Women’s US Open - 1st Rd (#4 Simona Halep v. Nicole Gibbs): How many GAMES will S. Halep WIN?

Inputs Needed To Solve

Service Games Won %

Simona Halep
Nicole Gibbs

##### User Estimates #####

SH_SRV_Wperct = .82
NG_SRV_Wperct = .45

## Inputs Defined in the Problem

games_won = 12

Method To Solve

[1] Simulate 9999 Sets between Simona Halep and Nicole Gibbs their respective Service Games Won Percent
[2] The ratio of Simulated Matches where Simona Halep wins exactly 12 games to the total number of Simulations is an estimate of the probability she wins 12 Games (p_12) based on the Monte Carlo Method.

## [1]

import numpy as np

def sim_game(server,perct1,perct2):
    if server:
        serve = np.random.choice([1,0],1,p=[perct1,1-perct1])
        if serve == 1:
            ans = '1'
        else:
            ans = '0'
        
    else:
        serve = np.random.choice([1,0],1,p=[perct2,1-perct2])
        if serve == 1:
            ans = '0'
        else:
            ans = '1'
        
    return ans

def set_over(winner):
    set_over = False
    
    if winner.count('1') >= 7:
        set_over = True
    if winner.count('0') >= 7:
        set_over = True
    if winner.count('1') >=6 and winner.count('0') < 5:
        set_over = True
    if winner.count('0') >=6 and winner.count('1') < 5:
        set_over = True
    if winner.count('0') == 6 and winner.count('1') == 6:
        set_over = True
    
    return set_over

def sim_set(perct1,perct2):
    winner = ''
    server = True
    set_over_ = False

    while not set_over_:
        game = sim_game(server,perct1,perct2)
        winner += str(game)
        server = not server
        set_over_ = set_over(winner)

    return winner

## [2]

iterations = 999
_12_games = 0
#H = 0

for i in range(iterations):
    SH = 0
    NG = 0
    total_games = 0
    
    while SH < 2 and NG < 2:
        winner = (sim_set(SH_SRV_Wperct,NG_SRV_Wperct))
        if winner.count('1') > winner.count('0'):
            SH += 1
        else:
            NG += 1
            
        total_games += winner.count('1')
            
    if total_games == games_won:
        _12_games += 1
    
    if i <10:
        print(total_games)
    
    #if winner.count('1') > winner.count('0'):
    #    H += 1
    

p_12 = _12_games/iterations

Solution

print("The probability S. Halep WINS 12 Games is ~%s" % round(p_12,3))

The probability S. Halep WINS 12 Games is ~0.712

Info

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email: krellabsinc@gmail.com
twitter: @KRELLabs

import sys
print(sys.version)

3.6.5 |Anaconda, Inc.| (default, Mar 29 2018, 13:32:41) [MSC v.1900 64 bit (AMD64)]

Posted on 8/27/2019