Consider a game where team-better has probability of winning $>50\%$ against team-worse. Intuitively, why should team-better prefer to play a best-of-N contest versus a single game?
Is there an easy way to prove that formally? Is there a closed form way to calculate the probability?
I can compute a recursion: $$ P(N,N) = x\cdot P(N-1,N) + (1-x)\cdot P(N,N-1) $$
but I don't know how to obtain a closed form equation from that.