There are approximately 35 mid heroes in dota 2. You are given a matrix winprob, where winprob[i][j] denotes the probability of ith hero winning against jth hero in midlane (matrix is derived from previously played games).
Problem : What's the minimum cardinal subset of heroes (to learn) such that when the opponent picks a mid hero, we can always pick a hero from our subset and get the probability of winning atleast (60%).
I can only think of bruteforce. Is there any better algorithm?