Some matches are played in best-of-seven way, that means the player who wins 4 times will be the winner.
To name a few, Meijin Match(Shogi), Japan Series(Japan Professional Baseball), World-series(Major League Baseball).
The probability can be calculated in the following way. Supporse winning chance = p.
4win 0loss : p4
4win 1loss : 4C3 *p3 * (1-p)1 * p (3win 1loss in the first 4 game, and wins the 5th.)
4win 2loss : 5C3 *p3 * (1-p)2 * p (3win 2loss in the first 4 game, and wins the 6th.)
4win 3loss : 6C3 *p3 * (1-p)3 * p (3win 3loss in the first 4 game, and wins the 7th.)
Here, we notate the number of combinations as 4C3.
Best of Seven
Best of Five