Best of Seven Match

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 : 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

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)


Tags:   probability   sports   simulation