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).

### Winning Probability

The probability can be calculated in the following way. Supporse winning chance = p.

4win 0loss : p^{4}

4win 1loss : _{4}C_{3} *p^{3} * (1-p)^{1} * p (3win 1loss in the first 4 game, and wins the 5th.)

4win 2loss : _{5}C_{3} *p^{3} * (1-p)^{2} * p (3win 2loss in the first 4 game, and wins the 6th.)

4win 3loss : _{6}C_{3} *p^{3} * (1-p)^{3} * p (3win 3loss in the first 4 game, and wins the 7th.)

Here, we notate the number of combinations as _{4}C_{3}.

### Best of Seven

4win 0loss | |

4win 1loss | |

4win 2loss | |

4win 3loss | |

Total (win) | |

0win 4loss | |

1win 4loss | |

2win 4loss | |

3win 4loss | |

Total (loss) |

### Best of Five

3win 0loss | |

3win 1loss | |

3win 2loss | |

Total (win) | |

0win 3loss | |

1win 3loss | |

2win 3loss | |

Total (loss) |

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