combat systems before, but they all had a fatal flaw: they take more than a sentence to explain. Okay, then, here's the sentence:

Like trad combat, but all attacks (which can only be against combatants lower in the initiative order) instantly hit to kill and initiative, which is a general measure of combat ability, is rolled every round

More formally, when you'd "roll for initiative:"

1. Everybody can choose to flee or parley, or keep fighting.
2. Everybody rolls a combat check (see below for a few system examples.)
3. Starting with the highest combat check and moving on down, combatants can choose to down one opponent with an equal or lower combat check. Combatants might also take some relevant non-combat action (such as fleeing.)
4. Go back to (1). 

Like all my quick combat systems, this is liable to be "swingy," which some people don't like. I prefer the designation fast and high-stakes, but note that designates the same thing.

General tips

1. Like with other combat systems, quick or not, "kill" doesn't mean actually mean kill. Down and out of combat. Maybe they can get healed later, with or without injuries. This system cannot overcome the fact that random character death can only be fun if character creation is fast, so adjust lethality accordingly.
   
2. Rather than rolling initiative, marking it up, and then going through each combatant's choice, call it down from the top like an auction block. Every number is a chance to die!

Mosaic Strict Version

The combat roll equals (combat bonus) + (1d6 exploding) + (any circumstantial bonuses GM sees fit to assign). 

Your combat bonus starts at 0, or whatever makes sense for your character. It goes up by 1 whenever you down a combatant whose combat bonus is greater than yours in a both absolute and circumstance-adjusted sense.. 

Implementation in D&D 5e

The combat roll is 1d20 + (damage on a successful hit or cantrip attack) + ((AC bonus + attack bonus) x (attacks you can make per round + lowest spell slot of three spells you're willing to expend)). The d20 explodes. 

For monsters, you can guesstimate the total bonus at 6 + (challenge rating * 3).

Implementation in Exalted

The combat roll has a pool of (Median Physical Stat, or highest Approach if Essence) + (combat ability). Each Charm you have in that skill beyond the Excellency raises the Excellency's die adder cap by 1.