Note: This post is different from Assigning health/attack/defense parameters to game character types $A$, $B$, $C$ so that $A$ always defeats $B$, $B$ defeats $C$, and $C$ defeats $A$? which asks about the values. This post asks about the models/tools/methods/approaches.
I'm developing a RPG game which has 3 types of characters, Tank, Warrior and Assassin. A post has already given the minimal values of HP, Attack and Defense for characters so that the Assassin is guaranteed to defeat the Tank, meanwhile, the Tank is guaranteed to defeat the Warrior whereas the Warrior is guaranteed to defeat the Assassin over multiple rounds of combat.
Assassin's maxHP: 1 Attack: 1 Defense: 1
Tank's maxHP: 5 Attack: 1 Defense: 0
Warrior's maxHP: 2 Attack: 2 Defense: 0
Is there a math tool that I can use to calculate the result above instead of brute force search as that post does?
It doesn't have to be multiple rounds of combat, any solutions or clues to both one-round and multiple rounds are appreciated.