With the baseball playoffs coming up, I was fiddling around with how to calculate the probability that one team would win a playoff series, given *P*, the probability that it would win any one game. The playoffs can be 1, 3, 5, or 7 games.

A 1-game playoff is easy. It's just *P*.

A 3-game series (first team to win 2 games) is:

Note that *Q* = 1-*P*.

A 5-game series is:

For a 7-game series (World Series), Team A must get to 4 wins before Team B does. That is, Team A could win 4-0, 4-1, 4-2, or 4-3. There is 1 way to win 4-0, 4 ways to win 4-1, 20 ways to win 4-2, and 20 ways to win 4-3:

Those coefficients look like half of a binomial series. It's not a full series because the powers of P are fixed at 4.

Is there a general formula for an n-game series?