Does considering b to be a kind of “misfortune reduction factor” help your intuition at all?

In an even-money bet (b=1), f⋆ is the edge: f⋆=p−q. No reduction of misfortune here.

For general b, f⋆ is the edge with misfortune q reduced by a factor of b: f⋆=p−q/b.

The same idea works for bets in which you forfeit a fraction a (not necessarily 1) of you bet upon losing: in that case, your good fortune p is effectively reduced by a factor of a: f⋆=pa−qb.

Does considering b to be a kind of “misfortune reduction factor” help your intuition at all?

In an even-money bet (b=1), f⋆ is the edge: f⋆=p−q. No reduction of misfortune here.

For general b, f⋆ is the edge with misfortune q reduced by a factor of b: f⋆=p−q/b.

The same idea works for bets in which you forfeit a fraction a (not necessarily 1) of you bet upon losing: in that case, your good fortune p is effectively reduced by a factor of a: f⋆=pa−qb.