Equality of Maker-first and Breaker-first minimum degrees

Determine whether s_{MB}^b(H)=s_{BM}^b(H) for every positive integer bias b and every graph H.

Background

The parameters s_{MB}^b(H) and s_{BM}^b(H) measure the smallest possible minimum degree of a minimal graph winnable when Maker or Breaker, respectively, is the first player. The paper establishes inequalities relating these parameters and exact equality for several graph families, but leaves open whether the first-player choice can ever affect the value.