We have all watched sport series based on winning the best of seven — or first team to win four games.
I consider two teams: Team A and Team B. Given the probability of Team A winning any one game, 
; therefore, Team B has 
probability of winning any one game.
The two teams have eight possible outcomes:
4-3, 4-2, 4-1, 4-0,
0-4, 1-4, 2-4, 3-4
Using hypergeometric probability, I calculate the likelihood of each of the 8 outcomes given each Team A probability (0.0 to 1.0).
Formula
The formula is as follows for a 7 game series:n = specific total number of games played for a given winning outcome (
total for a 4-2 series)
![\left[\frac{(n-1)!}{3!(n-4)!}\right]p^4(1-p)^{n-4}](https://www.mathpax.com/wp-content/ql-cache/quicklatex.com-791751dfba5573105e2ae0f79e05e58b_l3.png "Rendered by QuickLaTeX.com")
Permutations
The expression
calculates the number of permutations associated with a specific winning outcome (for example, 10 permutations for a 4-2 series where ). 
Example
Given: 
![\begin{align*} \\ \frac{(7-1)!}{3!(7-4)!}(0.81)^4(1-0.81)^{7-4}\\ \frac{6!}{3!3!}(0.81)^4(0.19)^3\\[4pt] (20)(0.00295)\\ 0.0591 \end{align*}](https://www.mathpax.com/wp-content/ql-cache/quicklatex.com-2b7aec2745dc1071474742649e692603_l3.png "Rendered by QuickLaTeX.com")
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Team A Winning Outcomes
The best of seven series steers the odds of winning in favor of the winning team. See table and chart below.
| Game p(A) | Series p(A) |
| 0.50 | 0.50 |
| 0.60 | 0.71 |
| 0.70 | 0.874 |
| 0.80 | 0.967 |
| 0.90 | 0.997 |
| 1.00 | 1.00 |
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Reference
